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Preparation for commissioning the triumf magnet Friesen, Errol Lane 1971

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PREPARATION FOR COMMISSIONING THE TRIUMF MAGNET by Er (rol Lane Fr iesen B . S c , S e a t t l e P a c i f i c Co l lege, 1968 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in the Department o f Phys i cs We accept t h i s t h e s i s as conforming to the requ i red standard THE UNIVERSITY OF BRITISH COLUMBIA Apr i1, 1971 In p resen t ing t h i s t hes i s in p a r t i a l f u l f i l m e n t o f the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree tha t the L i b r a r y sha l l make i t f r e e l y a v a i l a b l e f o r reference and study. I f u r t h e r agree t h a t permission f o r ex tens ive copying o f t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head o f my Department or by h i s r e p r e s e n t a t i v e s . I t i s understood tha t copying or p u b l i c a t i o n o f t h i s t hes i s f o r f i n a n c i a l gain sha l l not be al lowed w i thou t my w r i t t e n permiss ion . Department o f Phys ics The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8, Canada Date A p r i l 2 3 , 1971 ABSTRACT This repor t examines some of the work t ha t has been done in prepar ing f o r the shimming and subsequent t r imming involved in commissioning the TRIUMF magnet. A ser ies o f experiments was done to determine the exact changes in the average f i e l d and in the focus ing p r o p e r t i e s r e s u l t i n g when d i f f e r e n t s izes o f shims were placed a t var ious p o s i t i o n s on the pole p iece . The com-ponents o f the focus ing changes were broken down, using a l i n e a r approx imat ion , so as to examine the f a c t o r s causing them. In order to f a c i l i t a t e shimming, a computer program was developed which used t h i s data to p r e d i c t the amount of s tee l to be placed at each p o s i t i o n on the magnet pole piece in order to g ive the best improvement to both the avei— age f i e l d and the f o c u s i n g . This program was tes ted on a 10:1 model and found to reduce e r r o r s in the average f i e l d to 20% o f the o r i g i n a l a f t e r two i t e r a -t i o n s , at the same time improving the f o c u s i n g , a l though i t tended to break down at s i g n i f i c a n t s p i r a l angels when large c o r r e c t i o n s were r e q u i r e d . The cause f o r t h i s breakdown was ind ica ted and an improvement procedure recommended. F i n a l l y , a ser ies of exper iments, using a computer program, were made t o determine the t r i m c o i l c a p a c i t i e s tha t would be needed. I t was found tha t these c a p a c i t i e s were s i g n i f i c a n t l y lower than had p rev ious l y been expected. - i i -TABLE OF CONTENTS Page CHAPTER 1 THEORY OF SHIMMING AND TRIMMING 2 1.1 Phase s l i p 2 1 .2 Tolerances f o r phase s l i p 4 1.3 A d j u s t i n g the main c o i l e x c i t a t i o n 4 1.4 Tolerance on loca l f i e l d e r r o r s 5 1.5 Shimming to le rances 5 1.6 Trimming to le rances 6 CHAPTER 2 MEASUREMENT TECHNOLOGY AND ANALYSIS 9 2.1 Reasons f o r b u i l d i n g the 10:1 model 9 2.2 Data a c q u i s i t i o n using the model 10 2.3 Measurement to le rances 11 2.4 Ana lys is o f r e s u l t s 13 CHAPTER 3 SHIMMING THE MAGNET POLE PIECE 14 3.1 SHIMPOLE, a computer program 14 3-2 Results o f shim experiments 15 3.2.1 Shim experiments 16 3.2.2 SHIMPOLE t e s t s 26 3.2.3 Minimum shim th icknesses requ i red 32 3-3 ConcIus ions 34 CHAPTER 4 SETTING THE TRIM COIL CURRENT CAPACITIES 37 4.1 D e s c r i p t i o n o f TRIMF 1T 38 4.2 Computer experiments using TRIMFIT 39 4.2.1 Determining the we igh t ing f a c t o r s 40 4.2.2 Combinations o f 36 powered c o i l s 45 4.2.3 D i f fe rence f i e l d combinat ions 45 4.3 Trim c o i l behaviour 46 4.3.1 Re la t i onsh ip o f cu r ren ts to f i e l d grad i ents 46 4.3.2 Ma in coi1 e f f e c t 48 4.3.3 Noise e f f e c t s 48 4.3.4 E f fec t o f depowering c o i l s 50 4.4 Conclus ions 50 BIBLIOGRAPHY 53 APPENDIX A USER'S GUIDE TO SHIMPOLE 54 A . l I n t r o d u c t i o n 54 A.2 Use of SHIMPOLE 55 A.2.1 Input t o SHIMPOLE 55 A.2.2 Output from SHIMPOLE 58 - i i i -Page APPENDIX B USER'S GUIDE TO TRIMFIT 61 B. 1 1ntroduct ion B.1.1 Input to TRIMFIT B.1.2 Output - subrou t ine p r i n t (K,MATRIX) 61 61 64 APPENDIX C GUIDE TO THE GRID INTERPOLATION ROUTINE 66 C. 1 1ntroduct ion C . l . l Input C.1.2 Output 66 66 68 APPENDIX D LISTINGS OF COMPUTER PROGRAMS USED 69 D. D. 1 2 L i s t i n g o f SHIMPOLE and input data L i s t i n g o f TRIMFIT and input data 69 116 - i v -LIST OF TABLES Table Page I . Pred ic ted and exper imental minimum shim th icknesses necessary to meet a to le rance o f 1 G / f t 33 I I . E f fec t i veness o f d i f f e r e n t 36 c o i l combinat ions in producing a 5 i n . change and r e p a i r i n g a 1 G / f t g rad ien t e r r o r kk - v -LIST OF FIGURES - v i -Average f i e l d change of two ad jacent shims is the sum of the changes r e s u l t i n g when each shim is mounted separa te ly Focusing change curves between measured changes a t 253 and 308.5 inches as found by a l i n e a r i n t e r -p o l a t i o n r o u t i n e Improvements in the average f i e l d as compared t o the p red ic ted improvements a f t e r the f i r s t SHIMPOLE i t e r a t i o n Improvements in the v e r t i c a l focus ing as compared to the p red ic ted improvements a f t e r the f i r s t SHIMPOLE i t e r a t ion Improvements in the average f i e l d as compared to the p red ic ted improvements a f t e r the second SHIMPOLE i t e r a t ion Improvements in the v e r t i c a l focus ing as compared to the p red ic ted improvements a f t e r the second SHIMPOLE i t e r a t ion E f f e c t o f va ry ing K using 54 c o i l s to produce a 5 inch change and r e p a i r a ±1 g a u s s / f t g rad ien t e r r o r E f f e c t o f va ry ing K using a 36 c o i l combinat ion to produce a 5 inch change and r e p a i r a 1 g a u s s / f t g rad ien t e r r o r Re la t i onsh ip o f t r i m c o i l cu r ren ts to the g rad ien t o f the f i e l d e r r o r remaining a f t e r optimum main c o i l e x c i t a t i o n change Composite p i c t u r e o f the cu r ren ts in 54 t r i m c o i l s needed to produce a 5 inch change as we l l as r e p a i r var ious 1 g a u s s / f t g rad ien t e r r o r s Composite p i c t u r e o f the cu r ren ts in 36 t r i m c o i l s needed to produce a 5 inch.change as wel l as r e p a i r va r ious 1 g a u s s / f t g rad ien t e r r o r s Trim c o i l cu r ren t capac i t y envelope p red ic ted by TRIMFIT compared to the t h e o r e t i c a l p r e d i c t i o n ACKNOWLEDGEMENTS I t is a p r i v i l e g e to express my a p p r e c i a t i o n to Dr. E.G. A u l d , both f o r the o p p o r t u n i t y o f working on a very educat ional p r o j e c t , as we l l as f o r the encouragement g iven when d i f f i c u l t i e s were encountered. I would a lso l i k e to thank Dr. M.K. Craddock f o r the ideas which resu l ted in the computer program f o r shimming and Mr. Nick Rehl inger f o r the improved magnet measurement technology tha t made the program p r a c t i c a l . My thanks to Miss Nancy Palmer, who worked over t ime in order to type t h i s r e p o r t , as we l l as to Mr. Bob Gibbs and Mr. Peter Robinson f o r help in hand l ing the exper iments. INTRODUCTION The goal in the commissioning program f o r the TRIUMF magnet w i l l be to reduce the s l i p in the phase of an acce le ra ted ion to w i t h i n preset l i m i t s by means o f a c a r e f u l adjustment of the magnetic f i e l d s w i t h i n the magnet. At the same t i m e , the v e r t i c a l focus ing forces must be such as to avoid i n s t a b i l i t y at any p o i n t . Because the magnet f a b r i c a t i o n to le rances requ i red to achieve these l i m i t s cannot be r e a l i z e d , p r o v i s i o n must be made t o c o r r e c t the magnetic f i e l d e r r o r s a f t e r the magnet is assembled. With t h i s in v iew, the magnet pole p iece is p r e s e n t l y being manufactured approx imate ly 2 i n . unders ize f o r r a d i i less than 270 i n . , and some k i n . unders ize f o r r a d i i g rea te r than t h i s f i g u r e . A f t e r the magnet has been assembled at the TRIUMF s i t e , a shimming program w i l l be undertaken to reduce the magnetic f i e l d e r r o r s and to b r i ng the v e r t i c a l focus ing w i t h i n t o l e r a n c e s . The t r i m and harmonic c o i l s w i l l then be powered w i t h the goal of f u r t h e r reducing e r r o r s in the magnetic f i e l d so tha t the ion phase s l i p is f i n a l l y brought w i t h i n a c c e l e r a t i o n t o l e r a n c e s . - 2 -CHAPTER 1. THEORY OF SHIMMING AND TRIMMING 1.1 Phase s l i p The purpose o f both shimming the pole piece and powering the t r i m c o i l s is to reduce the phase d i f f e r e n c e between the a c c e l e r a t i n g vo l tage and the ion to w i t h i n c e r t a i n preset l i m i t s . I f the rad io - f requency a c c e l e r a t i n g vo l tage is g iven by V - Vw cos <j)D , § D being the time dependent angle o f the r a d i o - f r e q u e n c y , then an ion is said to have a c e r t a i n phase cx i f tf)D=o< when i t crosses an a c c e l e r a t i n g gap. For a c c e l e r a t i o n we must have tha t the time dependent angle o f the ion frequency 9 must be r e l a t e d to 4" by some in teger n in the way <|>= he . Due to s ize l i m i t a t i o n s , i t has been found necessary to set h = 5" f o r TRIUMF. 1 I f u) = et is the actual value o f the angular r o t a t i o n f o r the ion at some r a d i u s , and ho)' is the tuned c a v i t y f requency, then the ra te of change of phase <* = h(<o-o). Thus phase s l i p , occur ing when t h i s t ime d e r i v a t i v e is non-van ish ing , can be due to an i n c o r r e c t o) ' r e s u l t i n g from an i n c o r r e c t r a d i o - f r e q u e n c y , or to an i n c o r r e c t due to the average magnetic f i e l d va ry ing non - i sochronous1y. a) Phase s l i p caused by detuned rad io - f requency I t is assumed tha t one has a p e r f e c t l y isochronous magnetic f i e l d w i t h a corresponding ideal ion angular frequency The s l i g h t l y detuned r a d i o - f r e q u e n c y , however, is set to resonate w i t h , a s l i g h t l y d i f f e r e n t ion f requency. This r e s u l t s in a phase s l i p of the ion r e l a t i v e to the rad io - f requency a c c e l e r a t i n g v o l t a g e , which dur ing the course o f one t u r n has the value (1.1) where € v = (<*>'- A 0 ) / u ' and d t = t ' - T 0 , X being the per iod o f r o t a t i o n . - 3 -b) Phase s l i p caused by magnetic f i e l d e r r o r s In p r a c t i c e , when commissioning the magnet, the rad io - f requency w i l l be set and the magnetic f i e l d ad jus ted to reduce phase s l i p . Thus is f i x e d , and the phase s l i p is reduced by changing the magnetic f i e l d . Rea l i z ing tha t t h i s change w i l l a f f e c t both the ion angular frequency <*> and the radius at which the ion is o r b i t i n g , i t is f o u n d 2 t ha t • f i + T ) [ € B B + S B ( R ) ] ( 1 . 2 ) where B is the average magnetic f i e l d at some r a d i u s , h - =• is the r a d i a l f i e l d g rad ien t index, € B = is the o v e r a l l s c a l i n g e r r o r due to an i n c o r r e c t main magnet c o i l e x c i t a t i o n , and SB is the r a d i a l l y dependent f i e l d e r r o r remaining a f t e r a c o i l e x c i t a t i o n c o r r e c t i on . Combining these two equat ions and f o l l o w i n g the d e r i v a t i o n in re ference 1 , one f i n d s tha t the phase s l i p between the energies corresponding to Y, and #2 can be wr i t t e n . w ^ a ^ . - ^ - ^ f ^ ^ } o.3, where AH„;„ is the minimum number o f tu rns requ i red f o r the a c c e l e r a t i o n from V, to Vz , B c = B / y is the c e n t r a l magnetic f i e l d , R C = R / ^ and if and ^ are the usual r e l a t i v i s t i c v a r i a b l e s . For convenience in r e f e r r i n g to the components of t h i s phase s l i p , we de f ine the v a r i a b l e s A v = A n M i n G y (1 .h) A 8 = 2 ^ h /\rL; n €8 /y.y, (1.5) - h -( z l £B(R) (1.6) a w , The phase s l i p can thus be w r i t t e n A S i n ol = - A E — A L (1.7) 1.2 Tolerances f o r phase s l i p I t w i l l be no t iced tha t As ino \ is independent of the p a r t i c u l a r phase o f the ion tha t is being a c c e l e r a t e d , depending on ly on the energies between which a c c e l e r a t i o n occurs . Thus i t is poss ib le to set a phase s l i p to le rance which w i l l apply to the beam as a whole. In TRIUMF, the phase spread al lowed ions tha t are to be acce le ra ted w i l l be l i m i t e d to -65° < ^ 6 5 ° . 1 At the same t ime , the goal is to have a beam phase range A Sino<= 3. S no 4 0 ° . 3 Thus the maximum beam phase wander at any po in t must be less than 2 s in 65° _ 2 s in kO° = 0.526. Thus 1.3 A d j u s t i n g the main c o i l e x c i t a t i o n I t should be noted tha t i f we assume tha t £ v and £ 8 are composed o f the supe rpos i t i on of a systemat ic e r r o r and s t a t i s t i c a l e r r o r n o i s e , and i f i t is poss ib le to moni tor u) and 8 to the same accuracy as the s t a b i l i t y o f the c a v i t y f requency and c o i l power r e s p e c t i v e l y , then i t is poss ib le to ad jus t the main c o i l e x c i t a t i o n so as to s i g n i f i c a n t l y reduce phase s l i p . A n a l y s i s 3 shows tha t s e t t i n g the main c o i l e x c i t a t i o n leve l so t ha t = £ v reduces the phase s l i p due to cons tan t , measurable £ v and £ B to k% o f i t s former va lue . The random e r r o r s in these q u a n t i t i e s , however, cannot be balanced out in t h i s way, and hence have to be t r e a t e d d i f f e r e n t l y . A S i n cx k o.sxb (1.8) - 5 -1.k Tolerance on loca l f i e l d e r r o r s The design g o a l 4 is tha t C v - I0"S and £ B - 2.5 * 10 6 . The phase s h i f t due s o l e l y to a c c e l e r a t i n g an ion from i n j e c t i o n to f u l l energy through these imper fec t ions can be found by combining the r e s u l t i n g values of A v and A R .3 Since one is dea l i ng w i t h random noise from presumably indepen-dent power s u p p l i e s , i t is reasonable to combine these values as one would standard d e v i a t i o n s . The r e s u l t is a l i m i t on the s ize o f the loca l f i e l d e r r o r s , namely t ha t A L ^ 0.253 (1 .9) 1 .5 Shimming to le rances The design c h a r a c t e r i s t i c s tha t must be met invo lve i s o c h r o n i z i n g the average f i e l d so tha t •| £ - I | - 5 x I O ^ ( l . i o ) and l i m i t i n g the v e r t i c a l focus ing to the range 5 .0.2, t ^ t 0.4 , 50 i„. < R < 310 in. (1.11) The l i m i t on the ion frequency is a consequence o f equat ion ( 1 . 8 ) , whereas the v e r t i c a l f o c u s i n g f o r c e s have been t a i l o r e d such tha t ^ is halfway between V* = O and ^=0.5". When w i t h i n t h i s range, one must be ca re fu l when passing through the minor resonance + V? = 1 . 6 Because the magnet f a b r i c a t i o n to le rances requ i red to achieve these l i m i t s cannot be r e a l i z e d , p r o v i s i o n must be made t o c o r r e c t the magnetic f i e l d e r r o r s a f t e r the magnet is assembled. With t h i s in v iew, the magnet pole piece is p r e s e n t l y being manufactured approx imate ly 2 i n . under-s ize f o r r a d i i less than 270 i n . , and some k i n . unders ize f o r r a d i i g rea te r than t h i s f i g u r e . This d e f i c i t w i l l be made up by b o l t i n g - 6 -on metal shims, w i t h the tw in goal o f c o r r e c t i n g both the average f i e l d and the focus ing forces so tha t the f i n a l c o r r e c t i o n can be done by the t r i m and harmon i c co i 1s . In ana lyz ing the c o n t r i b u t i n g f a c t o r s to changes in the v e r t i c a l f o c u s i n g , use was made of the smooth a p p r o x i m a t i o n , 7 angle o f the f i e l d . The t r i m c o i l s have been des igned, to c o r r e c t a magnetic f i e l d g rad ien t e r r o r o f ±2 G / f t , w i t h an abso lu te e r r o r of ±50 G at the ins ide and ±7 G at the ou ts ide of the magnet. Separated t u r n a c c e l e r a t i o n would a l l o w a g r a d i -ent e r r o r of on ly ±1 G / f t . 4 These f i g u r e s must be accepted as the to le rances f o r the magnet shimming program. I t is ext remely u n l i k e l y tha t the magnet, when i t is assembled, w i l l have a f i r s t harmonic e r r o r g rea te r than 7-5 G . 8 The shimming procedure w i l l i nvo lve a 360 deg f i e l d survey, thus i nc lud ing a l l s i x s e c t o r s . The average f i e l d and the focus ing p r o p e r t i e s r e s u l t i n g from t h i s survey, these f i g u r e s being an average o f the p r o p e r t i e s f o r each i n d i v i d u a l s e c t o r , w i l l be the basis f o r shim c o r r e c t i o n s . Every sector w i l l thus be shimmed by the same amount. Any asymmetry which remains w i l l be co r rec ted by means of the 72 harmonic c o i l s , which are now sized so as to be ab le to c o r r e c t a f i r s t harmonic ampl i tude o f 7-5 G. 1.6 Trimming to le rances During the commissioning o f the magnet, the t r i m c o i l s w i l l be used as soon as the shimming program has reduced e r r o r s in the g rad ien t of the average magnetic f i e l d to ±2 G / f t . The goal w i l l be to reduce the phase (1.12) where F*= ( B l - B*J/ is the f l u t t e r of the f i e l d and £ is the s p i r a l - 7 -wander due to loca l f i e l d e r r o r s so as to s a t i s f y equat ion ( 1 . 9 ) . I f the values Rc = 410 i n . and B c = 3000 G are s u b s t i t u t e d i n t o equat ion (1.6), a c o n d i t i o n f o r loca l f i e l d e r r o r s can be f o u n d 4 cpuss - in?" (1.13) Thus a t 50 MeV one can have a bump w i t h an area of 15 G - i n ^ , whereas at 500 MeV on ly 6 G-in^ is acceptab le . Sometime a f t e r the o r i g i n a l commissioning, a f u r t h e r shimming and t r imming procedure is env i s ioned , - the purpose of which is to reduce the phase s l i p so tha t ion o r b i t s are separa te , improving the e x t r a c t i o n energy r e s o l u t i o n from ±600 keV to ±25 keV . 9 Shimming w i l l now have t o reduce the e r r o r in the g rad ien t of the average f i e l d to ±1 G - f t , a t which p o i n t the t r i m c o i l s w i l l reduce the loca l f i e l d e r r o r s to a to le rance 4.8 t imes as t i g h t as tha t given in equat ion ( 1 . 1 3 ) . During the ope ra t i on o f TRIUMF, the t r i m c o i l s w i l l a l so be used in c o n j u n c t i o n w i t h the main c o i l to change the radius at which the 500 MeV o r b i t occurs . This w i l l be done by s y s t e m a t i c a l l y r a i s i n g the average f i e l d throughout the magnet. O r i g i n a l l y the 500 MeV ion o r b i t w i l l be located at a radius of 312 i n . , a l l o w i n g a beam cu r ren t o f 200 uA before r a d i o a c t i v i t y l i m i t s are r e a c h e d . 9 Increasing the average f i e l d by means of t r i m c o i l s so t ha t the 500 MeV o r b i t occured at 308 i n . would a l l ow a maximum energy of 530 MeV to be e x t r a c t e d 1 0 a l though the beam cu r ren t would need to be g r e a t l y reduced due to increased H d i s s o c i a t i o n . Using geometr ic arguments, i t has been c a l c u l a t e d tha t 32 t r i m c o i l s are s u f f i c i e n t to b r i n g the phase s l i p w i t h i n the to le rances f o r normal a c c e l e r a t i o n , whereas 51 are requ i red to accomplish t h i s f o r separated t u r n a c c e l e r a t i o n . 4 TRIUMF has been f i t t e d w i t h 54 t r i m c o i l s , placed at the r a d i i g iven in re ference 11, o f which 36 w i l l be powered du r ing the o r i g i n a l - 8 -commissioning of the TRIUMF magnet. The 72 harmonic c o i l s are sized so as to be able to handle a f i r s t harmonic e r r o r o f ±7-5 G. They w i l l probably be ad jus ted along w i t h the c i r c u l a r t r i m c o i l s , so as to approach a u n i f o r m l y isochronous average f i e l d s o l u t i o n . Since no f i e l d measurement technique has s u f f i c i e n t reso-l u t i o n , a very low cu r ren t beam w i l l be used to detect e r r o r s in the average f i e l d tha t are to be cor rec ted by the t r i m and harmonic c o i l s . Er rors in the f i r s t harmonic, a t c e r t a i n r a d i i , w i l l need to be less than 0.2 G . 8 - 9 -CHAPTER 2 . MEASUREMENT TECHNOLOGY AND ANALYSIS A l l o f the experiments discussed in t h i s repor t were performed using an a c c u r a t e l y scaled down 10 :1 model o f the f i n a l TRIUMF magnet. The model included a l l s i x s e c t o r s , as w e l l as an i ron cen t re support and support s t r u c t u r e . The copper main e x c i t a t i o n c o i l cons is ted of two separate water cooled windings each w i t h 16 t u r n s . The maximum induc t ion poss ib le was 9 6 , 0 0 0 amp t u r n s . The power supp l ies respons ib le f o r powering these c o i l s d e l i v e r e d 3000 A regu la ted to one par t in 1 0 5 . 2 . 1 Reasons f o r b u i l d i n g the 10 :1 model P r e v i o u s l y , the most accurate model a v a i l a b l e was a 2 0 : 1 scale model, a s ize which d id not g ive enough p r e c i s i o n t o answer some quest ions con-c l u s i v e l y . 5 I t is p r e s e n t l y planned to loca te wedges ins ide the vacuum tank at the cen t re of the magnet in order to improve the average f i e l d in t h i s r e g i o n . Only the gross fea tu res o f wedge design could be s tud ied on the o lde r magnet, however. In a d d i t i o n , s tud ies o f the magnetic e f f e c t s which might a r i s e due to the main vacuum chamber c o n s t r u c t i o n were con t ingent on the development o f a l a rge r model. The 10 :1 model al lowed the accurate study of focus ing as we l l as average f i e l d changes due to the shims. Not on ly the gross fea tu res but a lso the l i n e a r i t y of these changes could be s t u d i e d . Tr im and harmonic c o i l d a t a , taken p r e v i o u s l y from experiments on the o ld 2 0 . 8 : 1 model, was not s u f f i c i e n t to determine the d e t a i l e d c o n t r o l f u n c t i o n s f o r the 54 t r i m and 72 harmonic c o i l s . A l a rge r model would prov ide the second order accuracy necessary to prepare these f u n c t i o n s . Because o f i t s l a rge r s i z e , the 10 :1 model could use a scaled down ve rs ion of the survey equipment env is ioned f o r the TRIUMF magnet, thus serv ing as a t e s t bed. A l s o , the la rge r model would prov ide a more - 10 -r e a l i s t i c t e s t f o r NMR probe c o n t r o l of the magnetic f i e l d . F i n a l l y , f r i n g e f i e l d s throughout the v i c i n i t y of the magnet could be much more thorough ly t e s t e d , thus g i v i n g one an idea o f the magnetic environment to be expected in the v a u l t . 2 .2 Data a c q u i s i t i o n us ing the model The data a c q u i s i t i o n was handled by a Hewlett Packard 2116B computer, run by a program c a l l e d MAGNT under the superv i s ion of Ken Poon. The mechanical d r i v e and measuring devices were designed by Nick Reh l inger . F ie ld values were read by a FC33 h a l l p l a t e mounted at one o f the p o s i t i o n s on a r a d i a l channel and moved a z i m u t h a l l y through a preset angu-la r range. Readings of the induced h a l l probe vo l tage were taken every degree and converted by a c a l i b r a t i o n polynomial i n t o k i l o g a u s s . A l l c a l i b r a t i o n s were referenced to NMR gaussmeter measurement. With the h a l l p l a t e pos i t i oned at a c e r t a i n radius and the channel moving a z i m u t h a l l y , readings were i n i t i a t e d when a wiper blade at tached to the r o t a t i n g channel i n te rcep ted a l i g h t beam. This method e l i m i n a t e d any backlash in the channel p o s i t i o n . The r e l a t i v e angular p o s i t i o n o f 1/8 i n . ho les , placed 1 deg apar t at a rad ius o f 2 5 . 5 i n . on a d i sk mechanica l ly connected to the probe channel , determined when a reading was taken. When-ever one o f these holes moved a z i m u t h a l l y so as to a l l ow a l i g h t beam to s t a r t passing th rough , the computer wai ted 0 . 7 sec and then s i g n a l l e d a d i g i t a l vo l tme te r to read the v o l t a g e on the h a l l p l a t e . This wa i t was int roduced to preclude the p o s s i b i l i t y o f azimuthal o s c i l l a t i o n o f the channel causing the l i g h t beam s t a r t i n g through the hole to f l i c k e r and cause two read ings . The d r i v e speed was set to a l l ow a reading cyc le to be completed before another hole moved in to p o s i t i o n . - 11 -When a preset number o f azimuthal readings had been made, the opera to r was given the o p t i o n o f accept ing or r e j e c t i n g the data by r e p l y i n g on a t e l e t y p e connected to the computer. Upon h is accept ing the d a t a , i t was t r a n s f e r r e d from the core memory to magnetic and paper tape, thus p r o v i d i n g double cop ies . The opera tor could then change the radius o f the h a l l p l a t e and repeat the azimuthal sweep. 2.3 Measurement to le rances Cer ta in to le rances w i l l be necessary in the TRIUMF magnet measurement system in order to make sure tha t the average f i e l d is s u f f i c i e n t l y i s o -chronous to b r i n g the phase s l i p w i t h i n l i m i t s and tha t the v e r t i c a l focus ing is w i t h i n t o l e r a n c e s . I f i t is des i red to know the v e r t i c a l focus ing 1^ w i t h i n 0 .02, an e r r o r in the s t a r t i n g p o s i t i o n o f the azimu-tha l sweep of 0.030deg or e q u i v a l e n t l y an e r r o r in the r a d i a l p o s i t i o n i n g o f the probe o f 0.04 model inches is a l l t ha t can be a l l owed . The absolu te va lue o f the magnetic f i e l d must be known to w i t h i n an abso lu te accuracy o f 10 G or b e t t e r , 5 because of the s t rong dependence o f the H d i s s o c i a t i o n losses on the exact value o f the maximum magnetic f i e l d . Eventua l ly i t w i l l be des i red to shim to a to le rance o f ±1 G / f t , a l though i n i t i a l l y ±2 G/ f t w i l l be s u f f i c i e n t . Thus the measuring system should be able to determine the g rad ien ts to t h i s degree o f accuracy. An accuracy in the r a d i a l p o s i t i o n i n g o f 0.002 model inches would eva lua te the f i e l d g rad ien t to an accuracy of ±1 G / f t . Since the 10:1 model is to be a t e s t bed f o r the TRIUMF magnet measurement techno logy, these to le rances should a lso be met in the 10:1 model. Er rors in the measured f i e l d g r i d would in general be due to d e v i a t i o n s in the vo l tage induced in the h a l l p l a t e by a magnetic f i e l d , readings taken at the wrong t imes due to inaccurac ies in the d isk p o s i t i o n , or misal ignment - 12 -o f the h a l l p l a t e channel . The v o l t a g e induced in the ha l l p l a t e was converted i n t o u n i t s o f k i logauss by a po lynomia l , the c o e f f i c i e n t s o f which were p e r i o d i c a l l y redetermined by a c a l i b r a t i o n procedure. The d r i f t t ha t was co r rec ted by t h i s procedure was s m a l l , w i t h two polynomials in general d i f f e r i n g by less than a gauss over, the range o f i n t e r e s t . The temperature o f the h a l l p l a t e was c o n t r o l l e d by a t h e r m i s t o r to b e t t e r than 1°C, r e s u l t i n g in a minimum s t a b i l i t y of b e t t e r than 3 G . 1 2 The holes in the sha f t encoder d i sk were d r i l l e d 1 deg apar t w i t h a to le rance of b e t t e r than 0.01 deg. R e p e a t a b i l i t y of read ings , as demon-s t r a t e d by a ser ies o f repeated azimuthal sweeps, was 0.005 deg. Since breaking the l i g h t beam t h a t s t a r t e d the azimuthal channel sweep on ly produced a readiness s t a t e , inducing a reading at the next sha f t encoder h o l e , i t s accuracy d id not enter i n t o the r e p e a t a b i l i t y c a l c u l a t i o n . The cen t re around which the channel ro ta ted was w i t h i n 0.050 i n . of the geometr ic cen t re o f the model magnet. Each radius p o s i t i o n on the channel had an accuracy, from the cen t re around which the channel r o t a t e d , of 0.005 i n . When the channel was examined, i t was found to have a s l i g h t S-shape, r e s u l t i n g in an azimuthal d e v i a t i o n of perhaps 0.005 i n . The r e p e a t a b i l i t y of p lac ing the h a l l p l a t e probe a t a given r a d i a l p o s i t i o n was est imated to be 0.002 i n . Thus, except f o r the r a d i a l p o s i t i o n i n g e r r o r f i g u r e , which never the less remains adequate f o r the purpose of the experiments descr ibed in t h i s r e p o r t , the to le rances on the 10:1 model are b e t t e r than those tha t w i l l be necessary in the f u t u r e TRIUMF magnet measurement system. C e r t a i n l y the r e p e a t a b i l i t y f i g u r e s are e x c e l l e n t . I t should be added tha t the experiments on the 10:1 model as descr ibed in t h i s repor t a l l involved a de te rm ina t ion of the average f i e l d and the - 13 -focus ing r e s u l t i n g w i t h the a d d i t i o n o f shims. Since the abso lu te e r r o r s were e s s e n t i a l l y the same in experiments w i t h and w i thou t shims in p lace , when the d i f f e r e n c e of the f i e l d and focus ing parameters was taken , the abso lu te e r r o r s l a r g e l y cance l led out and on ly r e p e a t a b i l i t y e r r o r s remained s i g n i f i c a n t . 2.4 Analys is of r e s u l t s During data a c q u i s i t i o n , the Hewlett Packard computer performed a p r e l i m i n a r y a n a l y s i s , f i n d i n g and record ing the average f i e l d and the f l u t t e r at each r a d i u s . The main a n a l y s i s , using the data s tored on magnetic tape , was done, however, by a se r ies o f IBM 36O computer programs c a l l e d REPLOT, POLICY, and CYCLOPS.13 The program of c h i e f i n t e r e s t in t h i s repor t was CYCLOPS, which solved the equat ions o f mot ion f o r a p a r t i c l e in the measured magnetic f i e l d , thus p r e d i c t i n g the v e r t i c a l o s c i l l a t i o n index . I t should be noted tha t the i s o c h r o n i z a t i o n o p t i o n in POLICY, which ad jus t s the f i e l d s in a way s i m i l a r to changing the pole w i d t h , so as to r e s u l t in an isochronous c o n d i t i o n , was never used in the a n a l y s i s . The remaining two parameters in the smooth approx imat ion were c a l c u -la ted from CYCLOPS o u t p u t . The f i e l d g rad ien t index was found by comparing the average f i e l d s at adjacent r a d i i . The tangent of the s p i r a l angle could be found by using a r e l a t i o n s h i p descr ibed in re ference 14, t ha t tan 6 = j^r-R , where 6 is the s p i r a l angle and i>k the phase of the s i x t h harmonic o f a f o u r i e r a n a l y s i s o f the f i e l d g r i d done i n t e r n a l l y w i t h i n CYCLOPS. The f a c t t ha t a l l o f the components o f the smooth approx imat ion could be c a l c u l a t e d w i t h o u t any knowledge of the focus ing i t s e l f al lowed an inde-pendent es t imate fo r the focus ing to be obta ined by combining these components. - ]k -CHAPTER 3 . SHIMMING THE MAGNET POLE PIECE 3•1 SHIMPOLE, a computer program For the shimming procedure to be s u c c e s s f u l , the d i f f e r e n c e s between the measured average f i e l d and the isochronous f i e l d and between the ideal V^. versus rad ius curve and the actua l versus radius curve must be minimized by using pole shims. In order to p r e d i c t the adjustments to the shims necessary to decrease these e r r o r s , the f o l l o w i n g expression must be min imized. K ? C ( 1 ) [ B 0 ( I ) - B ' ( l ) f + & £ E ( I ) [ ^ ( I ) - P t ' a ) f + M ^ N U f ( 3 . 1 ) where K, G, M, C, and E are cons tan ts , B 0 and X>^Q are the des i red average f i e l d and f o c u s i n g , and B ' and \ \ are the program cor rec ted f i e l d and focus ing as def ined below. The index I extends over a l l magnet r a d i i at which c o r r e c t i o n s are to be made, whereas the index J extends over a l l o f the shims. N( j ) is the th ickness of the shim change at the J t n shim p o s i t i o n . For B ' and , the program s u b s t i t u t e s the expressions B'd) = B(I) + £ AB~(I,J) • N(J ) ( 3 . 2 ) = + ? A ^ ( I , J ) ' N (J ) ( 3 . 3 ) where B and lV~ are the o r i g i n a l , uncorrected average f i e l d and focus ing r e s p e c t i v e l y , and A x ( l , J ) is the change in X at the l t n rad ius due to a t h u n i t shim change at the J shim p o s i t i o n . Let Lj be the number o f shims on the concave s ide o f the pole p iece , L Q the number on the convex, and L = L; + L Q . Then we de f i ne the g r i ds A B , A lV" and N in the f o l l o w i n g way - 15 -A B (I ,J) 1 ^ J L~ L; (3.4) A B 0(1 , J ) 1 «= J t L A V ^ I . J ) A V ^ ( I , J ) 1 - J - Li (3.5) L;+ 1 t J " L W (J) Ni(J) 1 «= J L t (3.6) N„(J) Li+ 1 fc J - L where the subsc r ip t s ( i ) and (o) r e f e r to the concave and convex sides o f the pole piece r e s p e c t i v e l y . The s o l u t i o n of the r e s u l t i n g m a t r i x equat ions f o r the vec to r N, the change in the th ickness of shims needed at each r a d i a l p o s i t i o n on the pole p iece , invo lves a f a i r l y s t r a i g h t f o r w a r d double p r e c i s i o n m a t r i x i n v e r s i o n , the procedure f o r which can be found descr ibed in re ference 11 . The constant M, which acts as a l i m i t on the s ize o f the shim changes, is very impor tan t , as w i thou t i t the s o l u t i o n involves large consecu t i ve l y p o s i t i v e and negat ive r e s u l t s . Increas ing M a l lows one, by reducing the magnitude o f the p red ic ted shim changes, to stay w i t h i n the l i n e a r range of the program. 3.2 Resul ts o f shim experiments The purpose of these experiments was to f i n d the g r i d s AVj" and AB and to determine t h e i r l i n e a r i t y , thus p r o v i d i n g both the input f o r and p r e d i c t i n g the e f f e c t i v e n e s s o f SHIMPOLE. - 16 -3-2.1 Shim experiments A ser ies o f 40 experiments was c a r r i e d th rough , i n v o l v i n g f i r s t the adding and then the s u b t r a c t i n g o f 0.1 and 0.2 i n . t h i c k shims from those shim p o s i t i o n s nearest the model rad ius R = 5, 12.5, 20, 25, and 30 i n . , on both the concave and the convex sides of the pole p iece . The f i e l d data was then analyzed to determine the changes in the aver -age f i e l d and in the v e r t i c a l f o c u s i n g . 3.2.1.1 F ie ld and focus ing changes The average f i e l d and v e r t i c a l focus ing changes tha t r e s u l t e d from the p lac ing o f 2 i n . shims are shown in F igs . 1 and 2 r e s p e c t i v e l y f o r shims placed on the concave s ide of the pole piece and in F igs . 3 and 4 r e s p e c t i v e l y f o r shims placed on the convex s ide o f the pole p iece . Accompanying these r e s u l t s were changes in the f l u t t e r , the g rad ien t of the average magnetic f i e l d , and the tangent of the s p i r a l ang le ; as d e t e r -mined in sec t i on 2.4. For a 2 i n . shim, these changes are shown in F igs . 5, 6, and 7 r e s p e c t i v e l y f o r shims placed on the concave s ide of the pole p iece , and in F igs . 8, 9» and 10 f o r shims placed on the convex s ide of the pole p iece . When these changes were inser ted i n t o the d i f f e r e n t i a l of equat ion (1.12), the p red ic ted changes in v e r t i c a l focus ing tha t resu l ted proved to be q u i t e c lose to the ac tua l changes. These p red ic ted changes are shown, again f o r 2 i n . shims, in F i g . 11 f o r shims placed on the concave and in F i g . 12 f o r the convex s ide of the p o l e . p i e c e . This c o r r e l a t i o n a l lows one, by s tudy ing the changes in the f l u t t e r , the g rad ien t o f the average magnetic f i e l d , and the tangent of the s p i r a l ang le , to gain a - 17 -Radius ( f u l l - s c a l e inches) F i g . 1 Changes in the average f i e l d caused by two inch shims placed on the concave s ide o f the pole piece _ - 1 0 -' I i I • i i J i i i i > i i i i i i I i — I — i I — i — i 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0 2 2 0 2 4 0 2 6 0 2 8 0 3 0 0 3 2 0 Radius ( f u l l - s c a l e inches) F i g . 2 Changes in the v e r t i c a l focus ing caused by two inch shims placed on the concave s ide of the pole p iece - 18 -l — i — i — i — i — i — i — i — i — i i i i i i i i i i i i i i 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0 2 2 0 2 4 0 2 6 0 2 8 0 3 0 0 3 2 0 Radius ( f u l l - s c a l e inches) F i g . h Changes in the v e r t i c a l focus ing caused by two inch shims placed on the convex s ide o f the pole piece - 19 -308.5' 2 0 i+0 6 0 8 0 . 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0 Radius ( f u l l - s c a l e inches) 2 2 0 2 4 0 2 6 0 2 8 0 3 0 0 3 2 0 F i g . 5 Changes in the f l u t t e r caused by two inch shims placed on the concave s ide o f the pole piece 10 ' 0 5 5 ° 0 5 1 0 1 5 2 0 4 0 F i g . 6 _i_ _i_ JL _ l _ _ l _ 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0 Radius ( f u l l - s c a l e inches) 2 2 0 2 4 0 2 6 0 2 8 0 3 0 0 3 2 0 Changes in the f i e l d g rad ien t index caused by two inch shims placed on the concave s ide o f the pole p iece - 20 -CM • 1 0 h • 0 5 • 0 5 • 1 0 • 1 5 -\ 253" xl/10 ^ ^ ^ 0 8 . . 1 . 1 . 1 . 1 . 1 . • . i . i . i . i . i i i i i 2 0 4 0 F i g . 7 6 0 8 0 1 0 0 1 2 0 1 4 0 .1 6 0 1 8 0 2 0 0 2 2 0 2 4 0 2 6 0 2 8 0 3 0 0 3 2 0 Radius ( f u l l - s c a l e inches) Changes in the s p i r a l angle tangent caused by two inch shims placed on the concave s ide of the pole piece * 2 CN 3 _1 1_ J L _ l _ _ l i _ 2 0 4 0 6 0 8 0 1 0 0 . 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0 2 2 0 Radius ( f u l l - s c a l e inches) 2 4 0 2 6 0 2 8 0 3 0 0 3 2 0 F i g . 8 Chang es in the f l u t t e r caused by two inch shims placed on the convex s ide o f the pole piece 1 5 h 21 c < 1 0 h 0 5 h 0 h 0 5 1 0 h 306.5' 1 5 _i I i 1_ _1_ 2 0 4 0 6 0 F i g . 9 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0 2 2 0 Radius ( f u l l - s c a l e inches) 2 4 0 2 6 0 2 8 0 3 0 0 3 2 0 Changes in the f i e l d g rad ien t index caused by two inch shims placed on the convex s ide o f the pole piece xl/10 306,5' F i g . 10 T 4 0 1 6 0 1 8 0 2 0 0 2 2 0 ~ Radius ( f u l l - s c a l e inches) Changes in the s p i r a l angle tangent caused by two inch shims placed on the convex s ide o f the pole piece - 22 -2lb ' 40 ' 60 ' 80 ' 100 ' 120 ' l U ' 160 ' l'so' 20*0 ' 220 ' 240 ' 'Ao ' 2*80 " 3 o'0 ' 320 Radius ( f u l l - s c a l e inches) F i g . 11 Smooth approx imat ion p r e d i c t i o n s o f changes in the v e r t i c a l focus ing caused by two inch shims on the concave s ide o f the pole piece I — i — l i I — i I i i i I i i i I i i i i i I . I . I . i • • 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 Radius ( f u l l - s c a l e inches) F i g . 12 Smooth approx imat ion p r e d i c t i o n s o f changes in the v e r t i c a l focus ing caused by two inch shims on the convex s ide o f the pole piece - 23 -b e t t e r understanding of the reasons f o r a p a r t i c u l a r t o t a l change in v e r t i c a l f o c u s i n g . 3 . 2 . 1 . 2 L i n e a r i t y of f i e l d and focus ing changes Since SHIMPOLE is a program composed of l i n e a r e lements, i t is essen t ia l t h a t the exper imental e f f e c t s which i t desc r i bes , namely the changes in the average f i e l d and in the f o c u s i n g , be at leas t approx imate ly l i n e a r . In f a c t , experiments i n d i c a t e tha t the l i n e a r i t y is more than adequate. L i n e a r i t y of the g r i d s w i t h respect to shim th ickness was impl ied in the previous sec t ion in tha t graphs f o r on ly one o f the four shim th icknesses were g i v e n . The l i n e a r i t y w i t h respect to shim th ickness of the maxima of the d i f f e r e n t shim th ickness AB curves and the two maxima o f the d i f f e r e n t shim th ickness A^V" curves is shown in F igs . 13, 14, and 15 f o r shims placed on the concave s ide o f the pole p iece . The s i t u -a t i o n is equa l l y s a t i s f a c t o r y f o r shims on the convex s i d e . Experiments were done to con f i rm tha t the changes due to mounting two shims adjacent to each o ther were the same as the numerical sum of the changes found when each shim was mounted and analyzed s e p a r a t e l y . F i g . 16 shows the l i n e a r i t y , in t h i s respec t , o f the average f i e l d . The v e r t i c a l focus ing a lso behaved in an a d d i t i v e manner, g i v i n g s i m i l a r e r r o r s . I t was found, however, tha t a l though the ampl i tude of the changes due to a la rge shim was p r o p o r t i o n a l to t h a t f o r a smal ler shim, the actua l change i t s e l f would s h i f t r a d i a l l y , depending on the th ickness o f the shim. That t h i s is p h y s i c a l l y reasonable can be seen by r e a l i z i n g , f o r example, t h a t p u t t i n g - 24 -Shim th ickness (model inches) F i g . 13 V a r i a t i o n of the ABmax w i t h shim th ickness fo r the concave s ide of the pole piece * 48" 1 l _ i 1 - 1 0 +1 + 2 Shim th ickness (model inches) F i g . 14 V a r i a t i o n o f the negat ive maximum in A v z2 w i t h shim th ickness f o r the concave s ide of the pole piece - 25 -1 F i g . 15 0 +1 + 2 Shim th ickness (model inches) V a r i a t i o n of the p o s i t i v e maximum in A v z2 w i t h shim th ickness fo r the concave s ide o f the pole piece 0 A © p h y s i c a l sum of the two change curves shown A change when both shims mounted s imul taneous ly 2 5 0 2 6 0 2 7 0 2 8 0 2 9 0 3 0 0 Radius ( f u l l - s c a l e inches) F i g . 16 Average f i e l d change o f two adjacent shims is the sum of the changes r e s u l t i n g when each shim is mounted separa te ly - 26 -a large shim on the outer concave s ide of the pole piece involves adding metal a t lower r a d i i as wel l as t h a t of the shim p o s i t i o n , because o f the s i g n i f i c a n t s p i r a l ang le . This e f f e c t w i l l be seen to necess i ta te the m o d i f i c a t i o n of SHIMPOLE so as to c o r r e c t the data g r i d s , based on the r e s u l t s o f the previous i t e r a t i o n s . Of p r a c t i c a l i n t e r e s t was the e f f e c t o f the a i r gaps t h a t would be present between the shims necessary to make up some p a r t i c u l a r th ickness o f me ta l . Experiments were done in which the e f f e c t of a .180 i n . shim was compared w i t h tha t of th ree .060 and s i x .030 i n . shims. Mechan ica l l y , the .180 and .060 i n . shims were f a i r l y r i g i d , whereas the .030 i n . shims could be bent q u i t e e a s i l y when bo l ted i n t o p o s i t i o n . Ana lys is showed tha t the a i r gaps reduced the changes caused by the three .060 i n . shims to 90% o f the changes caused by a s i n g l e .180 i n . shim. The s i x .030 i n . shims, on the o ther hand, had changes w i t h i n 35% t ha t o f the s o l i d .180 i n . shim. Thus i t would appear tha t the number o f shim i n te r faces does not in p r a c t i c e a f f e c t the l i n e a r i t y as long as each shim is c a r e f u l l y molded to the shape o f the pole p iece . With t h i n shims, t h i s can be accomplished pure ly by the a c t i o n o f b o l t i n g . 3.2.2 SHIMPOLE t e s t s 3.2.2.1 I n t e r p o l a t ion In order to have SHIMPOLE p r e d i c t the change in the th ickness o f shims at each.shim p o s i t i o n , i t was necessary to have the changes in the average f i e l d and the focus ing not on ly at f i v e , but at a l l , o f the shim p o s i t i o n s . This was'acom-p l i shed by the use of the simple l i n e a r i n t e r p o l a t i o n program - 27 -descr ibed in Appendix C. The focus ing change g r i d was more d i f f i c u l t to i n t e r p o l a t e than was the f i e l d change g r i d , because o f the steeper g rad ien ts involved in the focus ing change curves. As is ind ica ted in F i g . 17, which shows an i n t e r p o l a t i o n in the focus ing g r i d , the r e s u l t was c e r t a i n l y adequate f o r the pur-poses of a t e s t however. I t should be added tha t e r r o r s in i n t e r p o l a t i o n were probably caused l a r g e l y by a random uncer-t a i n t y o f up to ±0.10 i n . in the knowledge of the shim p o s i t i o n r a d i i . The s i g n i f i c a n c e of a systemat ic e r r o r o f t h i s type is discussed in sec t ion 3-3. 3 .2.2.2 P red i c t i ons o f SHIMPOLE The average f i e l d and the focus ing p r o p e r t i e s of pole 3 on the 10:1 model were measured and g iven to SHIMPOLE as inpu t . The program then p red ic ted the arrangement of shims tha t would g ive the ,bes t combina t ion , in a leas t squares sense, o f the average f i e l d and focus ing improvements. The p red ic ted shim changes were made and the f i e l d and focus ing p r o p e r t i e s measured. F i g . 18 shows the o r i g i n a l and the improved average f i e l d compared to the average f i e l d p red ic ted by SHIMPOLE, and F i g . 19 shows the same r e s u l t f o r the v e r t i c a l f o c u s i n g . The new f i e l d and focus ing p r o p e r t i e s were again g iven to SHIMPOLE, and a p r e d i c t i o n f o r f u r t h e r improvement o b t a i n e d . The r e s u l t s of t h i s p r e d i c t i o n on the average f i e l d and the focus ing can be seen in F igs . 20 and 21 r e s p e c t i v e l y . I t should be noted tha t the region less than 100 i n . was not f i t t e d because the pole was not s u f f i c i e n t l y undercut to a l l ow shimming. This s i t u a t i o n has s ince been r e c t i f i e d . OO I 1 1 1 1 1 I I I ' ' I .1 1 1 I 1 — I. I " 2 2 0 2 4 0 2 6 0 2 8 0 ' 3 0 0 3 2 0 1 Radius ( f u l l - s c a l e i n c h e s ) F i g . 17 F o c u s i n g change c u r v e s between measured changes a t 253 and 308.5 inches as found by a l i n e a r i n t e r p o l a t i o n r o u t i n e - 29 -6 0 20 r 1 5 10 0 5 CM. N C M — N • or ig inal e r r o r X p red ic ted improvement © a c t u a l improvement 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0 2 2 0 Radius ( f u l 1 - s c a l e inches) 2 4 0 2 6 0 2 8 0 3 0 0 3 2 0 F i g . 18 Improvements in the average f i e l d as compared to the p red ic ted improvements a f t e r the f i r s t SHIMPOLE i t e r a t i on ' o r i g i n a l e r r o r x pred ic ted improvement ac tua l improvement • 0 5 - • 10 - • 1 5 20 4 0 60 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0 2 2 0 2 4 0 2 6 0 2 8 0 3 0 0 3 2 0 Radius ( f u l 1 - s c a l e inches) F i g . 19 Improvements in the v e r t i c a l focus ing as compared to the p red ic ted improvements a f t e r the f i r s t SHIMPOLE i t e r a t i o n - 30 -• . i . i • i . i • i • i . i . i - • i i i i i i . i 20 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0 2 2 0 2 4 0 2 6 0 2 8 0 3 0 0 3 2 0 Radius ( f u l l scale inches) F i q . 20 Improvements in the average f i e l d as compared to the pre-d i c t e d improvements a f t e r the second SHIMPOLE i t e r a t i o n " • 1 5 i • • . i . i . i . i . i . i . i i • i i i i I i I i ' 20 4 0 6 0 80 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0 2 2 0 2 4 0 2 6 0 2 8 0 3 0 0 3 2 0 Radius ( f u l l - s c a l e inches) F i g . 21 Improvements in the v e r t i c a l focus ing as compared to the p red ic ted improvements a f t e r the second SHIMPOLE i t e r a t i o n - 31 -I t can a lso be seen t h a t the second p r e d i c t i o n broke down a t 280 i n . f o r the average magnetic f i e l d and perhaps 255 i n . f o r the v e r t i c a l f o c u s i n g . As w i l l be discussed l a t e r , t h i s is due to the f a c t tha t the g r i d s s h i f t w i t h radius when shim changes accumulate, as discussed in sec t ion 3.2.1.2. This e f f e c t can in p r i n c i p l e be compensated f o r , and poss ib le procedures w i l l be discussed in sec t ion 3-3. However, from 100 i n . to 280 i n . , the region o f the pole piece in which SHIMPOLE in i t s present form could be t e s t e d , average f i e l d e r r o r s which o r i g i n a l l y averaged kO G were reduced to 23 G a f t e r the f i r s t , and 6 G a f t e r the second i t e r a t i o n . This is an improvement dur ing the course o f the i t e r a t i o n o f r e s p e c t i v e l y k0% and then 70%. The smal ler im-provement dur ing the f i r s t i t e r a t i o n was due f i r s t o f a l l to the f a c t t ha t SHIMPOLE was weighted to produce smal ler shim changes, and secondly to the f a c t tha t much more care was taken dur ing the shimming f o r the second i t e r a t i o n to reduce a i r gaps and to choose the most e f f i c i e n t combinat ion o f shim th icknesses . In commissioning the magnet, i t would seem reasonable to expect at leas t a k0% improvement in the average f i e l d a f t e r each i t e r a t i o n , using SHIMPOLE in i t s present form and c o r r e c t -ing the g r i d s a f t e r each i t e r a t i o n . I f i t e r a t i v e behaviour is in t roduced i n t o SHIMPOLE i t s e l f , i t is poss ib le t ha t t h i s f i g u r e could be s i g n i f i c a n t l y improved. The focus ing can be seen to be ra ther b e t t e r , a l though not yet w i t h i n t o l e r a n c e s . The problem appears to be tha t SHIMPOLE in i t s present fo rm, w i t h no compensation provided f o r - 32 -the r a d i a l s h i f t in the g r i ds as shim changes accumulate, e s s e n t i a l l y l i m i t s one t o on ly small changes about the nominal shim p o s i t i o n . Macroscopic changes in the s p i r a l ang le , p ro -duced by p r o g r e s s i v e l y moving more shims from one s ide to the o ther w i t h r a d i u s , invo lve changes too la rge f o r SHIMPOLE to consider in i t s present fo rm. Yet these are the changes tha t a f f e c t the v e r t i c a l focus ing the most. I n t roduc ing c o r r e c t i o n s to SHIMPOLE to a l l ow f o r r a d i a l s h i f t should a l l ow i t to make the gross changes in the s p i r a l angle necessary t o c o r r e c t the v e r t i c a l focus ing along w i t h the average f i e l d . An experiment was done to show t h a t simultaneous c o r r e c t i o n of the average f i e l d and the focus ing is p o s s i b l e . A macroscopic s p i r a l angle change was made which e l im ina ted the imaginary p o s i t i o n o f the v e r t i c a l focus ing at 260 i n . as seen in F i g . 21 and a t the same time re ta ined the previous isochronism. 3.2.3 Minimum shim th icknesses requ i red The experiments descr ibed in t h i s repor t have made i t poss ib le to check the minimum shim th icknesses p red ic ted in re ference 8. This th ickness has to be small enough to change both the focus -ing and the average f i e l d at any rad ius by an amount less than the to le rance in these parameters. The v e r t i c a l focus ing Y\ has a t o l e r -ance of ±0.1 f o r 50 i n . < R < 310 i n . The average f i e l d , however, has a to le rance of ±1 G / f t f o r separated t u r n a c c e l e r a t i o n , and t h i s turns out to be the l i m i t i n g c o n s i d e r a t i o n . Table 1 presents the est imated and the exper imental values f o r the minimum shim th icknesses at several r a d i i . The exper imental va lue is tha t th ickness of 12 i n . long shim which changes the g rad ien t of - 33 -TABLE I Pred ic ted and exper imental minimum shim th icknesses necessary to meet a to le rance o f 1 G / f t Concave Convex — — t p red. t exp. t p red. t exp. ( i n . ) (MeV) ( i n . ) ( i n . ) 307 480 .021 .042 .034 .035 280 350 .033 .035 .050 .047 250 250 .040 .042 .055 -047 200 135 .044 .053 .050 .053 125 50 .032 .026 .032 .026 - 34 -the average magnetic f i e l d by ±1 G / f t . I t was assumed t h a t the g rad ien t f o r a 12 i n . long shim w i l l be the same as tha t found exper imen ta l l y f o r 20 i n . long shims of the same t h i c k n e s s . To leave the s p i r a l angle o f the pole unchanged, shim changes should be made to both sides of the po le . To a l l ow f o r t h i s , the shim th icknesses found above were halved and then l i s t e d in the t a b l e . I t should be noted t h a t experiments i n d i c a t e t h a t p lac ing a shim on on ly one of the top and bottom pole pieces has h a l f the e f f e c t on both the average f i e l d and the focus ing o f p lac ing the same s ize o f shim on both p i e c e s . 5 I f t h i s f a c t were made use of in TRIUMF, the minimum th icknesses l i s t e d in .Tab le 1 could again be doubled. 3.3 Conclus ions I t was noted in sec t i on 3 - 2 . 1 . 2 tha t a l though the ampl i tude of the changes due to a la rge shim was p r o p o r t i o n a l to t ha t f o r a smal ler shim, the actua l change i t s e l f would s h i f t r a d i a l l y depending on the th ickness of the shim. This s h i f t w i l l be seen to necess i t a te an i t e r a t i v e m o d i f i c a t i o n to SHIMPOLE. I f one considers a pole edge at an angle £ w i t h respect to the radius v e c t o r , a t r i g o n o m e t r i c argument shows tha t a f t e r one adds a shim th ickness t , one is no longer at the radius R D , but ra ther at the radius RQ + t s in 6. This is the s i t u a t i o n t h a t would r e s u l t a f t e r SHIMPOLE had been used once and had p red ic ted a shim o f th ickness t at radius R D . This change cannot be made at radius R Q , however, but at the d i f f e r e n t radius RQ + t s i n C . Thus e r r o r is in t roduced. That t h i s e r r o r is s i g n i f i c a n t can be shown by cons ide r ing a radius o f 305 i n . , w i t h a radius vec to r to pole edge angle of -70 deg. A shim change t of 1 in . .now in t roduces a radius change of 0.94 i n . F igs . 1 and 2 - 35 -i n d i c a t e t ha t a t the po in t where the g rad ien ts of the focus ing and f i e l d changes are s teepes t , t h i s p a r t i c u l a r r a d i a l s h i f t can r e s u l t in a maximum e r r o r in o f 0.013 and in the average f i e l d of 1.1 G. Now the g rad ien ts remain steep over a radius range o f perhaps 20 i n . Because of the la rge s p i r a l ang le , there are some e i g h t o ther shim p o s i t i o n s , t h ree on the con-vex s ide and f i v e on the concave, w i t h i n 10 i n . r a d i a l l y of the p o s i t i o n at 305 i n . , each w i t h perhaps an equ iva len t e r r o r . This leads to a cumulat ive e r r o r o f 0.11 in V^" and 9 G in the average f i e l d . This c a l c u l a t i o n takes i n t o account on ly the e f f e c t of one of the g rad ien ts o f each o f the curves. The average f i e l d change has two steep g rad ien t slopes in the shape o f a b e l l cu rve , whereas the focus ing change curve has three steep g rad ien t slopes in the shape of a h o r i z o n t a l S-curve. Even though a p a r t i c u l a r g rad ien t s lope remains s i g n i f i c a n t on ly f o r curves w i t h i n a reg ion of some 20 i n . , curves f a r t h e r away can be s i g n i f i c a n t by b r i n g i n g another o f t h e i r g rad ien t slopes i n t o e f f e c t . In t h i s way, curves o u t s i d e the range from 295 to 315 i n . w i l l a lso a f f e c t the f i e l d and focus ing at 305 i n . when phase s h i f t s in the g r i d occur . This e f f e c t , coming i n t o p lay from both sides of the 20 i n . rad ius range being cons idered , could q u i c k l y double the e r r o r s , to perhaps 18 G in the average f i e l d and 0.22 in . I f cumulat ive shim changes of g rea te r than 1 i n . were con-templa ted, e r r o r s would be cor respond ing ly g r e a t e r . The necessary m o d i f i c a t i o n to SHIMPOLE could be performed in two ways, a) A f t e r each i t e r a t i o n , a separate program could be r u n , using the p red ic ted shim changes as i n p u t , which would s h i f t the g r i ds tha t are used by SHIMPOLE by the necessary amount. The g r i ds f o r each shim p o s i t i o n would need to be s h i f t e d r a d i a l l y by an amount t s in £ , where £ would have been measured f o r each shim p o s i t i o n . Taking a - 36 -f o u r i e r ana lys i s of each g r i d would then a l l ow an accurate s h i f t to be made q u i t e s imp ly . b) The program descr ibed above could be incorporated i n t o SHIMPOLE along w i t h an i t e r a t i v e loop. SHIMPOLE could then i t e r a t e , keeping CUWAIT h igh to avo id 1arge shim changes, s h i f t the g r i d s r a d i a l l y by the appropr ia te amount, and i t e r a t e aga in . The advantage of t h i s p r o -cedure is tha t the shimming procedure would converge much more r a p i d l y , s ince each p r e d i c t i o n would be b e t t e r . I t would seem tha t the f i r s t procedure descr ibed above might be a good i n t e r i m one, to be used u n t i l an i t e r a t i v e procedure can be p e r f e c t e d . - 37 -CHAPTER 4. SETTING THE TRIM COIL CURRENT CAPACITIES The TRIUMF magnet has been f i t t e d w i t h 54 t r i m and 72 harmonic c o i l s . As has been discussed in sec t i on 1.6, these w i l l i n i t i a l l y c o r r e c t a maxi -mum e r r o r in the g rad ien t of the average f i e l d of ±2 G / f t , and maximum f i r s t harmonic e r r o r of ±7-5 G. During t h i s o r i g i n a l commissioning o f the magnet, i t is expected t h a t on ly 36 c o i l s w i l l be powered. Later on, in order to a l l ow separated t u r n e x t r a c t i o n , the t r i m c o i l s w i l l be asked to r e p a i r a g rad ien t e r r o r o f ±1 G / f t , f i n i s h i n g w i t h a phase s l i p t o le rance 4.8 t imes as t i g h t as the o r i g i n a l , t h i s procedure poss ib l y r e q u i r i n g the use of a l l 54 t r i m c o i l s . The t r i m c o i l s a lso have to be capable of changing the 500 MeV radius from a lower.energy high cu r ren t mode to a higher energy low cu r ren t one. The purpose of the study descr ibed here was f i r s t to es t imate the t r i m c o i l cu r ren ts tha t would be needed, both dur ing t r imming to i n i t i a l t o l e r -ances and l a t e r t o separated t u r n t o l e r a n c e s . Also des i red was an i n d i c a t i o n as to whether the o r i g i n a l 36 power supp l ies would remain adequate f o r separated t u r n t r imming , or whether a l l 54 would be necessary. At a l l t imes , the t r i m c o i l s had to be s ized so as to be ab le to change the 500 MeV rad ius from the o r i g i n a l 312 i n . to the higher energy mode f i g u r e o f 308 i n . Using an IBM/360 program c a l l e d TRIMFIT, these quest ions were s tud ied by look ing at the e f f e c t i v e n e s s , in both the i n i t i a l . a n d the separated t u r n t r imming , o f 54 t r i m c o i l s as wel l as d i f f e r e n t combinat ions o f 36 t r i m c o i l s when asked to repa i r a given e r r o r f i e l d . The e f f e c t o f the harmonic c o i l s was not examined. This study was based on two previous e x p e r i m e n t s , 1 1 performed on the 20.8:1 model magnet. Tr im c o i l s had been placed at r a d i i o f 124.8 and 249.6 f u l l scale inches, and measurements taken o f the e f f e c t on the mag-n e t i c f i e l d of powering these c o i l s . As descr ibed in re ference 11, a l i n e a r - 38 -i n t e r p o l a t i o n procedure was then used to es t imate the e f f e c t s o f t r i m c o i l s placed a t a l l o f the 54 t r i m c o i l r a d i i . The e f f e c t o f the main c o i l was measured on the 20:1 model by comparing two runs w i t h d i f f e r e n t pot s e t t i n g s , both runs i n c l u d i n g the metal support s t r u c t u r e . The r e s u l t i n g g r i d was used as the input f o r the program TRIMFIT. • Al though the t r i m c o i l data was some-what ske tchy , i t was judged to be s u f f i c i e n t l y p rec ise to a l l o w the f i n a l s e t t i n g o f the t r i m c o i l cu r ren t c a p a c i t i e s , as we l l as to i n d i c a t e the number o f t r i m c o i l s t h a t might need to be powered. 4.1 Desc r i p t i on of TRIMFIT The program TRIMFIT, as o r i g i n a l l y w r i t t e n by Jon Rivers-More, is descr ibed in reference 11. Appendix B conta ins a u s e r ' s guide f o r TRIMFIT in i t s present fo rm, necessary because of the m o d i f i c a t i o n s tha t were made dur ing the course o f t h i s s tudy. TRIMFIT c a l c u l a t e s the t r i m c o i l cu r ren ts necessary to produce a given isochronous f i e l d from a given measured f i e l d , the d i f f e r e n c e between these two being c a l l e d the d i f f e r e n c e f i e l d . This is done by min imiz ing the express ion where WT, Bd, and Be are r e s p e c t i v e l y the r a d i a l we igh t ing f a c t o r , the d i f f e r e n c e f i e l d , and the f i e l d due to a l l t r i m c o i l s at the i t n r a d i u s ; C ( j ) is the cu r ren t in the j t n t r i m c o i l ; and K is the we igh t ing f a c t o r t ha t 1imi ts the s ize o f the c u r r e n t s . The we igh t ing f a c t o r K was o r i g i n a l l y in t roduced to reduce the tendency of the program to g ive s o l u t i o n s w i t h high and a l t e r n a t i n g cu r ren ts in adjacent c o i l s . This f a c t o r , however, was found t o a lso a l l ow a t r a d e - o f f between the s ize o f the phase s l i p and the (4.1) - 39 -s ize o f the c u r r e n t s . The main e x c i t a t i o n c o i l , i t should be added, was t rea ted as an a d d i t i o n a l t r i m c o i l , and could be de le ted from the s o l u t i o n i f d e s i r e d . Each TRIMFIT s o l u t i o n thus gave the change in the e x c i t a t i o n of the main c o i l as wel l as the t r i m c o i l cu r ren ts tha t would best minimize average f i e l d e r r o r s . The l e f t hand s ide of equat ion (1.13) was included in TRIMFIT in order to f i n d the amount of phase s l i p tha t would occur in any p a r t i c u l a r t r i m c o i l s o l u t i o n . This was done by d e f i n i n g a v a r i a b l e W = max |P(n) - P ( n ' ) | , where (4.2) n P(n) = 2 R( i ) - AF ( i ) • AR, (4.3) A B being the e r r o r remaining uncorrected by t r i m c o i l s at the i t n r a d i u s , and A R the constant d is tance between rad ius i and i + 1 . The number W was thus a d i r e c t measure of the phase s l i p t ha t would occur in an a c c e l e r a t i o n between radius 1 and rad ius n. Since the f i e l d e r r o r s A B were o f the same s ign over a cons iderab le range o f r a d i i , the number W could exceed i t s to le rances even when the i n d i v i d u a l f i e l d e r r o r s were w i t h i n t h e i r s . The goal was thus to f i n d the most economical set o f cu r ren ts tha t would keep W below 1800 G i n . f o r low r e s o l u t i o n and 375 G i n . f o r separated t u r n acce le ra t i on . 4.2 Computer experiments us ing TRIMFIT Experiments were done in which a l l 54 t r i m c o i l s and then var ious combinat ions o f on ly 36 c o i l s were used to c o r r e c t d i f f e r e n c e f i e l d s com-posed of the supe rpos i t i on of a 5 i n . change in the 500 MeV radius w i t h var ious ±1 G e r r o r s in the average f i e l d superposed. Since the plan is to change the 500 MeV radius from 312 to 308 i n . , study of a 5 ra ther than - 4o -a 4 i n . change int roduced somewhat o f a sa fe ty f a c t o r . When s tudy ing g rad ien t e r r o r s of ±1 G / f t , the goal was to reduce the phase s l i p to separated t u r n t o l e r a n c e s . At the end of the s tudy , i n fo rmat ion gleaned from look ing a t ±1 G / f t g rad ien t e r r o r s al lowed the de te rm ina t ion o f the c o i l c u r r e n t s necessary to repa i r ±2 G / f t e r r o r s . The procedure used w i t h 54 t r i m c o i l s was to choose a t y p i c a l d i f f e r -ence f i e l d , f i n d the weights necessary to b r ing the phase s l i p w i t h i n t o l e r a n c e s , and then use these weights to study o ther d i f f e r e n c e f i e l d s . The procedure w i t h 36 c o i l s was more compl i ca ted , in t ha t a f t e r the best we igh t ing was found, the best and most e f f i c i e n t combinat ion of powered c o i l s had to be found, before o ther d i f f e r e n c e f i e l d s could be s t u d i e d . 4.2.1 Determining the we igh t ing f a c t o r s 4.2.1.1 Radial we igh t ing Our des i re was to choose the r a d i a l we igh t ing f a c t o r s WT in such a way as to g ive a s i m i l a r amount o f phase s l i p at each r a d i u s . From equat ion (4 .3) , i t is ev ident t ha t f o r a phase s l i p increment constant w i t h radius we must have AB(R) propor-t i o n a l to 1/R, meaning tha t the ou ts ide o f the magnet must be more c l o s e l y f i t t e d by a f a c t o r R. The s ize o f A B ( i ) depends approx imate ly on the t r i m c o i l spacing at rad ius i . Looking at the t a b l e of t r i m c o i l r a d i i in re ference 11, we see tha t the spacing v a r i e s roughly as S~R , thus making the o u t s i d e eas ier to f i t by the same f a c t o r SR . Thus f o r constant phase s l i p , we need to weight the f i e l d e r r o r s A B by the f a c t o r R / SR = J~R . Since WT m u l t i -p l i e s the square of the f i e l d e r r o r s in TRIMFIT, we must ensure - 41 -t h a t , f o r constant phase s l i p , WT(i) is p r o p o r t i o n a l to the rad i us i . This phys ica l argument was borne out expe r imen ta l l y in some t e s t cases in tha t W, a measure o f the maximum phase s l i p occur ing dur ing a c c e l e r a t i o n , was minimized w i t h t h i s w e i g h t i n g . The above we igh t ing was thus used th roughout . 4 . 2 . 1 . 2 Weight ing o f main c o i l r e l a t i v e to t r i m c o i l s I t is expected tha t the main c o i l f o r the TRIUMF magnet w i l l probably have an e x c i t a t i o n of 800,000 to 900,000 amp-turns. During the t r imming procedure, the main c o i l e x c i t a t i o n w i l l be ad jus ted at the same t ime tha t the t r i m c o i l s w i l l be powered. TRIMFIT gives the optimum change in the main c o i l e x c i t a t i o n as we l l as the optimum t r i m c o i l cu r ren t s e t t i n g s to reduce the e r r o r s in the magnetic f i e l d t o a minimum. In e a r l y TRIMFIT runs, s o l u t i o n s gave main c o i l e x c i t a t i o n changes o f some 40,000 amp-turns assoc ia ted w i t h t r i m c o i l cu r ren ts o f perhaps 200 amp-turns. I t was f e l t , however, t ha t i t would be b e t t e r to ad jus t the e x c i t a t i o n o f the main c o i l , which a l ready had a la rge power supp ly , by a la rge amount, than to have to supply l a rge r t r i m c o i l c u r r e n t s . An o p t i o n was thus int roduced i n t o TRIMFIT which al lowed one to weight changes in the main c o i l e x c i t a t i o n more heav i l y than the cu r ren ts in the t r i m c o i l s . Since e a r l y runs had shown a r a t i o in these two q u a n t i t i e s of approx imate ly 200, i t was f e l t t ha t t h i s would be a phys ica l value t o use as a we igh t . As a r e s u l t , the p red ic ted change in the main c o i l e x c i t a t i o n rose to s l i g h t l y over 50,000 amp-turns, w i t h a - 42 -corresponding drop in the p red ic ted t r i m c o i l c u r r e n t s . A weight o f 200 was used th roughout . 4.2.1.3 Weight ing f a c t o r K This f a c t o r , as has been ment ioned, was used to prov ide a t r a d e - o f f between the s ize of the c o i l cu r ren ts and the cumu-l a t i v e amount o f phase s l i p . F i g . 22 shows how d i f f e r e n t values of K a f f e c t the c u r r e n t s , phase s l i p , and RMS f i e l d e r r o r s in the case o f 54 t r i m c o i l s r e p a i r i n g an e r r o r f i e l d composed o f a 5 i n . change and a ±1 G / f t g rad ien t e r r o r . Ev iden t l y the value K = 10" 3 is the best one, g i v i n g the minimum cu r ren ts necessary f o r a phase s l i p a l l o w i n g separated t u r n a c c e l e r a t i o n . I t w i l l be noted tha t the main c o i l cu r ren t is e s s e n t i a l l y cons tan t , and tha t the t r i m c o i l cu r ren ts change r e l a t i v e l y s lowly compared to the huge v a r i a t i o n in the phase s l i p W. To study the e f f e c t of K on 36 c o i l s , the f o u r t h ar range-ment in Table 2 was used. F i g . 23 shows the r e s u l t o f d i f f e r e n t K values under these c o n d i t i o n s . I t w i l l be noted tha t a value of K = 10" 3 reduces the phase s l i p to a f i g u r e below the separated t u r n t o l e r a n c e . As w i l l be d iscussed, the phase s l i p can be r e -duced s t i l l f u r t h e r by t a i l o r i n g the arrangement o f powered c o i l s to f i t the p a r t i c u l a r e r r o r f i e l d needing to be r e p a i r e d . This would invo lve measuring the p a r t i c u l a r e r r o r f i e l d , and then powering more c o i l s where the g rad ien t e r r o r s were higher and fewer where they were lower, s t i l l r e t a i n i n g the same t o t a l number o f co i1s . - 43 -o I i ' . i ; . i —_ — i . '.—I o 10" h 1 0 " 3 K 1 0 " 2 10" 1 F i g . 22 E f fec t of va ry ing the weight f a c t o r K us ing 5h t r i m c o i l s to produce a 5 inch change in the 500 MeV radius and repa i r a ±1 g a u s s / f t g rad ien t e r r o r 1 I I : 1 - i — -10" k 10" 3 K T O " 2 10" 1 F i g . 23 E f fec t of va ry ing the weight f a c t o r K using 36 t r i m c o i l s to produce a 5 inch^change in the 500 MeV radius and repa i r a ±il) g a u s s / f t grad ien t e r r o r - 44 -TABLE I I E f fec t i veness of d i f f e r e n t 36 c o i l combinat ions in producing a 5 i n . change and r e p a i r i n g a 1 G/ f t g rad ien t e r r o r RMS Weighted F ie ld W Error (G) 1) S t a r t i n g w i t h f i r s t c o i l , every o ther c o i l is powered u n t i l 18 un~ powered coi1s are accumulated. 0.141 791 2) Same s i t u a t i o n except c o i l #2 is powered and c o i l #38 de-powered. 0.149 790 3) Every t h i r d c o i l is de-powered w i t h the f i r s t two co i1s powered. 0.133 582 4) S t a r t i n g w i t h the f i r s t , every o ther c o i l is powered u n t i l we have 12 powered c o i l s , then 2/3 are powered u n t i l we have the next 12, then every coi1 is powered. 0.100 352 5) Includes every c o i l t ha t has over 50 a . t . in 54 coi1 s o l u t i o n , plus coi1 54. This happens to be 36 c o i l s . 0.078 342 6) As in 4, but coi1s 53 and 54 d e l e t e d , coi1s 2 and 42 added, w i t h c o i l s 3 through 38 replaced by next h igher c o i I s 0.111 335 Main Coi l RMS Trim Max.Trim Current Coi l Coi l Current Current ( real ( rea l ( real a . - t . ) a . - t . ) a . - t . ) 53,300 208.3 868.5 53,540 181.0 462.0 54,200 223.7 584.0 53,280 217.3 868.9 53,560 187.5 455-6 52,480 192.2 436.8 - 45 -4.2.2 Combinations o f 36 powered c o i l s The e f f e c t of d i f f e r e n t combinat ions of 36 o f the o r i g i n a l 54 c o i l s being powered is shown in Table 2. Al though the RMS t r i m c o i l cu r ren t remains c lose to 200 amp- turns, the maximum t r i m c o i l cu r ren t as wel l as the phase s l i p vary g r e a t l y . During the ac tua l commissioning o f the magnet, i t may we l l be advantageous to recom-bine c o i l s in order to t r y f o r a more e f f i c i e n t combina t ion , in the manner ind ica ted in t h i s t a b l e . Powering o f every o ther c o i l appears to be s u f f i c i e n t near the cen t re o f the magnet, whereas every c o i l is needed at the o u t s i d e . The problem is thus to e f f e c t a smooth t r a n s i t i o n between these extremes, i f poss ib le powering more c o i l s where g rad ien t e r r o r s are known to be h igher . 4.2.3 D i f fe rence f i e l d combinat ions The d i f f e r e n c e f i e l d is the d i f f e r e n c e between the des i red isochronous f i e l d and a given measured f i e l d . A d i f f e r e n c e f i e l d w i l l in p r a c t i c e r e s u l t from a des i re to reduce g rad ien t e r r o r s in the average f i e l d t o b r i n g phase s l i p w i t h i n to le rances and from a des i re to change the 500 MeV radius so as to enter a h igher energy mode o f a c c e l e r a t i o n . The t r i m c o i l s must be sized so as to be always capable of accompl ishing both o f these o b j e c t i v e s . The d i f f e r e n c e f i e l d thus always included a 5 i n . f i e l d , t h i s being the d i f f e r e n c e between an isochronous f i e l d w i t h the 500 MeV radius a t 312 i n . and one w i t h the 500 MeV radius at 307 i n . In most cases, a g rad ien t e r r o r o f ±1 G / f t was superposed on t h i s . Since a random e r r o r w i l l be encountered dur ing commissioning, many d i f f e r e n t g rad ien t e r r o r s were s t u d i e d . - 46 -a) R§Qdgm_wal_k_error_f | e H s . S t a r t i n g w i t h t h e inner-most r a d i u s , t h e f i e l d a t each r a d i u s was found by a d d i n g t o the f i e l d a t the p r e v i o u s r a d i u s a number from a normal d i s t r i -b u t i o n so a r r a n g e d t h a t a s t a n d a r d d e v i a t i o n v a l u e would produce a g r a d i e n t o f ±1 G / f t . S e v e r a l d i f f e r e n t f i e l d s were produced, u s i n g d i f f e r e n t i n i t i a l i z a t i o n s o f t h e UBC 360/67 1 i b r a r y r o u t i n e RANDN. b) §iDy so Xda X_er r o r _ f j e ^ d s . F i e l d s w i t h w a v e l e n g t h X = 10, 15, 20, 30, 40 i n . and v a r i o u s phases, a l l h a v i n g a maximum g r a d i e n t o f e x a c t l y 1 G / f t were used. 4.3 T r i m c o i 1 b e h a v i o u r When s t u d y i n g t h e e f f e c t o f 36 and 54 t r i m c o i l s , i t was hoped t o f i n d e f f e c t s common t o a l l o f the e r r o r f i e l d s , e f f e c t s one c o u l d thus w i t h r e a s o n a b l e c e r t a i n t y e x p e c t t o e n c o u n t e r from the e r r o r f i e l d o b t a i n i n g when a c t u a l l y c o m m i s s i o n i n g the magnet. The f o l l o w i n g t r i m c o i l p r o p e r t i e s were i m p o r t a n t i n l e n d i n g c o n f i d e n c e t o the f i n a l c o i l s i z e e n v e l o p e . 4.3-1 R e l a t i o n s h i p o f c u r r e n t s t o f i e l d g r a d i e n t s One o f t h e b a s i c f a c t s t h a t came out o f t h i s i n v e s t i g a t i o n was t h a t the c u r r e n t i n a t r i m c o i l a t some g i v e n r a d i u s i s p r o p o r t i o n a l t o t he g r a d i e n t o f t h e f i e l d e r r o r r e m a i n i n g a t t h a t r a d i u s a f t e r t he main c o i l c u r r e n t has been s e t a t i t s optimum v a l u e . The t o p two graphs o f F i g . 2h i l l u s t r a t e t h i s f o r a pure 5 i n . d i f f e r e n c e f i e l d w i t h 54 c o i l s . L o o k i n g a t t h e bottom graph o f t h i s f i g u r e , one wonders a t f i r s t whether TRIMFIT has not chosen t o o h i g h a main c o i l c u r r e n t and thus o v e r c o r r e c t e d the o r i g i n a l e r r o r . But t h i s "over c o r r e c t i o n " - 47 -in c 3 I E 4 0 0 " 2 5 -0 l . i . l I V I • I . I i I t I i I I I i I • L 1 1 2 0 4 0 6 0 80 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0 2 2 0 2 4 0 2 6 0 2 8 0 3 0 0 3 2 0 Radius ( f u l l - s c a l e inches) F i g . 24 R e l a t i o n s h i p of t r i m c o i l cu r ren ts to the g rad ien t o f the f i e l d e r r o r remaining a f t e r optimum main c o i l e x c i t a t i o n change - 48 -is a consequence of the high g rad ien ts to be cor rec ted at the ou ts ide (as seen in the middle graph o f F i g . 2 4 ) , which cause high c o i l cu r ren ts at the o u t s i d e , a l l o f which are of the same s ign thus p ro-ducing a negat ive average f i e l d c o r r e c t i o n toward the middle o f the machine, one which the main c o i l must compensate f o r , causing an apparent "over c o r r e c t i o n " . 4.3.2 Main c o i l e f f e c t Looking again at the bottom graph o f F i g . 24, which compares the optimum main c o i l c o r r e c t i o n to a pure 5 i n . e r r o r f i e l d , one f i n d s tha t the two curves are q u i t e s i m i l a r . This happy co inc idence i s , in f a c t , the reason f o r the r e l a t i v e l y low t r i m c o i l cu r ren ts t ha t have been ind ica ted by TRIMFIT. Most of the e r r o r f i e l d can be f i t t e d q u i t e we l l using on ly the main c o i l . I t should be noted t h a t t h i s f a c t adds r e l i a b i l i t y to the c o i l cu r ren t envelope. The e f f e c t of the main c o i l , s ince i t was measured on the more accurate 20:1 model and involved no i n t e r p o l a t i o n e r r o r s , could be found q u i t e a c c u r a t e l y . Thus, even though the t r i m c o i l data had s i g n i f i c a n t e r r o r s due to i n t e r p o l a t i o n , the importance and accur -acy o f the main c o i l data assured tha t the t r i m c o i l cu r ren t envelope would be of the r i g h t order o f magnitude. 4.3-3 Noise e f f e c t s F i g . 25 is a composite p i c t u r e o f the cu r ren ts f o r many e r r o r f i e l d s , both random walk a n d ' s i n u s o i d a l , . e a c h superposed onto a 5 i n . f i e l d . A l l 54 c o i l s are powered. F i g . 26 shows the s i t u a t i o n when on ly 36 c o i l s are powered. The c i r c l e d cu r ren ts are in each case those obta ined when on ly a 5 i n . e r r o r f i e l d is f i t t e d . Ev iden t l y the main r e s u l t o f the noise is to spread the cu r ren ts in a band about the pure 5 i n . s o l u t i o n . - ks -4 0 0 -i n c 3 0 0 1_ •3 4-> Q_ E 2 0 0 <TJ (0 <U s_- 1 0 0 i n -w -c 0 cu i_ 1_ o — - 1 0 0 o o E - — _ 2 0 0 t-11 2 0 4 0 F i g . 25 0 I 6 0 . 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0 2 2 0 Radius ( f u l l - s c a l e inches) 2 4 0 2 6 0 2 8 0 3 0 0 3 2 0 Composite p i c t u r e o f the range of cu r ren ts in 54 t r i m Coils needed to produce a 5 inch change in the 500 MeV radius as wel l as repa i r var ious 1 g a u s s / f t g rad ien t e r r o r s c !_ 3 4J I D, E TO m •L. c CO 3 4 0 0 -3 0 0 2 0 0 1 0 0 o - 1 0 0 o E . 2 0 0 2 0 2 6 i 2 4 0 2 6 0 2 8 0 3 0 0 3 2 0 4 0 6 0 8 0 1 0 0 1 2 0 ; 1 4 0 1 6 0 . 1 8 0 2 0 0 2 2 0 Radius-.( ful 1-'scale inches) F i g . 26 Composite p i c t u r e o f the range o f cu r ren ts in 36 (tr|im coi 1 s needed to produce a 5 inch change in the 500 MeV radius as we l l as repa i r var ious 1 g a u s s / f t g rad ien t e r r o r s - 50 -With the advantage o f h i n d - s i g h t , one can see tha t t h i s is to be expected. In t roduc ing no i se , whatever the t y p e , has produced a constant spread in the e r r o r f i e l d g rad ien t o f ±1 G / f t . Since c o i l cu r ren ts are p r o p o r t i o n a l to the g rad ien ts to be c o r r e c t e d , i t would be s u r p r i s i n g not to see t h i s band develop in the c u r r e n t s . 4.3-4 E f f e c t of depowering c o i l s Comparing F i g . 25, w i t h 54 c o i l s , and F i g . 26, w i t h 36 c o i l s , i t is ev ident t ha t the cu r ren t magnitudes are very s i m i l a r . Refer-ence 11, which g ives graphs of the e f f e c t of t r i m c o i l s on the average f i e l d , i nd ica tes tha t a t r i m c o i l has i t s g rea tes t e f f e c t in i t s immediate v i c i n i t y . The s i m i l a r i t y o f the cu r ren t envelopes would thus appear to be a consequence o f t h i s , in tha t s ince a c o i l a f f e c t s predominant ly i t s own r a d i u s , i t cannot take over the f u n c t i o n o f i t s neighbour w i thou t complete ly des t roy ing the s o l u t i o n at i t s own r a d i u s . 4.h Conclus ions The f i n a l t r i m c o i l cu r ren t envelope should s ize the c o i l s so t ha t they are able to change the 500 MeV radius by 5 i n . , a t the same t ime c o r -r e c t i n g a g rad ien t e r r o r of ±2 G / f t . Since the experiments ind ica ted tha t a g rad ien t e r r o r o f ±1 G / f t , o f whatever fo rm, on ly in t roduced a band spread in the c u r r e n t s , the t r a n s i t i o n to a c a p a b i l i t y of c o r r e c t i n g ±2 G / f t g rad ien t e r r o r s was made by adding another noise band to the c o i l envelope a l ready determined. This c o i l envelope, as we l l as the t h e o r e t i -cal envelope p red ic ted in the o r i g i n a l s p e c i f i c a t i o n 1 5 , is shown in F i g . 27. Since depowering c o i l s does not s i g n i f i c a n t l y a f f e c t the c u r r e n t s , t h i s envelope should be adequate whether 54 or 36 t r i m c o i l s are used in t r imming to phase s l i p t o l e r a n c e s . 3 0 0 -/ 6 0 0 h . / I 5 0 0 |- / pred ict ion j / / • •^» • • / • • • • j i _ 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0 2 2 0 2 4 0 2 6 0 2 8 0 3 0 0 3 2 0 Radius (full-scale inches) Fig. 27 Trim coil current capacity envelope predicted by TRIMFIT compared to the theoretical prediction - 52 -When commissioning the magnet, 36 t r i m c o i l s w i l l be s u f f i c i e n t to reduce g r a d i e n t e r r o r s o f ±2 G / f t so as to b r ing the phase s l i p w i t h i n i n i t i a l t o l e r a n c e s . This study has i n d i c a t e d , however, tha t i f f u r t h e r shimming is done to reduce g rad ien t e r r o r s to ±1 G / f t , 36 t r i m c o i l s w i l l probably remain s u f f i c i e n t to reduce the phase s l i p to separated t u r n t o l e r a n c e s . - 53 -REFERENCES 1. M.K. Craddock and J . Reginald Richardson, p r i v a t e communication (1969) 2. W. Joho, Tolerances f o r the SIN R ing -Cyc lo t ron , SIN-TM-11-4 (1968) 3. M.K. Craddock, p r i v a t e communication (1970) 4. M.K. Craddock and J . Reginald Richardson, p r i v a t e communication (1968) 5. E.G. A u l d , p r i v a t e communication (1969) 6. W. Walkinshaw and N.M. K ing, L inear Dynamics in Sp i ra l Ridge Cyc lo t ron Design, AERE GP/R 2050 (1956) 7. K.R. Symen, D.W. Kers t , L.W. Jones, L . J . L a s l e t t and K.M. T e r w i l l i g e r , Fixed F i e l d A l t e r n a t i n g Gradient P a r t i c l e A c c e l e r a t o r s , Phys. Rev. 103, 1837 (1956) 8. J .R. Richardson, p r i v a t e communication (1970) 9- J . Reginald Richardson and M.K. Craddock, p r i v a t e communication (1969) 10. E.G. Au ld , S. Oraas, A . J . O t t e r , G.H. Mackenzie, J . Reginald Richardson and J . J . Burger jon , p r i v a t e communication (1969) 11. J . R ivers-More, p r i v a t e communication (1970) 12. Siemens, Semi-Conductor Manual, 1968-69 13- M.J. L i n t o n , p r i v a t e communication (1970) 14. S. Oraas, p r i v a t e communication (1970) 15- A . J . O t t e r , p r i v a t e communication (1969) - 54 -APPENDIX A. USER'S GUIDE TO SHIMPOLE A. 1 I n t r o d u c t ion SHIMPOLE is a program designed to minimize the d i f f e r e n c e s between the measured average f i e l d and the isochronous average f i e l d and between the ideal V 4 versus R curve and the actua l V4 versus R curve by p r e d i c t i n g app rop r ia te changes in the pole shim th i cknesses . The g r i d s A B(l ,J) and A ^ ( l . j ) , the changes in the average f i e l d and the v e r t i c a l focus ing at the l t n radius due to the J t n shim, are the input to the program. These g r i d s compile the changes due to a u n i t t h i c k -ness o f shim change at every shim p o s i t i o n . V i t a l to the working o f SHIMPOLE are the f a c t s t ha t the ampl i tude o f the changes in both the average f i e l d and the focus ing are d i r e c t l y p r o p o r t i o n a l t o the s i ze of the shim change and tha t the changes due to two adjacent shims are the sum of the changes due to each shim placed s e p a r a t e l y . These f a c t s a 11ow SHIMPOLE to mix app rop r ia te ampl i tudes of the changes at each shim p o s i t i o n , found in a leas t squares sense, in order to a r r i v e at the best combinat ion . This best combinat ion is in f luenced by three bas ic we igh t ing f a c t o r s : WTN, WTB, and CUWAIT. Increas ing WTN b e t t e r s the focus ing f i t a t the expense o f the average f i e l d , inc reas ing WTB b e t t e r s the average f i e l d at the expense o f the f o c u s i n g , whereas increas ing CUWAIT decreases the average s ize o f the p red ic ted shim changes. In using SHIMPOLE, the r e l a t i v e values o f WTN and WTB were f i r s t ad jus ted so as to p r e d i c t improvements in the average f i e l d o f approx imate ly 50%. The p red ic ted changes in the focus-ing were then checked and i f improvement was s t i l l s u b s t a n t i a l , WTB was increased f u r t h e r . When a s a t i s f a c t o r y balance between p red ic ted average f i e l d and focus ing c o r r e c t i o n s had been found by a d j u s t i n g WTB and WTN, the f a c t o r CUWAIT was ad justed so as to g ive the des i red magnitude of shim - 55 -changes. Perhaps 0.5 f u l l - s c a l e inches o f change should be considered a maximum at the ou ts ide of the magnet, inc reas ing to an inch elsewhere. The f i n a l s o l u t i o n is approached by an i t e r a t i v e procedure, w i t h each i t e r a t i o n performed according, to the above procedure. Typica l values o f the we igh t ing f a c t o r s might be 10-3, 10"2, and 1. f o r WTB, WTN, and CUWAIT r e s p e c t i v e l y . A.2 Use o f SHIMPOLE With ease of comprehension in v iew, SHIMPOLE has been made as s i m i l a r as poss ib le to TRIMFIT 1 1 , a program which p r e d i c t s the optimum e x c i t a t i o n leve ls f o r the t r i m c o i l s . When p o s s i b l e , s i m i l a r v a r i a b l e s have been given the same name. A . 2 . 1 Input to SHIMPOLE SHIMPOLE reads data from two f i l e s l a b e l l e d 5 and 7- The f i l e referenced by 5 should con ta in the f o l l o w i n g cards or records , a) JR, L l , LO, RMIN, RMAX, DR, WTB, WTN, LIM, ITER, MATRIX, KPRINT, CUWAIT - (313, 2F6.1, Fk . 1 , 2 F 1 5 - 1 0 , 4 I5/F15-10) where JR = number of radius values in the ar rays NUZSQD(l), DNUZSQ_(l,J) and so on . Ll = number o f shims on the " i n s i d e " or concave s ide o f the pole p iece . LO = number of shims on the " o u t s i d e " or convex s ide o f the pole p i ece. RMIN radius range over which the f i t is made. I f RMIN and RMAX =are not a c t u a l l y one o f the JR radius va lues , then TRIMFIT RMAX conver ts them to the nearest o f these v a l u e s . DR = radius increment. The f i r s t of the JR radius values in the ar rays must be at rad ius DR. - 56 -WTB = the we igh t ing f a c t o r f o r the average f i e l d . The g rea te r the va lue o f WTB, the more SHIMPOLE w i l l tend to c o r r e c t the aver -age f i e l d e r r o r s at the expense of focus ing e r r o r s . WTB is i d e n t i c a l to the v a r i a b l e K in sec t ion 3-1. I f WTB ^ 0, SHIMPOLE becomes a program which deals w i t h focus ing o n l y , in tha t average f i e l d d a t a , as descr ibed l a t e r , is not even read i n. WTN = the we igh t ing f a c t o r f o r the f o c u s i n g , and is i d e n t i c a l to the v a r i a b l e G in sec t ion 3-1. Aga in , i f WTN != 0, SHIMPOLE deals on ly w i t h average f i e l d e r r o r s , and does not even read in focus ing d a t a . LIM = maximum number o f i t e r a t i o n s permi t ted in l i m i t i n g shim changes to the range (NMIN, .NMAX). NMIN and NMAX are def ined 1ater. ITER = accomplishes the same f u n c t i o n as LIM, but a l lows one to l i m i t i t e r a t i o n s by s p e c i f y i n g the maximum amount o f computing t ime to be used ra the r than the maximum number o f i t e r a t i o n s . ITER takes e f f e c t i f i t is more than kO t imes la rge r than the va lue of LIM. SHIMPOLE then terminates i t e r a t i o n s as soon as the cumulat ive computer t ime used by the end o f the l a s t i t e r a -t i o n is w i t h i n 30 sec o f the value of ITER. MATRIX = 1 i f i t is des i red to p r i n t a sample o f the m a t r i x A ( I , J ) every c y c l e . This m a t r i x is def ined such tha t 2 .A ( I , J ) • N ( J ) = D ( l ) , where N( j ) is the J t n shim change. = 0 i f no t . KPRINT = p r i n t op t i on f o r p r i n t o u t from the f i r s t i t e r a t i o n (see next s e c t i o n ) . Normally one sets KPRINT=0. - 57 -CUWAIT = the we igh t ing f a c t o r which reduces the shim changes, equ iv -a l e n t to the f a c t o r M in sec t ion 3 . 1 . For SHIMPOLE i t is important t o set CUWAIT high enough to keep the p red ic ted shim changes s m a l l , ad jus t the g r i ds f o r r a d i a l s h i f t , and then repeat , thus approaching a s o l u t i o n in an i t e r a t i v e manner. Thus CUWAIT is important in avo id ing n o n - l i n e a r i t i e s . b) I f WTN > 0, a se r ies of JR cards or records f o l l o w , the J t n o f which conta ins NUZSQD(j), NUZSQA(J), E(J) -• (3F10.5) where NUZSQD(J) is the des i red value o f V^7" a t radius J , NUZSQA(J) is the present va lue of \)^~ at t h i s radius and E(J) is the loca l we igh t ing f a c t o r f o r the d i f f e r e n c e between the two. c) I f WTB > 0, JR cards or records f o l l o w , the J t n o f which conta ins t h i s t ime BAVD(j), BAVA(j) , C ( j ) - (3F10.5) where BAVD(J) is the des i red average f i e l d at radius J , BAVA(J) is the actua l or present average f i e l d and C(J) is again the local we igh t ing f a c t o r f o r the d i f f e r e n c e . d) F i n a l l y i f LIM > 0 or ITER > 40, a sequence of LI+LO cards or records f o l l o w s , w i t h the J t n con ta in ing NMIN(J) , NMAX(J) - (2F10.5) where NMIN is the maximum a l lowab le d e l e t i o n and NMAX the maximum a d d i t i o n of shim metal at the J t n shim pos i t i on . The f i l e referenced by 7 should con ta in the f o l l o w i n g cards or records . a) I f WTN > 0, then [(LI+LO) x JR +7]/8 cards or records should appear, c o n t a i n i n g DNUZSQ(I,J), the change in at the l t n - 58 -radius due to a u n i t change o f metal a t the J t n shim p o s i t i o n , read in as {[DNUZSQO , J ) , 1=1, JR] , J=l , LI+LO} - (8F10.5) b) I f WTB > 0, then the same number o f cards or records f o l l o w , con-t a i n i n g DBAV( | ,J ) , the change in B a t the I t h rad ius due to a u n i t change o f metal a t the J shim p o s i t i o n , read in using the same fo rmat . I t should be noted tha t as SHIMPOLE is set up now, a u n i t change o f metal is i n t e r p r e t e d as 2 i n . on the f u l l s i ze magnet. A.2.2 Output from SHIMPOLE The output to u n i t 6 from SHIMPOLE is handled by subrou t ine PRINT, which is c o n t r o l l e d by the v a r i a b l e s KPRINT and MATRIX. The va lue o f KPRINT is supp l ied by SHIMPOLE every t ime t h a t PRINT is c a l l e d , except f o r the l a s t c a l l to PRINT, when the va lue of KPRINT is set to be the same as the va lue o f the v a r i a b l e o f the same name inpu t ted on u n i t 5- A l l column graphs are done by the subrou t ine ERROR, which is c a l l e d by PRINT when needed. a) KPRINT = 1. I f WTB > 0, then a t a b l e is g iven o f the r a d i i and E, the weight at each r a d i u s , w i t h adjacent tab les and column graphs o f the o r i g i n a l f i e l d e r r o r to be c o r r e c t e d , the f i n a l f i e l d e r r o r , and the weighted f i n a l f i e l d e r r o r l e f t a f t e r optimum c o r r e c t i o n . I f WTN > 0 , s i m i l a r tab les are given of the r a d i i and the loca l focus ing weight C, t h i s t ime w i t h adjacent tab les and column graphs of the o r i g i n a l focus ing e r r o r to be c o r r e c t e d , the f i n a l focus ing e r r o r , and the weighted f i n a l focus ing e r r o r l e f t a f t e r optimum c o r r e c t i o n . b) KPRINT = 0. I f LIM > 0 or ITER > kO, the above output is preceded by a t a b l e o f NMIN(J) and NMAX(J) f o r both the concave and the con-vex sides o f the pole p iece . When LIM — 0 or ITER — hO, the output f o r KPRINT = 1 is reproduced e x a c t l y by KPRINT = 0. - 5 9 " c) KPRINT = 2. This p r i n t s the r e p e t i t i o n or cyc le number (IFLAG), the average f i e l d we igh t ing f a c t o r (WTB), the focus ing we igh t ing f a c t o r (WTN), and the determinant and c o n d i t i o n number o f the m a t r i x A. The p red ic ted shim changes f o r shim p o s i t i o n s on the ou ts ide o f the pole piece are then l i s t e d in separate t a b l e s . I t should again be noted tha t a shim change o f u n i t y , f o r example, impl ies the a d d i t i o n o f two f u l 1 - s e a 1e inches of shims to whatever c o n f i g u r a t i o n is at the p a r t i c u l a r shim p o s i t i o n . S i m i l a r l y , negat ive numbers imply d e l e t i o n o f shims. I f MAT >^ 0, a sample (every 5^ row and column) o f m a t r i x A and vec to r D is p r i n t e d . The vec to r D is the r i g h t s ide of the m a t r i x equa t ion . During the f i r s t i t e r a t i o n on ly (IFLAG=1), a complete t a b l e of the r i g h t s ide o f the m a t r i x e q u a t i o n , the l e f t s i d e , and the d i f f e r e n c e is p r i n t e d (D, D3, D4) . Since the l e f t s ide o f the m a t r i x e q u a t i o n , to be quoted as a numerical r e s u l t , must con ta in numerical cu r ren t va lues , i t s accuracy is d i r e c t l y l i nked to the accuracy of the m a t r i x i nve rs ion involved in f i n d i n g the shim changes N. Thus a zero d i f f e r e n c e between l e f t and r i g h t s ides impl ies p e r f e c t m a t r i x i n v e r s i o n . As the program stands at p resen t , i t is set i n t e r n -a l l y to produce the output KPRINT=2 at every c y c l e . The input parameter KPRINT (not the subrou t ine dummy v a r i a b l e KPRINT) d e t e r -mines the a d d i t i o n a l output to be produced on the l a s t c y c l e . That i s , on the l a s t cyc le TRIMFIT c a l l s PRINT t w i c e , the f i r s t t ime i t s e l f s e t t i n g KPRINT=2, the l a s t t ime s e t t i n g KPRINT=KPRI NT (these v a r i a b l e s being the subrout ine dummy v a r i a b l e and the input - 60 ~ parameter r e s p e c t i v e l y ) . U s u a l l y , one sets the input KPFUNT=0, thus g i v i n g an ana lys i s of the e r r o r s a f t e r the f i n a l i t e r a t i o n . On u n i t 2, TRIMFIT outputs a rev ised t a b l e of NMIN and NMAX tha t takes i n t o account the p red ic ted shim changes. That i s , a f t e r the changes p red ic ted by.SHIMPOLE have been made, the new l i m i t s on shim changes w i l l be j u s t those g iven on u n i t 2. S to r ing t h i s output on a f i l e e l im ina tes the hand computat ion t h a t would o therw ise be necessary before doing a f u r t h e r i t e r a t i o n . I f t h i s i n fo rmat ion is not d e s i r e d , the statement 2=*DUMMY* on the run c a r d , w i l l cancel i t . - 61 -APPENDIX B. USER'S GUIDE TO TRIMFIT B.1 In t roduc t ion TRIMFIT was o r i g i n a l l y w r i t t e n by Mr. Jon Rivers-More, who repor ted on the design and use o f h is program in the note " T r i m f i t - Least Squares F i t t i n g Program f o r Trim C o i l s " . 1 1 Since then TRIMFIT has been q u i t e e x t e n -s i v e l y mod i f ied and expanded as f a r as output format and a v a i l a b l e op t ions are concerned. The format o f t h i s appendix is the same as tha t of the p o r t i o n of the above note t ha t i t is to rep lace . I t is hoped tha t t h i s w i l l add c l a r i t y f o r those who have a l ready s tud ied the prev ious r e p o r t . B . l . l Input to TRIMFIT TRIMFIT reads data from two f i l e s l a b e l l e d 5 and 7. The f i l e referenced by 5 should con ta in the f o l l o w i n g cards or records , a) JR., NT, RMIN, RMAX, DR, CUWAIT, LIM, MATRIX, KPRINT, MCFREE, TRDIVR, MNDIVR, SCALE, RELWT, LGPLOT, ITER, NPARLL - (215, 4F10.5, 4I5/4F10.5, 315) where jR = number of radius values in the ar rays B l ( l ) , BE(1)> W T ( | ) , B T R ( I , J ) . NT = number o f t r i m c o i l s RMIN radius range over which the f i t is made. I f these are not = ac tua l data po in ts then TRIMFIT conver ts them to the nearest RMAxJ data p o i n t s . DR = radius increment. CUWAIT = c u r r e n t we igh t ing (equ iva len t to the f a c t o r K in the o r i g i n a l equat ion) . LIM = maximum number of i t e r a t i o n s permi t ted in l i m i t i n g cu r ren ts - 62 -to the range (CM IN, CMAX). = 0 i f no l i m i t s are. d e s i r e d . MATRIX = 1 i f des i red to p r i n t a sample o f the m a t r i x A ( I , J ) every c y c l e . This m a t r i x is de f ined such tha t ^ A(N,J ) -C(J ) = D(N), where C(J) is the J t n t r i m c o i l c u r r e n t . = 0 i f no t . KPRINT = p r i n t op t i on f o r p r i n t o u t from f i r s t i t e r a t i o n (see next s e c t i o n ) . Normally one sets KPRINT = 0. TRDIVR = actua l number of c o i l s used when measuring the t r i m c o i l BTR at a c e r t a i n r a d i u s . This is u s u a l l y 2, t ha t i s , one on the top and one on the bottom pole o f the magnet. MNDIVR = actua l number o f main e x c i t a t i o n c o i l s in the model f o r which the main c o i l BTR was measured. This was 12 on the 20:1 model. SCALE = the sca le of the model. This would be 20 f o r the 20:1 model. TRDIVR, MNDIVR, and SCALE are used to conver t the cu r ren t to u n i t s o f real amp- turns. RELWT = the ac tua l f a c t o r by which the main co i1 is weighted over the t r i m c o i l s . Un l i ke CUWAIT ( K - f a c t o r ) , which m u l t i p l i e s the square o f the c u r r e n t s , RELWT is converted to a square in the program, so tha t in e f f e c t i t m u l t i p l i e s the f i r s t power o f the c u r r e n t s . LGPL0T = 1 w i l l l i s t the cu r ren ts on a log s c a l e , so tha t none appear o f f sca le . ^ 1 w i l l l i s t cu r ren ts on a l i n e a r sca le . In both cases a " + " represents p o s i t i v e and a " - " negat ive c u r r e n t s . ITER y 0 w i l l s teer the program i n t o an exper imental sec t i on tha t performs ITER i t e r a t i o n s in order to approximate a Chebyshev mini-max f i t . This sec t i on is s t i l l being worked on. - 63 -— 0 would normal ly be chosen to bypass t h i s s e c t i o n . NPARLL !> 0 a l lows c o i l s to be l inked in complete ly a r b i t r a r y groups, so tha t TRIMFIT w i l l f i n d the best s o l u t i o n w i t h the r e s t r i c -t i o n t ha t a l l c o i l s in a group have the same c u r r e n t . The magnitude o f NPARLL should be the des i red number o f groups o f 1i nked co i1s. b) I f NPARLL !> 0, then a sequence of NPARLL cards or records f o l l o w s , the J t n o f which c o n t a i n s : MCOIL(J), NCOIL(J) - (1215) where MCOIL is the number of the f i r s t c o i l in the J t n group and NCOIL is the number of the l a s t c o i l in t h i s group. c) A sequence of JR cards or records f o l l o w s , the J t n o f which c o n t a i n s : B I ( J ) , BE(J) , WT(J) - (3F10.5) where Bl is the des i red average f i e l d at radius J and BE is the ac tua l uncorrected average f i e l d a t t h i s r a d i u s . d) F i n a l l y , i f LIM ^ 0, a sequence of NT cards or records f o l l o w s , w i t h the J t n c o n t a i n i n g : CMIN(J), CMAX(J) - (2F10.5) where CM IN is the minimum and CMAX the maximum a l lowab le c u r r e n t , o f e i t h e r s i g n , a t radius J . The f i l e referenced by 7 should con ta in the f o l l o w i n g cards or records . a) [(NTxJR) +7]/8 cards or records , c o n t a i n i n g BTR(I ,J) read as { [ B T R ( | , J ) , 1=1, JR ] , J = l , NT} - (8F10.5) b) I f McFREE = 1, the main c o i l BTR, the change in the average f i e l d at each radius due t o an increase in the main power supply cu r ren t - 6h -of 1 A, should be added, beginning w i t h a new r e c o r d , a t the end of the t r i m c o i l BTR. This is a sequence of (JR+7)/8 cards or records in format (8F10.5)-.2 Output - subrout ine p r i n t (K,MATRIX) K=l P r i n t s a t a b l e of the rad ius and the weight at tha t r a d i u s ; w i t h adjacent tab les and column graphs of the o r i g i n a l f i e l d e r r o r to be c o r r e c t e d , the f i n a l f i e l d e r r o r , and the weighted f i n a l f i e l d e r r o r l e f t a f t e r optimum c o r r e c t i o n . Then a s i m i l a r phase s l i p a n a l y s i s t a b l e is p r i n t e d o f the radius and i t s we igh t ; again w i t h adjacent tab les and column graphs, t h i s t ime o f the number o f e r r o r f i e l d bumps occur ing before the present r a d i u s , the magnitude and sense of the phase s l i p caused by each bump, and the va lue o f P (a measure of accumulated phase s l i p ) a t the present r a d i u s . K=0 I f LIM y 0, t h i s precedes the above output w i t h a t a b l e o f CMIN(J) and CMAX(j) f o r each t r i m c o i l J . I f LIM = 0, the output in (a) is reproduced e x a c t l y . K=2 P r i n t s the r e p e t i t i o n or cyc le number ( lFLAG), CUWAIT, and the determinant and c o n d i t i o n number o f the m a t r i x A. I f MAT = 1, a sample (every 5 t n row and column) of m a t r i x A and vec to r D is p r i n t e d . The vec to r D is the r i g h t s ide o f the matr ix equat i on . During the f i r s t i t e r a t i o n on ly ( lFLAG=l) , a complete t a b l e of the r i g h t s ide of the m a t r i x e q u a t i o n , the l e f t s i d e , and the d i f f e r e n c e is p r i n t e d (D, D2, D3). Since the l e f t s ide o f the m a t r i x e q u a t i o n , to be quoted as a numerical r e s u l t , must con ta in - 65 -numerical cu r ren t v a l u e s , i t s accuracy is d i r e c t l y l i nked to the accuracy o f the m a t r i x i nve rs ion involved i n - f i n d i n g the c u r r e n t s . Thus a zero d i f f e r e n c e between l e f t and r i g h t s ides impl ies pe r fec t m a t r i x i n v e r s i o n . Then, depending on whether LGPLOT = 1, e i t h e r a log scale or l i n e a r scale p l o t of the cu r ren ts is g i v e n , w i t h the main c o i l cu r ren t l i s t e d at the bottom of the p l o t . As the program stands at p resen t , i t is set i n t e r n a l l y to produce the output K=2 a t every c y c l e . The input parameter KPRINT determines the a d d i t i o n a l output to be produced on the l a s t c y c l e . That i s , on the l a s t cyc le TRIMFIT c a l l s PRINT t w i c e , the f i r s t t ime i t s e l f s e t t i n g K=2, the l a s t t ime s e t t i n g K=KPRI NT. Usual ly we set KPRINT=0, thus g i v i n g an a n a l y s i s o f the e r r o r s a f t e r the f i n a l i t e r a t i o n . - 66 -APPENDIX C. GUIDE TO THE GRID INTERPOLATION ROUTINE C.1 I n t roduc t ion The changes due to the a d d i t i o n and d e l e t i o n o f shims were measured at f i v e shim p o s i t i o n s on both the concave and the convex s ide of the pole p iece . In order to run SHIMPOLE, however, the changes at a l l o f the shim p o s i t i o n s were necessary. To prov ide t h i s d a t a , a l i n e a r i n t e r p o l a t i o n p r o -gram was designed which would i n t e r p o l a t e al1 o f the in te rmed ia te data between any two shim p o s i t i o n s . Thus, by running t h i s program e i g h t t imes , four t imes f o r each s ide o f the pole p iece , the e n t i r e g r i d could be c a l c u l a t e d . The r a d i i , in model inches, o f the centres of the shim p o s i t i o n s were measured w i t h i n an accuracy o f ±0.1 i n . On the concave s ide of the pole p iece , the cent res occurred at the fol1owi ng rad i i : 4.8 6.8 8.8 10.8 12.8 14.8 16.8 18.7 20.6 22.35 24.0 25.3 26.45 27.50 28.45 29-3 30.1 30.85 31.3 31.55 31.7 On the convex s ide o f the pole p iece , the cent res occurred at the f o l l o w i n g rad i i : 5.8 7.8 9.8 11.8 13.8 15.8 17.8 19.8 21.7 23.5 25.1 26.75 28.05 29.0 29.8 30.65 31 .5 32.4 33-35 C.1.1 Input Data f o r the i n t e r p o l a t i o n r o u t i n e was read from two f i l e s , l a b e l l e d 4 and 6. The f i l e referenced by 4 should con ta in the f o l l o w -ing cards or records . - 67 -a) A sequence o f 8 cards or records con ta in ing the vec to r A ( l ) -(8F10.5) where A ( l ) is the f i r s t o f the two vec to rs between which one wishes to i n t e r p o l a t e . Each of the 6k components o f A rep re -sent the change in e i t h e r the average f i e l d or the v e r t i c a l f o c u s i n g , a t one o f the 5 i n . radius increments from 5 i n . to 320 i n . , due to a two i n . shim added t o some p a r t i c u l a r shim pos i t i on. b) A sequence of 8 cards or records c o n t a i n i n g the vec to r B ( l ) -(8F10.5) where B ( l ) is the second of the two vec to rs between which i n t e r p o l a t i o n is d e s i r e d , and represents the changes due to a shim at a la rge r shim p o s i t i o n . The f i l e referenced by 6 should con ta in the f o l l o w i n g cards or records , a) I I , J J , N I , N2, NUM, S - (211, 213, 12, F10.5) where I I =1 means tha t the g r i d A w i l l appear in the output and ^ 1 causes i t not to appear. JJ = number o f g r i ds to be produced by i n t e r p o l a t i o n . This does not inc lude the o r i g i n a l two g r i d s . NI = f i r s t r a d i u s , in f u l l scale inches, f o r which the vec to r A has a non van ish ing component. The program conver ts the NI tha t i t is given i n t o the l a r g e s t m u l t i p l e of f i v e not g rea te r than N I . N2 = f i r s t r a d i u s , in f u l l scale inches f o r which the vec to r B has an equ iva len t non van ish ing component. Again N2 is converted i n t o a m u l t i p l e o f f i v e . NUM = the number o f vec to r components tha t are to be produced by i n t e r p o l a t i o n . This would be set equal t o the number o f non-vanish ing components in A, or in B. Care must be taken - 63 -that neither Nl + NUM or N2 + NUM exceed 64, the total number of vector components. S = the radial separation, in full-scale inches, of the two shim positions that are responsible for producing the vctors A and B. b) A sequence of cards then follows which contains the JJ components of the vector D - (8F10.5) where D(l) is the radial distance of the shim position responsible for the l t n interpolated vector from the shim position responsible for the vector A. The f i r s t interpolated vector should be the one closest to the vector A. C.1.2 Output The output is printed on unit 6 and contains the following cards or records. a) If II = 1, then the vector A is printed in format (8F10.5). If the original and the interpolated grids are being progressively copied onto a f i l e in order to produce a grid complete for a l l shim positions, the vector A should only be copied during the f i r s t interpolation. This is to avoid duplication, as the vector B during the f i r s t interpolation becomes the vector A during the second. b) The JJ interpolated vectors appear in format (8F10.5) followed by the vector B in the same format. - 69 -APPENDIX D. LISTINGS OF COMPUTER PROGRAMS USED D.1 L i s t i n g o f SHIMPOLE and input data The computer program SHIMPOLE was designed to be an a id in the f u t u r e commissioning o f the TRIUMF magnet. Given c e r t a i n measured e r r o r s in the average f i e l d and in the focus ing as a f u n c t i o n o f r a d i u s , SHIMPOLE p r e d i c t s the shim changes, on both sides o f the pole p iece , t h a t w i l l best r epa i r these e r r o r s . The computer f i l e s t ha t were used in running SHIMPOLE are given in t h i s s e c t i o n . a) T(],3kS) conta ins the actua l code f o r SHIMPOLE. The l i s t i n g o f t h i s code is preceded by a f l o w c h a r t of the l o g i c used in the code. b) J conta ins a l i s t i n g o f the l i n e a r g r i d i n t e r p o l a t i o n program descr ibed in Appendix C. This program was used to f i n d the com-p l e t e average f i e l d change and focus ing change g r i d s from the exper imental d a t a . c) N conta ins the complete focus ing change g r i d as found by i n t e r -p o l a t i o n . The changes f o r the 21 shim p o s i t i o n s on the concave s ide o f the pole piece are fo l lowed by the changes f o r the 17 shim p o s i t i o n s on the convex s i d e . d) B, in a s i m i l a r manner to the g r i d N, conta ins the complete average f i e l d change g r i d as found by i n t e r p o l a t i o n . e) X conta ins most of the input t h a t is read in on SHIMPOLE u n i t 5. The f i r s t 64 l i n e s con ta in the des i red v e r t i c a l f o c u s i n g , the actua l v e r t i c a l f o c u s i n g , and the loca l weight f o r each o f the 64 r a d i i from 5 i n . to 320 i n . in 5 i n . increments. The next 64 l i n e s con ta in the same in fo rmat ion f o r the average f i e l d . The res t o f the f i l e conta ins a p a r t i c u l a r set of l i m i t s on the shim changes, the f i r s t 21 l i n e s c o n t a i n i n g the maximum d e l e t i o n and - 70 " addition at each of the positions on the concave, and the next 17 on the convex side of the pole piece. A typical SHIMPOLE run is then given. This run made use of the option allowing one to iteratively limit the shim changes. The output for the f i r s t and the last iterations only is given, that for the intervening five being deleted. The final part of the output predicts the improvement in the average field and in the focusing as a result of making the predicted shim changes. - 71 -READ 5, JR, L I , LO, RMIN, RMAX, DR, WTB, WTN, LIM, ITER, MATRIX, KPRINT, CUWAIT L = LI + LO NC = L S = SCLOCK(0.) <gTN = 0 > N ° READ 7, DNUZSQ(1^JR, l-H.) YES DNUZSQ(1+JR, l-H.) = 1 . NO READ 7, DBAV(1+JR, 1-H_) YES DBAV(1-*JR, l-H.) = 1 NO READ 5, NUZSQD(1-»JR) , NUZSQA(1+JR), E(l->JR) NUZSQD(KJR) = 1 NUZSQ_A(1+JR) = 1 E(I-KJR) = 1 . NO READ 5, BAVD(1+JR), BAVA(l+JR), C(KJR) BAVD(1->JR) = 1. BAVA(1->JR) = 1 . C(1+JR) = 1. NRMAX = MIN(JR, RMAX/DR) NRMIN = RMIN/DR LIM < 0 / AND > — READ 5, NMI N (1-»NC) , NMAX(l^NC) ITER < 0 ' YES - 72 J - 1 M = J I (J) = J I NRMAX A(J,M) = S WTB-C(i)-DBAV(i,M)-DBAV(i,J) + WTN•E(i)•DNUZSQ(i,M)•DNUZSQ_(i,J) i=NRMIN A(M,J) = A(J,M) M = M+l YES <M < NC A(J ,J ) = A (J , J ) + CUWAIT J = J+l NOTE - The v a r i a b l e I appears in the cod i ng as I I . DI( IR) = WTB-C(IR).[BAVD(|R)-BAVA(|R)] D2(IR) = WTN.E(|R)'[NUZSQD(|R)-NUZSQA(|R)] IR = IR+1 YES MR <_ NRMAX> NO I FLAG = 1 J = N [ I ( J ) ] = 0. NRMAX D(J) = I ( D l ( i ) DBAV[i , I (J)] + D2( i ) DNUZSQ[ i , I (J) ] } i =NRMIN J = J+l - 73 -J = 1 M = 1 AINV(J.M) = A(J,M) M = M+l CALL DINVRT (AINV,NC,100,DET,COND) WRITE MATRIX DET IS ZERO NO J = 1 NC N[l ( J ) ] = E A I N V ( J , i ) - D ( i ) i = I J = J+l YES CALL PRINT(2,MATRIX) KILL = 0 CM = 0 NEXT = NC-1 J = 1 5 - Ik -CD = NMIN[I ( J ) ] - N [ l ( J ) ] CM = 0 J = 1 CD = N [ | ( J ) ] - N M A X [ l ( J ) ] ^ — < £ b > CM> CM = CD K I L L = J J = J + 1 • I K I L L = I ( K I L L ) KK = 4 0 - L I M WRITE THAT ITERATION T I M E L I M I T EXCEEDED WITH SHIM I K I L L S T I L L OUTSIDE L I M I T S ~ 5 ~ 75 N(IKILL) = NMAX(IKILL) WRITE 6, IKILL, NMAX(IKlLL) IR = NRMIN Dl ( IR) = D l ( IR) D 2 ( | R ) = D 2 ( | R ) IR = IR + 1 N ( | K I L L ) - D B A V ( I R , I K I L L ) - W T B - C ( l R ) N ( I K I L L ) - D N U Z S Q ( | R , I K I L L ) - W T N - E O R ) YES <IR < NRMAX > I K I L L = I ( K I L L ) KK = 4 0 L I M <ITER > KK> YES T = SCLOCK(S) 7 ) -^<IFLAG>LIM> NO < I T E R < T + 3 0 > NO YES WRITE THAT ITERATION TIME LIMIT EXCEEDED WITH SHIM IKILL STILL OUTSIDE LIMITS N(IKILL) = NMIN(IKlLL) WRITE 6 , IK ILL,NMIN( lKILL) IR = NRMIN D 1 ( | R ) = D 1 ( | R ) - N (IKlLL)-DBAV(IR,IKlLL)-WTB-C(IR) D 2 ( | R ) = D 2 ( | R ) - N(lKILL)-DNUZSQ(lR,IKILL)-WTN-E(lR) IR = IR + 1 YES ^ I R < NRMAX> - 76 -YES YES YES J = KILL M = 1 l ( J ) = l ( J + l ) ± A(J,M) = A (J+1 , M) M = M+l J = KILL M = 1 A(M,J) = A(M,J+1) M = M+l <M < NEXT> J = J + YES •<J < NEXT> YES NC = NEXT I FLAG = I FLAG + 1 WRITE THAT LIMIT ON ITERATIONS REACHED WITH SHIM IKILL STILL OUTSIDE LIMITS CALL PRINT (KPRINT,0) I = 1 NMIN(I) = NMIN(l) - N ( l ) NMAX(I) = NMAX(I) - N ( l ) WRITE 2 NMIN(I),NMAX(|) i < L; STOP END - 77 -SUBROUTINE PRINT (KPRINT, MAT) LIM < 0 YES < AND > J ITER < 0 NO WRITE 6, LIMITS ON SHIM NUMBERS J,NMIN(J),NMAX(J),J = 1,LI J,NMIN(J),NMAX(J),J = L l+ l ,L Y E S <WTB^g> HEADING FOR LISTING RADIUS, WEIGHTS ON F, B ERRORS, WEIGHTED B ERRORS IR = NRMIN n EB = 0. J = 1 EB = EB + N[l(J)J-DBAVlIR,I(J)J-C(lR)-WTB J = J + 1 DBFW(IR) = D l ( IR) - EB DBF ( I R) = D.BFW(IR)/[C(|R)«WTB] - 78 -YES YES HEADING FOR LISTING RADIUS, WEIGHTS ON V z > V z ERRORS, WEIGHTED V z ERRORS IR = NRMIN EN = 0. J = 1 A EN = EN + N[ l (J)J-DNUZSQflR, I (J)J•E( IR)-WTN J = J + 1 DNFW(IR) = D2(|R) - EN DNF(IR) = DNFW(IR)/[E(|R)-WTN] IR = IR + 1 <IR < NRMAX> CALL ERROR (NRMIN,NRMAX,DR,E,DNF,DNFW,NUZSQD,NUZSQA) RETURN - 79 -WRITE 6 PUT DOWN REPETITION NUMBER, WTB, WTN, DETERMINANT, COND. NO. I FLAG,WTB,WTN,DET,JEXP,COND WRITE 6 SHIMS ON INSIDE J,N(J) ,J = 1 ,LI WRITE 6 SHIMS ON OUTSIDE J-LI ,N(J) ,J = Ll + l , L YES WRITE 6, VECTOR D, MATRIX A HEADING J = 1 WRITE 6, D(J) , A(J,M),M = I ,NC,5 J = J+5 J = 1 Ji D 4 ( j ) = 0. D3(J) = 0. M = 1 D3(J) = D3 (J) + ACJ,M)-N[I (M)] M = M+1 ; WRITE 6 HEADING RIGHT SIDE MATRIX EQUATION, LEFT SIDE, DIFFERENCE D(J) ,D3 (J) , D 4 ( j ) ,J = I,NC YES YES < I FLAG > 1> RETURN END S L I S T ( l , 3 4 9 ) \ 1 I M P L I C I T R E A L * 8 ( A - H , 0 - Z ) f ?- REAL*8 N U Z S U D , N U Z S 0 A , N M IN , N M A X , N s 3 REAL*4 S,T 4 DIMENSION DNUZS0 12 0 0 , 1 0 0 ) . D B A V I 2 0 0 , 1 0 0 ) , N U Z S O D I 2 0 0 ) , N U Z S n A 1 2 0 0 ) , 5 IE (200 ) , I3AVDI2O0 ) , BAVAI200 ) , C( 200) , MM INI 100) , NMAXI 100 ) , I I ( 100 ) , 6 , 2AI 1 0 0 , 1 0 0 ) , A I N V I 1 0 0 , 1 0 0 ) , 0 1 1 2 0 0 ) , 0 2 ( 2 0 0 ) , N I 1 0 0 ) , D ( 100) 7 C0MM0M/P/NMIN,NMAX,WTB,N,DBAV,C,IU,UR,BAVD,BAVA,HTN,DNUZSQ,i:,D2, 8 1C0N0,D ET,D,A,NUZSOD,NUZSOA,LIM,ITER,LI, L , L 0, NRM IN , NC , 9 2NRMAX,IFLAG,I I I 0 CUMMON/MATEXP/JEXP 11 10 F O R M A T ( 3 I 3 , 2 F 6 . 1 , F 4 . 1 , 2 F 1 5 . 1 0 , 4 I 5 / F 1 5 . 1 0 ) 12 15 F0RMATI8F10.5) 13 20 FORMAT(3F10.5) 14 25 FORMA T ( 2 F 10 . 5 ) 15 30 FORMAT(/////' MATRIX DETERMINANT I S ZERO 1 , 1 0 ( " * » * * * i ) ) ... 16 3.5_ _ FORMAT.!./ ///_/ i_IT.ERAT_ION TI HE_L I.MI T..EXC.EED.ED WI.TH_SH.IML, I.5.,JLST.I.LL_.0 _ 17 10TSIDE L I M I T S • , 1 0 ( • * * * * * • ) ) l i t 40 FORMAT(/////' SHIMS AT 1 , 1 5 , 1 EXCEEDED UPPER L I M I T . SET EOOAL T u ' , 19 1 F 6 . 2 , 1 , THIS L I M I T . ' , 1 0 1 • * * * * * ' ) ) 20 45 FORMAT!///// 1 SHIMS A T 1 , 1 5 , ' EXCEEDED LOWER L I M I T . SET EQUAL T O 1 , 21 1 F 6 . 2 , ' , THIS L I M I T . ',10<•*****•>) ?? 5.0, _FURMAT(///y/.J_L.IM_IT_. DN.._ITERA_TI.ONS. REACHED, ..WI.TJH SHIMS .AT ' , I 5 , _ _ ... „ 23 1' S T I L L OUTSIDE L I M I T S . >,10(******M) 24 READ(5,10) JR,LI,L0,RMIN,RMAX,DR,WTB,WTN,LIM,ITER,MATRIX,KPRINT 24 . 0 2 5 1,CUWAIT 25 L=L I+LII 26 NC=L . 27 S = SCI.nr,K ( 0 . ) 28 IF (WTM.GT.O.) GO TO 100 29 DO 110 1=1,J R 30 DO 110 J=1,L 31 110 D N U Z S O I I , J ) = 1 . 32 GO TO 120 33 100 DO 130 .1 = 1,L 34 130 R E A D ( 7 , 1 5 ) ( D N U Z S O I I , J ) , 1 = 1 , J R ) 35 120 IFIWTB.GT.O.) GO TO 140 36 DU 150 1=1.JR 37 DO 150 .1 = 1,L 38 150 D B A V ( I , J ) = 1 . 39 GO TO 160 40 140 DO 170 J=1,L 41 170 READ 17,15) I D B A V l I , J ) ,1 = 1,JR) 42 160 IF IWTM.GT.O.) GO TO 200 43 DU 180 I=1,JR 44 NUZSODI I ) = 1 . 45 NU7S0A I I ) =1. . 46 180 E I I ) = 1 . 47 GO TO 190 48 200 READ I 5 , 2 0 ) ( N U Z S Q D I I ) . N U Z S O A I I ) , E ( I ) ,1 = 1,JR) 49 190 IFIWTB.GT.O.) GO TO 210 50 DO 220 1=1,JR 51 B A V 0 ( I ) = 1 . 52 B A V A ( I ) = 1 . 53 220 C ( I ) = 1 . 54 GO TO 230 55 210 READ(5 , 2 0 ) ( 8 A V D ( I ) , B A V A ( I ) , C ( I ) , I = 1 , J R ) \ 56 2 3 0 NRMAX=M I NO ( J R , 10 I NT ( ! RMAX/OR ) + 0 . 5 ) ) 57 N R M I N = I D I NT( (RMIN/OP. 1 + 0 . 5 ) 58 I F t L I M . L E . O . A N D . I T E R . L E . O ) GO TO 240 59 RE A D ( 5 , 2 5 ) ( M M I N I I ) , N M A X < I ) , I = 1,NC) s 60 2 4 0 00 2 5 1 J = l , N C / 61 I I ( J ) = J s 62 ' DO 250 M=J,NC 63 A ( J . 11 1 = 0 . 6 4 DO 260 I=NRMIN,NRMAX 65 A U , M ) = A ( J , M > + W T B * C ( I ) * D B A V ( I , M ) * D B A V ( I , J ) 66 2 6 0 A (J ,H )=A 1 J ,H ) + HTN*E ( I KDNUZSQ ( I ,M) *DNUZSQI I . J ) 67 2 50 A ( M , J ) = A ( J , M ) 6 7 . 0 7 5 2 5 1 A 1 J , J ) = A ( J , J ) + C U W A I T .68 DO 270 IR=NRMIN,NRMAX 69 D l ( I R ) = W T B * C ( I R ) * ( B A V O ( I R l - B A V A ( I R ) ) 70 2 7 0 D2( I R ) = W T N * E ( I R ) * ( M U Z SOU( I R 1 - N U Z S 0 A I I R ) ) 71 IFLAG=1 72 5 CUNTIMUE 73 UO 280 J = 1 , M C 74 N ( I I ( J ) ) = 0 . 75 D ( J ) =0 . 76 DO 280 I=NRMIN,NRMAX 77 0 1 J ) = D ( J ) + D l ( I ) * D B A V ( I , I I ( J ) ) 78 280 D ( J ) = 0 ( J ) + D 2 ( I ) * D N U Z S O ( I , I I ( J ) ) 79 DO 2 90 J=.1,NC 80 0 0 2 90 M='1,NC 8 1 2 9 0 A I N V ( J , M ) = A ( J , M ) 82 CALL D I N V R T ( A I N V . N C , 1 0 0 , D E T , C O N D ) 83 I F ( D E T . N E . 0 . ) GO TO 3 0 0 84 W R I T E ( 6 , 3 0 ) 85 3 0 0 DO 310 J = 1 , N C 86 DO 310 1 = 1 , NC 87 3 1 0 " N ( 1 I ( J ) ) =N( I I < J ) ) + A I N V < J , I ) * D ( I ) 88 CALL P R I N T ( 2 , M A T R I X ) 89 I F I L I M . L E . O . A N D . I T E R . L E . O ) GO TO 1 90 K I L L = 0 91 CM = 0 . 92 NEXT=NC-1. 93 DO 320 J = 1 , N C -94 CD=NMIM( I I ( J ) ) - N ( I I ( J ) ) 95 I E ( C D . L E . C M ) GO TO 3 2 0 96 CM=CD 97 K I L L = J 98 3 2 0 COMTIMUE 99 I F ( K I L L . G T . O ) GO TO 4 100 CM=0. 1 0 1 DO 330 J = 1 , N C 102 C D = N ( I 1 ( J ) ) -NMAX( I I ( J ) ) 103 I F ( C D . L E . C M ) GO TO 3 3 0 104 CM=CD 105 K I L L = J 106 330 CONTINUE 107 I F ( K I L L . L E . O ) GO TO 1 108 IK I L L = I I ( K I L L ) 109 K K = 4 0 . * L I M 110 I F ( I T E R . L E . K K ) GO TO 3 4 0 1 1 1 T=SCLOCK(S) 112 I F ( I T E R . G . E . T + 3 0 . ) GO TO 3 5 0 113 W R I T E ( 6 , 3 5 ) I K I L L f 114 GU TO 1 115 340 IF(IFLAG.GE.LIM) GO TO 7 116 350 N (IK ILL)=NMAX(IK ILL ) 117 WRITE(6,40) IKILL,i'!MAX(IKILL> 118 00 360 I R=NRMIN,NRMAX 119 01(IR)=D1(IR)-N(IK ILL)*DBAV(IR,IKILL)*WTB*C( IR) / r 120 360 D2(IR)=02(IRl-N!IKILL>*DNUZS0(1R,IKILL)*WTN*E(IR) 121 GU TO 3 1 ? ? _4_ CONTINUF 123 I K I L L = I I (KILL) -124 KK=40*LIM 125 IF(ITEK.LE.KK) GO TO 370 126 T=SGLOCKIS) 127 IF(ITEP..GE.T+30.) GO TO 380 128 WRITE (6,35) IK 1 Ll. 129 GO TO 1 130 370 IF(IFLAG.GE.LIM) GO TO 7 131 300 N( IKILL)=NMIN( IKILL) 132. WRITE(6,45) IKILL ,NM IN(IKILL) 133 00 390 IR=NKMIN,NRMAX 134 Dl(IR )=D1(IR)-N(IKILL)*OBAV(IR,IKILL)*HTR*C( IR) 135 3~90 D2(IR)=02(IR)-N(IKILL)*DNUZSO(IR,IKILL)*WTN*E(IR) 136 3 CONTINUE 137 DO 400 J=KILL,NEXT 13H I I(J)=1 I ( J + l ) 139 00 400 M=1,NC 1 40 400 A(J,M)=A(J+l.Ml 141 DU 410 J=KILL,N6XT 142 DU 410 M=1,NEXT 143 410 A(M,J)=A ( M,J+l) 144 NC=NEXT 145 IFLAG=IFLAG+1 146. „ GU TO 5 147 CUNTINUE 148 WRITE(6,50) IKILL 149 1 CONTINUE 150 CALL PRINT(KPRINT,0) 151 no 420 1=1,L 1 5 2 _ NHIN(I)=MMIM(I)-N(I) 153 NHAX ( I )=NMAX(I ) -N( I ) 154 420 WRITE (2 ,25 ) NMIM ( I ) ,NMAX ( I )' 155 STOP 156 END 157 SUBROUTINE PR I NT 1KPRI NT,MAT, 158 1MPI ICTT RFAI * R(A - H.n-7 ) 159 REAL-^8 NUZS0D,NUZSOA,NMIN,NMAX,N 160 DIM EMS ION DNHZSO(200, 100) . D B A V(200, 100),NUZSODI200),NUZSOAI 200) , 161 IE I 200 ) , " A V D I 2 00),BAVAI200) ,CI 200),NMIMl 100) ,NMAX( LOO) , I I { )00) 162 2 ,A ( 100 , 101) 1 , A1NV ( 100, 100) , 01 ( 20(1) , 02 ( 200) , N( 1.00 1,01 100) , DBFW I 200 ) , 163 3DBFI 200),DNFW1200) ,DNF(200) ,D3I 100),D4I 100) 164 COMMnM/P/NMIN.NMAX,WTB,N,nBAV.C,Dl , DR . BA VD . BA V A . WT N . ONII7 SO . F . 165 1D2,COND,D E T,0,A,NU Z SOD,NUZ SOA, LIM,ITER,LI,L,LO,NRMIN, 166 3NC,NRMAX,IFLAG,I I 167 COMMON/MATEXP/JEXP 168 ' 10 FORMAT I ' 1 LIMITS ON INSIDE SHIM NUMB ER S 1///5 X, 'SHIM' ,7X, 169 1 •MINI M UM ' ,3X, 'MAXIMUM' /V/(5X,I5,5X,2F10.5)> 170 12 FORMAT! M IIMTTSON riOTSIDF SHIM NUMB FR S ' / / / 5X , ' SH T M ' , . _ .. ... 171 17X, 'MINI MUM•,3X, 'MAXIMUM'///) 172 15 FURMATI5X,I5,5X,2F10.5) 173 20 FURMATI '1 ' ,24X, 'PRESENT MINUS' ,22X , 'UMWFIGHT FD FPROR * ,20X . 'WFIGHTF J r • 174 ID ERROR'/25X,'DESIRED FIELD'» 2 2 X ,'AFTER F I N A L ' , 2 5 X , 1 A FTER F I N A L ' / -\ . 175 2 4 X, 'RADIUS', 5 X,'WEIGHT',4X,'IMITI A L L Y ' , 2 6 X , ' ITERATION' , 2 7 X , 1 I T E R A T 176 3 ION'//) 177 25 FORMAT( ' 1' ,24X, 'PRESENT MINUS',22X,'UNWEIGHTED ERROR',20X,'WEIGHTE 178 ID ERROR'/25X, 'DESIRED 'FOCUSING', 19X,'AFTER F I N A L * , 2 5 X , 'AFTER FINAL I 179 2'/4X, 'RADIUS',5X, 'WE IGHT' , 4 X , ' I N l T l A L L Y • , 2 6 X , ' ITERATION' ,27X,' ITER / 180 3AT ION 1//) \ 181 30 F O R M A T ( ' l ' / / / / / / 1 0 ( ' * * * * * ' ) , ' R E P E T I T I O N NUMBER = ' , I 3 , 3 X , 1 0 ( ' * * * * * ' 182 l ) / / / / i **** OVERALL F I E L D WEIGHT = ' , F 1 0 . 7 , ' #*#*•////• **** 183 2OVERALL FOCUSING WEIGHT = ' , F 1 0 . 7 , ' »***•///• DETERMINANT = 184 4E8.1 , • * ( 1 0 * * ' , 14, • ) '//• CONDITION NUMBER = ' , E 8 . D 185 35 FORMAT( '1'//1QX » 'SHIM NUMBERS FOR IN S I D E OF POLE P I E C E ' / / / 186 1 ( 1 OX,15,1 O X , F 7 . 2 ) ) ' , 187 37 FORMAT( '1'//10X, 'SH IM NUMBERS FOR OUTSIDE OF POLE P I E C E ' / / / ) 188 40 F 0 R M A T ( 1 0 X , I 5 , 1 0 X , F 7 . 2 ) 189 45 FORMAT!'1 VECTOR D MATRIX A'//) 190 50 F ORMAT(F10.5,1 O X , 1 1 F 1 0 . 5 / 1 2 0 X , 1 1 F 1 0 . 5 ) ) 191 55 FORMAT( '1 R.S. MATRIX EOUATION L . S . MATRIX EQUATION DIFFERENCE 192 l ' / / ( 4 X , F 1 5 . 8 , 8 X , F 1 5 . 8 , 5 X , F 1 5 . 8 ) ) 193 K=KPRINT+1 194 GO TO ( 1,2,3 ),l< 195 1 I F I L I M . L E . O . A N O . I T E R . L E . O ) GO TO 2 196 WR I T E ( 6 , 1 0 ) ( J , N M I N ( J ) , N M A X ( J ) , J = l , L I ) 197 W R I T E ( 6 , 1 2 ) 198 L I 1 = L I + 1 199 DO 210 .1=LI1,L 200 J J = J - L I . _ _ 201 210 W K I T E ( 6 , 1 5 ) J J , N M I N ( J ) ,N M A X ( J ) 202 2 IF(WTB.LE.O.) GO TO 100 203 W R I T E ( 6 , 2 0 ) 204 DO 110 IR=NRMIN,NRMAX 205 EB = 0. 206 DO 120 J=1,MC 207 120 EB = EB+H( I I ( J ) )*DKAV( IR , I I ( J ) )*C( IR)*WTB 208 D B F W I I R ) = 0 1 ( I R J - E B 20 9 110 D B F ( I R ) = D B F W ( I R ) / ( C ( I R ) * W T R ) 210 CALL ERROR (NRM I N , NRM AX ,l)R , C, DBF , DBFW, BAVD, BAVA) 211 100 IFIWTN.LE.O.) GO TO 130 212 .WRITE (6 , 2 5 ) 1 _ . _ . .. _'. 213 DO 140 IR=NRMIN,NRMAX 214 EN=0. 215 DO 150 J=1,MC 216 150 EN=EN+N( I I ( J ) )*ONUZS0( IR , I I ( J ) )*E( IR )*WTN 217 D N F W ( I R ) = 0 2 ( I R l - E N 218 140 DNF( IR)=DNFW( I R ) / ( E ( IR)*WTN) 219 CALL ERROR (NRMIN ,NRMAX,DR ,E ,ONF , DNFW , NUZ SQD , NU 7.S0A ) 220 130 CONTINUE 221 RETURN 222 3 W R I T E ( 6 , 3 0 ) I FLAG,WTB,WTN,OET,JEXP.CONO 223 W R I T E ( 6 , 3 5 ) ( J , N ( J ) , J = 1 , L 1 ) 224 W R I T E ( 6 , 3 7 ) . . 225 L I 1 = L I + 1 226 DO 220 J = L I 1 , L 227 J J = J - L 1 228 220 W R I T E ( 6 , 4 0 ) J J , N ( J ) 229 I FI MAT.LE.0) GO TO 160 230 W R I T E ( 6 , 4 5 ) 231 DO 170 J=1,NC 232 170 W K1TE(6,50) 0 ( J ) , ( A ( J , M ) , M = 1 , N C ) 233 160 I F ( I F L A G . G T . l ) GO TO 180 J 2 3 4 DU 190 J = 1 , N C 235 0 4 ( J ) = 0 . 2 3 6 D 3 ( J ) = 0 . 237 DU 200 M=1,NC 2 3 8 2 0 0 D 3 ( J ) = D 3 ( J ) + A ( J , M ) * N ( I I ( H I ) 2 3 9 190 0 4 ( J ) = 0 3 ( J ) - 0 ( J ) 2 4 0 W R I T E ( 6 , 5 5 ) ( D ( J ) , D 3 ( J ) , 0 4 ( J ) , J = 1 , N C ) 2 4 1 180 CONTINUE 2 4 2 RETURN 243 END 2 4 4 SUB ROUTINE ERROR(NRMIN,NRMAX,DR,C,DBF,DBFW,BAVD,BAVA) 245 I M P L I C I T R E A L * 8 ( A - H , 0 - 7 _ > 2 4 6 REAL*8 L I N E A , L I N E B , L I N E C 247 0 I MENS ION C ( 2 0 0 1 , D B F ( 2 0 0 ) , D B F W ( 2 0 0 ) , B A V O ( 2 0 0 ) , B A V A ( 2 0 0 ) , L I N E A ( 2 1 1 , 2 4 8 1 L 1 M E B ( 2 1 ) , L I N E C I 2 1 ) , Y A ( 2 0 0 ) 2 4 9 DATA D O T , S T A R , B L A N K , E D G E / ' . ' , ' * ' , ' ' , ' : ' / . . . . 2 50 10 F 0 R M A T ( 3 X , F 7 . 1 , 3 X , F 7 . 3 , 3 X , F 8 . 3 , 5 X , 2 1 A 1 , 1 X , F 9 . 5 , 5 X , 2 1 A 1 , 1 X . F 9 . 5 , 2 5 1 1 5 X , 2 1 A 1 ) 252 15 FORMAT( /3X, •RMS E R R O R S ' , 4 5 X , F 9 . 5 , 2 7 X , F 9 . 5 ) 253 DMINA=0. 2 5 4 DM I MB =0 . 255 DMINC=0. 2 5 6 DMAXA=Cl. 257 DMAX8=0. 2 5 8 DHAXC=0 . 2 5 9 SUW=0. 2 60 s q = n . . . 2 6 1 DENUM=NRMAX-NRMIN+1 262 DO 100 IP.=NRM IN ,NRMAX 263 SQW=SOW+DBFW(IR)*DBFW(IR) 2 6 4 100 S« = S0+DBF( IR 1 * 0 B F ( I R ) 265 RMS B W = 0 S Q R T ( S 0 W / D E N 0 M ) . 2 6 6 RHSB=DSOKT(SO/DENOM) 267 DO 110 J = l , 2 1 2 6 8 L I N E A ( J ) = B LANK 2 6 9 L I NEB ( J ) =BI.ANK 2 7 0 110 L I N E C ( J ) = B L A N K 2 7 1 00 120 J=NRMIN,NRMAX 2 7 2 Y A ( J ) = B A V D ( J 1 - B A V A I J ) 273 IF ( Y A ( J ) . G T . D H A X A ) UMAX A = Y A ( J ) 2 7 4 IF 1 Y A ( J ) . L T . D M IN A) D M I N A = Y A ( J ) 275 IF ( D B F ( J ) . G T . D M A X B ) DMAXB=DBF(J) 2 7 6 I F I U R F ( J ) . L T . O M I N B ) DMINB=DBF(J ) 277 IF (DBFW(J ) .GT.DMAXC) DHAXC=DBFW(J) 2 7 8 1.20. IF (DBF W (.1 l . l T .DM INC ) DMINOOBFW ( J ) 2 7 9 K Z A = - 2 0 . * D M I N A / ( D M A X A - 0 M I N A ) + 1 . 2 8 0 KZB = - 2 0 . * D M I N B / ( D M A X B-DMIN B ) + 1 . 2 8 1 K Z C = - 2 0 . * U M I N C / ( O M A X C - U M I N C ) + 1 . 2 8 2 DO 130 J=NKMIN,NRMAX 2 83 L I N E A ( 1 ) = E 0 G E 2 8 4 L I N E B I l ) = F D G F 285 L I NEC(11=EDGE 2 8 6 L INEA(211=E0GE 287 L I NEB(211=EOGE 2 8 8 LINEC(211=EOGE 289 L INEA(KZA)=DOT 2 9 0 LINEB(KZR1=DOT 2 9 1 L1NEC(KZC)=DOT 2 9 2 KPA = 2 0 . * ( Y A ( J ) - D M I N A ) / ( D M A X A - D M I N A 1 + 1 . • 2 9 3 K P B = 2 0 . * ( D B F ( J l - D M I N B ) / ( D M A X B - D M I N B ) + 1 . / -e r r " J 2 9 4 295 296 2 97 29! ! 2 9 9 K P C = 2 0 . * ( D B F W ( J ) - D M I N C I / ( 0 M A X C - D M I N C ) + 1 . L INEA(KPA)=STAR L1NEB(KPB)=ST AR L INEC(KPC)=STAR KAIJ«J*DR '.•MITE ( 6 , 1 0 ) RAD,C ( J ) ,YA( J ) , L I N E A , D l l F ( J ) , L I NEB, DBFW! J ) , L I NEC O ! o I o : °l o I I J I o o o 300 L1NEA(KPA)=BLANK 3 0 1 L1NER(KPB)=BLANK 302 130 L I NET. (KPC ) =BLANK 303 W R I T E ( 6 , 1 5 ) RMSB.RMSBW 304 RETURN 305 END END UF F I L E SCOP - S K I P 3 O O o o o o o o o o RFS NU. 036330 UNIVERSITY OF B C COMPUTING CENTRE MTS1AN120) 14:25:06 04-2 3-71 o O o o o o o o o o o o o o o o SSIG T KL F **LAST S1GN0N USER "TRL F" SLIS J . 1 2 3 4 5 PLEASE RETURN TO TRIUMF ** WAS: 14:23:49 04-23-71 SIGNED ON AT 14:25:09 ON 04-23-71 DI MENS ION A(64),B(flO),G(8,80),D(0),C(8,80) 10 FORMAT ( OF 10 ..5.). . . 15 F0RMAT(2I1,2I3,I2,F10.5) 20 FORMAT(SF10.5) READI4,10)(A(I),I=1,64)  6 7 8 8 .025 8.05 9 60 T o -i l 12 12. 13 14 READ(4,10)(B(I),I=1,64) READ(6,15)11,JJ,N1,N2,NUM,S READ (6,20) (0( I 1 = 1, JJ) DO 60 1=65,80 8(I>=0. N1=IM1/S N2=N2/ DO 70 1=1,8 DO 70 J=l,64 C I I,J)=0. G(I,J1=0. DO 100 1=1,JJ 70 T5 16 16.1" 16.2 17 18 2-Nl+0.5)*DlI)/S Tirrr 18.2 18.3 18.4 18.5 95 K=N1+(N2 KF IN=K+NUM T= FLOAT (Nl ) +FL0AT (N2-N1 1*01 U/S F = T- FL DAT ( K > DO 95 J=K,KFIN G ( I ,J1=A(Nl+J-K1*IS-D(I 11/S+BIN2+J-K) •D(I)/S =INl=KFIN-i DU 96 J=K,KFIN1 C( I ,J )=G( I ,J )+F*JG( I , J + l l - G U , J ) ) C(I,KFIN)=G i I ,KFIN)+F*(G( I,KFIN-1)-G(I,KFIN1 } 00 97 J=l,64 [1,J)=C(I,J)*1.05  INUE 19 20 21 22 23 24 END OF FILE 3C0P *SK.IP : II F ( I I . N E . l ) GO TO.75 WRITE (5 ,20 M A I L ) , 1 = 1,64.) WRITE(5,20)((C(I,J1,J=1,641,J WRITE(5,201(B(I 1, 1 = 1,641 E NO =1,JJ) o o o o o RFS N O . 0 3 6 3 3 0 U N I V E R S I T Y OF B C COMPUTING CENTRE M T S ( A N 1 2 0 ) 1 4 : 1 9 : 1 1 0 4 - 2 3 - 7 1 )|s ;|; # ;|t sj; :|! sjt ^{ # & s;< )^  S $ S I G T R L F * * L A S T SIGNON USER " T R L F " ****** P L E A S E RETURN TO TRIUMF WAS: 2 2 : 5 7 : 5 6 0 4 - 2 2 - 7 1 SIGNED ON AT 1 4 : 1 9 : 1 5 ON 0 4 - 2 3 - 7 1 ******************* S L I S N 1 2 _ 3 4 0 . 0 0 . 0 0 5 0 0 . 0 . 0 0 . 0 0 . 0 - 0 . 0 2 2 0 0 J?.? i l45.Q0_ 0 . 0 0 . 0 0 . 0 - 0 . 0 3 8 0 0 _Q.JAI.5O.O_ 0 . 0 0 . 0 0 . 0 6 7 8 9 10 11 0 . 0 0 . 0 0 . 0 0 . 0 - 0 . 0 3 5 1 1 0 . 0 3 6 3 6 0 . 0 O . U 0 . 0 0 . 0 - 0 . 0 5 0 1 4 0 . 0 1 2 4 0 0 . 0 0 . 0 0 . 0 0 . 0 - 0 . 0 4 5 6 7 0 . 0 0 4 5 9 0 0 0 0 0 1 7 8 5 0 0 1 3 8 0 . 0 0 . 0 0 . 0 . 0 . 0 0 . 0 3 0 5 8 0 . 0 0 . 0 0 . 0 . 0 . 0 -6 .00223 0 . 0 7 1 0 7 0 . 0 0 . 0 0 . 0 _o.o - 0 . 0 0 6 1 0 0 . 0 7 9 4 7 0 . 0  0 . 0 0 . 0 _ . U . 0 _ -6 .01641 0 . 0 6 3 2 6 0 . 0 12 13 14 15 16 17 0 . 0 0 . 0 _ 0 . 0 0 . 0 0 . 0 O . U 0 . 0 0 . 0 0 . 0 . 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 . 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 o.o . 0 . 0 . 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 _ 0 . 0 . 0 . 0 0 . 0 0 . 0 .  0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 18 19 .20 21 22 23 0 . 0 0 . 0 5 2 5 0 0 . 0 . 0 . 0 0 . 0 0 . 0 - 0 . 0 0 4 7 2 0 . 0 7 8 4 9 0 . 0 . .. . . 0 . 0 0 . 0 0 . 0 - 0 . 0 1 1 2 9 0 . 0 7 3 7 6 . 0 . 0 .. . 0 . 0 0 . 0 0 . 0 . 0 2 6 7 7 , 0 5 1 9 7 • 0 . .0 .0 ,0 - 0 . 0 4 8 5 6 0 . 0 2 6 7 7 0 . 0 0 . 0 0 . 0 0 . 0  - 0 . 0 5 9 3 2 0 . 0 0 9 7 1 - 0 . 0 0 . 0 0 . 0 0 . 0 - 0 . 0 4 3 0 5 0 . 0 0 3 6 7 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 0 2 1 0 0 . 0 0 0 7 9 . 0 . 0 . . . 0 . 0 0 . 0 0 . 0 24 25 _ 2 6 _ 27 28 29 0 . 0 . 0 . 0 0 . 0 - 0 . 0 1 4 8 3 0 . 0 6 3 7 9 O.O 0 . 0 0 . 0 0 . 0 . - 0 . 0 3 8 0 0 0 . 0 4 2 1 3 0 . 0 0 . 0 0 . 0 . 0 . 0 - 0 . 0 4 2 0 0 0 . 0 0 1 6 4 0 . 0 0 . 0 0 . 0 . 0 . 0 0 . 0 3 5 8 3 0 . 0 0 . 0 0 . 0 0 . 0 r Q . 0 0 381 . . 0 . 0 7 8 6 8 0 . 0 0 . 0  0 . 0 0 . 0 - 0 . 0 0 5 3 2 . 0 . 0 9 0 7 6 0 . 0 0 . 0 30 31 _ 3 2 _ 33 34 35 0 . 0 0 . 0 0 . 0 . 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 . 0 . 0 . 0 . 0 0 . 0 0 . 0 0 . 0 0 . 0 O.o. 0 . 0 0 . 0 - 0 . 0 0 6 0 0 0 0 0 _ . 0 0 0 1 0 0 0 0 . 0 0 . 0 o.o. 0 . 0 0 . 0 - 0 . 0 2 4 0 0 0 . 0 0 . 0 _o.o 0 . 0 0 . 0 - 0 . 0 4 9 0 0 36 37 . . 3 8 . . 39 40 41 - 0 . 0 2 1 0 0 0 . 0 0 1 0 0 .0 .0 . 0 . 0 0 . 0 0 . 0 0 . 0 5 5 0 0 0 . 0 . . 0 _ . 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" 20.00186 0 .0 0.0 0.0 . 0..0 0.0 25.72011 0.0 0.0 0.0 _ 0 . 0 0.0 21.71323 0.0 0.0 0.0 0.0 1.41294 13.88216 0.0 0.0 0.0 .0.0 2.80310 8.38543 0.0 0.0 0.0 0.0 4.37809 5.51429 0.0 0.0 0.0 O.U 6.51115 2.74743 0.0 0.0 U.O o.o . 10.96866 1.36063 0.0 2 82 283" 2 84 "2 85 286 2 87 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0 .0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 . 0. 0 0.0 0.0 0.0 0.0 0 . 0 0. 0 _ 0.0 0.0 0.69900 0.0 0.0 n. o _ 0.0 0.0 1.3B604 0.0 0.0 .0.0 0.0 0.0 2.436U4 0.0 0.0 0.0 0.0 0.0 4.08393 288 28 9 290 "2 91 2 92 293 8.27402 0.0 0.0 "o.o 0.0 0.0 16.95232 0.0 _o. o o".o o. o o.o 23.76598 0 . 0 . 0 . 0 * 01 0 0.0 0.0 20.85138 0.0 0.0 "o.o ' 0.0 0.0 13.02927 0.0 0.0 0.0 0.0 0.0 6.6 6546 0.0 0.0 _ 0.0 0 . (1 0.0 3.69201 0.0 _o.p 0.0 0.0 0.0 1.32175 0.0 o.o _ 0.0 0.0 0.0 o o "TxTTxTxTx^xxxxxxxxxxxxxxxxxxxxxxxxxxxxkx O O ' O o o o o o o o o o o o o o o u o o o o i s s 3 1 1 d dO UNrl 00000'Zl 00000 '<. I OOOOO'OT. OOOOS*z OOOOS'O 0*0 O'O O'O o-o O'O O'O O'O 0*0 0*0 0*0 O'O £0£ 0 * o 0*0 ~ * O'O" 0~*"0 0' u" " 0*0 " ' " 0'* 0 "_ ' O'O "Z0£ O'O O'O 0*0 O'O O'O O'O O'O • O'O lot. \ O'O O'O O'O O'O O'O 0*0 0*0 O'O OOE ? O'O O'O 0*0 O'O O'O O'O O'O O'O (S6Z O'O O'O O'O o'o O'O 0*0 0*0 O'O HftZ O'O 0*0 O'O O'O O'O O'O O'O O'O Z.6Z ooooo'z 00000's OOOOO'ZI 00005 * 6T 00000*12 ooooo*et 00000*5 OOOOS'T 96Z OOOOS'O O'O O'O 0*0 0*0 o'o O'O o*o S6Z - O'O O'O O'O 0*0 0*0 0*0 0*0 O'O <?6Z c c o RFS NO. 036330 UNIVERSITY OF B C COMPUTING CENTRE MTSIAN120) 14:23:46 04-23-71 ( ******** ***** ******* PLEASE RETURN SSIG TRLF *#LAST S I ON ON WAS: 14:21 :32 04-23-71 . USER " TRLF" SIGNED ON AT 14:23: 49 ON 04-23-71 / SLIS X \ 1 0.12 500 0.0 1.00000 2. .0.12500. _ 0 ._>.__ .. 1.00000 . . _ _ 3 0. 12500 0.0 1.00000 • '+ 0.12500 0.0 1.00000 5 0 .12500 0.0 1.00000 6 0.12500 0.0 1.00000 7 0. 12500 0 . 0 1.00000 .... B 0.12500 0 .0 1.00000 9 0 . 125U0 -0.03500 1.00000 10 0.12500 -0 .02500 1.00000 11 0.12500 -0.01000 1.00000 12 0.12500 0.01500 1.00000 13 0. 1250O 0.03000 1 . 0 0 0 0 0 14 ..0.12500 .0.06 000 . 1.00000 15 0.12500 0.08500 1.00000 16 0.12500 0.11500 1.00000 17 0.12 500 0.13000 1.00000 18 0.12500 0.13500 1.00000 19 0.12500 0.12000 1.00000 20. ...0 .12500 .0.10000.. 1. uOOOO . . . . _ 21 0. 12500 0.08 000 l.OOUOO 22 0.12500 0.08000 1.00000 23 0.12 500 0.12000 1.0 0000 24 0.1 2 Sou 0.13500 1.00 000 25 0.12500 . 0.14000 1.00000 26 0.12 500. 0.13 000 . 1.00000 . . . 27 0.12 500 0.11500 1.00000 28 0.12500 0.10 500 1.00000 29 0. 12500 0.11000 I.00000 30 0 .12500 0.12000 1.00000 31 0.12500 0.13 000 1 • O L I O 00 . .. . .32 . 0.12500. _ ..0.13500 l . o o o o o . _ . . . 33 0.12500 0.13500 1.00000 34 0.12500 0.12500 1.00000 3 5 0.12500 0.12 000 1.0 0000 36 0.12.500 0.11000 1.OOOoO 37 0.12500 0.11000 1.00000 . 3 8 _0.12500 _ _0 .110.00 1.00000 3 9 0.12500 0 . 10500 1.00000 40 0.12.500 0.0 9 000 1.OOOOO 41 0.12500 0.06 000 1.UOOOO 4 2 0.12500 0.02 5 00 1.00000 4 3 0.12500 0 . 0 1.00000 44 .0.12500 0 • (J 1.00000 _ . _ ._ . _ . . 45 0.12500 -0.01000 1.uOOOO 46 0.12500 -0.03000 1.UOOOO 47 0.12 500 -0.05000 l.OOUOO 4 8 0.12 5 0 0 -0 .04500 1.00000 49 0.12500 -0.03500 1.OOOOO 50 0.12500 -0.0 1500 \.OOOOO 51 0. 12500 -0.00 5 00 1.00000 52 0.12500 -0.00 5 00 1 . 0 0 0 0 0 53 0.12500 0.00500 1.OOOOO -f • 54 0 . 12 500 0.025 00 1.00000 55 0.12 500 0.07000 1.00000 56 0.12500 0. 13500 1.00000 57 0.12500 0.175 00 1.00000 58 0.12500 0. 15500 1.00000 \ 59 0 .12500 0.11500 1.00000 J 60 0.12500 0.035 00 1.00000 s 61 0.12500 -0.185 00 1.00000 62 0.12500 -0.42 000 1.00000 63 0.12500 -0.195 00 1.00000 64 0.12500 0.0 1.00000 65 3035. 3076. 1. 66 3036. 3090. 1. 67 3037. 3049. 1. 68. 3038. 2 977. 1. 69 3039. 2952 . 1. 70 • 3041. 2 961. 1. 71 3042 . 2977 . 1. 72 3044. 2997. 1. 73 3047 . 3026. 1. 74 3050. 3059. 1. 75 3053 . 3085 . 1. 76 3057. 3101. 1. 7 7 3062. 3109. 1. 78 3066. 3116. 1. 7 9 3072 . 3125. 1. .80 3078. 3131. 1 . ~81 ~ 3085 . 3132. 1 . 82 3092. 3132. 1. 83 3100 . 313 5. 1. 84 3109. 3142. 1. 85 3118. 3154. 1. 86 3128. 3169. 1. 87 3138 . 3181. 1. 88 3150. 3190. 1. 89 3162 . 3198. 1. 90 3174. 3 207. 1. 91 3187. 3219. 1. 92 3200. 3232. 1. 93 3214. 3246. 1 . 94 3228. 3261. 1. 9 5 3246 . 3275 . 1. 96 3264. 3289. 1. 97 3283 . 3304. 1. 98 3303. 3318. 1. 9 9 " 3324."" 3334. 1. 100 3 347. 3351 . 1. 101 33 71 . 3370. 1. . 102 3396. 3389. 1. 103 3422 . 3409. 1. 104 3450. 3430. 1. 105 3479 . 3455 . 1. 106 3509. 3484. 1. 107 3543 . 3 518. 1. 108 3578. 3555. 1. 109 3614 . 3594. j.. 110 3653. .3636. 1. 111 36 94. 3683. 1. 112 3737. 3734. 1. 113 37 82 . 37 85 . 1. 11'I 115 116 117 111! 119 120 121 ,122. 123 124 125 126 127 . 128 129 1311 131 132 133 134 135 136 137 138 139 140 141 142 143 144 14D 146 147 148 149 150 151 152 153 154 155 156 157 . . 158. 159 160 161 162 163 1.64 165 166 167 168 169 192 END OF 3830 . 3879. 3932. 3 988. 4048. 4110. 4176 . 424 5. 43 21... 4405. 4497 . 4590. 4674 . 4747. 4846 0. U . O . - .43 - . 70 -.93 5. -.935 -.935 -.935 - .935 -.935 -.935 -.935 -.935 -.935 '..33 -.935 -.935 . -.93 5 - .935 -. 93 5 0 . 0. 0. -.56 -.72 -.93 5 - .935 -.935 -.9?5_ -.935 -.935 -.935 - .93 5 -.935 -.935 -.935 -.935 -0.8 -0.8 -0.8 3838. 3892. 3 948. 4 006. 40 6 8 . 4131. 4193. 4256. 4322.. 4395. 4475. 4569. 1. 1. A. 1. 1. 4680. 4777. 4802. .935 .935 . 93 5 . 1. . .93 5 .93 5 .935, .93 5 .935 .935 .935 .935 . .935, .93 5 .935 .935 .93 5 .935 .935 .935 .935 . 935 .935 .93 5 .93 5 .935 .935 . 935 .935 .935 .93 5, .93 5 .935 .935 .935 . 935 .935 . 935 .935 0.3 0.8 0.8 F ILE o RFS NO. 0 3 5 3 1 8 UNIVERSITY OF B C COMPUTING CENTRE MTSIAN120) 1 5 : 4 1 : 5 1 0 2 - 2 3 - 7 1 ******************** PLEASE RETURN TO TRIUMF *************************** $ S I G TRLF T=150 P=150 0 2 - 2 3 - 7 1 15:41:55 ON 02-23-71 **LAST SIGNON WAS: 15:37:22 USER "TRLF" SIGNED ON AT $RUN *FORT RAN SCARDS=*SOURCE* SPUNCH=-A EXECUTION BEGINS FORTRAN IV G COMPILER MAIN 02-23-71 15:41:59 PAGE 0001 0001 0002 0003 0004 DIMENSION A(150),B(150),C(150) WTB=.0Ol WTN=.01 CUWAIT=1. 0005 0006 0007 0008 0009 00 10 LIM=10 ITER=0 JR = 64 L 1=21 L0=17 DR = 5. 0011 0012 0013 0014 0015 RMIN=75. RMAX=320. MATRIX=0 _ KPRINT=0 WRITE(5,10) JR,LI,L0,RMIN,RMAX,OR,WTB,WTN,LIM,ITER,MATRIX,KPRINT 1,CUWAIT 0016 0017 10 FORMAT(3I3,2F6.1,F4.1,2F15.10,4I5/F15.10) END TOTAL MEMORY REQUIREMENTS 000962 BYTES COMPILE TIME = 0.7 SECONDS EXECUTION TERMINATED SRUN -A 5=-B 7=X EXECUTION BEGINS STOP 0 EXECUTION TERMINATED SRUN TI350) 5=-B+X 7=N+B 2=*DUMMY* EXECUTION BEGINS o f o o o s. 3 o f * * « * # * # # * # « « * * * » * » * « * * « * * # * * * * * $ * ^ NUMBER = 1 o r\ * * * * O V E R A L L F I E L D WEIGHT = 0 . 0 0 1 0 0 0 0 * * * * o o * * * * O V E R A L L F O C U S I N G WEIGHT = 0 . 0 1 0 0 0 0 0 * * * * o o D E T E R M I N A N T = 0.5D 1 3 * ( 1 0 * * 0 ) o o C O N D I T I O N NUMBER = 0.6D 01 o o o : u _, . _ . . . . . o h o ; jo o 1 o ] o © o © o © _ . . _ ...... o o O j o 1 I o ! 1 o o ! 0 o o ) c o o O o o o o • o o o O ! o o o o o o o o ; t o ; o • I • I O ! o i SHIM NUMBERS FOR INSIDE OF POLE PIECE o o o o o o o.oo 9 10 n 12 13 15 16 17 18 19 ^ 0 21 - 0 . 2 0 - 0 . 3 7 - 0 . 3 3 - 0 . 2 6 - 0 . 2 5 - 0 . 2 9 - 0 . 0 1 0 . 2 9 0 . 2 9 0 . 2 2 - 0 . 0 3 - 0 . 0 9 - 0 . 2 1 - 0 . 2 8 - 0 . 1 2 0 . 1 6 0 . 1 7 0 . 0 1 - 0 . 0 2 - 0 . 0 9 I o o o Q o : ° O O o o o o SHIM NUMBERS FOR OUTSIDE OF POLE PIECE -_' o o o 2 3 5 6 -0.07 -0.32 -0.23 -0.37 -0.23 -0.35 - - o o o 0 7 8 9 10 11 12 -0.06 0.27 0.28 0.04 " -0.09 -0.17 - - - - • o o o o 13 14 15 16 17 -0.13 0.03 0.18 0.22 0.01 -- o o o !o o I — ._- o o o 0 o o o © o © o o . . . . o o o o o o J o o o f R . S . M A T R I X E Q U A T I O N L . S . M A T R I X E Q U A T I O N D.EFERENCS: o 0 . 0 0 0 0 0 2 2 0 0 . 0 0 0 0 0 2 2 0 0 . 0 0 0 0 0 0 0 0 - 3 . 5 7 0 5 5 0 3 8 - 3 . 5 7 0 5 5 0 3 8 - 0 . 0 0 0 0 0 0 0 0 - 1 2 . 8 2 0 0 8 8 2 2 - 1 2 . 8 2 0 0 8 8 2 2 - 0 . 0 0 0 0 0 0 0 0 o < - 1 1 . 5 6 1 6 7 4 0 3 - 1 1 . 5 6 1 6 7 4 0 3 - 0 . 0 0 0 0 0 0 0 0 ? - 7 . 1 9 6 9 9 9 0 3 - 7 . 1 9 6 9 9 9 0 3 - 0 . 0 0 0 0 0 0 0 0 < o - 6 . 2 2 9 9 7 9 1 4 - 6 . 2 2 9 9 7 9 1 4 - 0 . 0 0 0 0 0 0 0 0 - 3 . 7 1 6 2 2 0 6 2 - 3 . 7 1 6 2 2 0 6 2 - 0 . 0 0 0 0 0 0 0 0 - 0 . 0 7 6 3 6 0 6 5 - 0 . 0 7 6 3 6 0 6 5 •o.oooooooo " " 2 . 4 4 4 7 1 2 8 6 2 . 4 4 4 7 1 2 8 6 - 0 . 0 0 0 0 0 0 0 0 o 2 . 9 5 1 3 6 9 8 8 2 . 9 5 1 3 6 9 8 8 - 0 . 0 0 0 0 0 0 0 0 1 . 9 8 3 9 4 9 6 4 1 . 9 8 3 9 4 9 6 4 0 . 0 0 0 0 0 0 0 0 o - 0 . 3 8 9 6 2 4 0 1 - 0 . 3 8 9 6 2 4 0 1 - 0 . 0 0 0 0 0 0 0 0 - 1 . 5 0 8 4 7 1 6 1 - 1 . 5 0 8 4 7 1 6 1 - 0 . 0 0 0 0 0 0 0 0 - 2 . 2 9 5 2 4 2 4 3 - 2 . 2 9 5 2 4 2 4 3 - 0 . 0 0 0 0 0 0 0 0 o - 2 . 0 7 0 9 1 9 0 3 - 2 . 0 7 0 9 1 9 0 3 - 0 . 0 0 0 0 0 0 0 0 - 0 . 9 3 4 3 0 6 7 7 - 0 . 9 3 4 3 0 6 7 7 - 0 . 0 0 0 0 0 0 0 0 0 . 4 1 8 6 2 6 1 4 0 . 4 1 8 6 2 6 1 4 - 0 . 0 0 0 0 0 0 0 0 " o 0 . 7 4 2 6 2 0 3 8 0 . 7 4 2 6 2 0 3 8 0 . 0 0 0 0 0 0 0 0 0 . 4 0 6 8 6 2 1 1 0 . 4 0 6 8 6 2 1 1 0 . 0 0 0 0 0 0 0 0 0 . 2 8 8 3 2 2 2 7 0 . 2 8 B 3 2 2 2 7 0 . 0 0 0 0 0 0 0 0 o 0 . 1 3 5 6 0 1 4 4 0 . 1 3 5 6 0 1 4 4 0 . 0 0 0 0 0 0 0 0 - 1 . 2 4 6 9 7 8 5 3 - 1 . 2 4 6 9 7 8 5 3 - 0 . 0 0 0 0 0 0 0 0 - 6 . 5 8 1 9 5 4 9 4 - 6 . 5 8 1 9 5 4 9 4 - 0 . 0 0 0 0 0 0 0 0 - 1 2 . 1 4 4 6 2 2 8 0 - 1 2 . 1 4 4 6 2 2 8 0 - 0 . 0 0 0 0 0 0 0 0 o - 9 . 9 0 8 2 9 9 6 9 - 9 . 9 0 8 2 9 9 6 9 - 0 . 0 0 0 0 0 0 0 0 - 6 . 6 2 1 9 6 9 3 4 - 6 . 6 2 1 9 6 9 3 4 - 0 . 0 0 0 0 0 0 0 0 - 5 . 1 6 4 9 8 1 9 4 . - 5 . 1 6 4 9 8 1 9 4 - 0 . 0 0 0 0 0 0 0 0 o - 0 . 3 7 7 9 0 0 6 7 - 0 . 3 7 7 9 0 0 6 7 - 0 . 0 0 0 0 0 0 0 0 2 . 2 3 1 7 6 9 7 3 2 . 2 3 1 7 6 9 7 3 - 0 . 0 0 0 0 0 0 0 0 o 2 . 9 5 8 0 5 8 9 7 2 . 9 5 8 0 5 8 9 7 0 . 0 0 0 0 0 0 0 0 0 . 3 9 0 5 1 8 5 0 0 . 3 9 0 5 1 8 5 0 - 0 . 0 0 0 0 0 0 0 0 - 1 . 2 6 3 3 1 6 8 2 - 1 . 2 6 3 3 1 6 8 2 - 0 . 0 0 0 0 0 0 0 0 • - - -- 1 . 9 9 9 7 0 1 4 5 - 1 . 9 9 9 7 0 1 4 5 - 0 . 0 0 0 0 0 0 0 0 © - 0 . 9 2 0 5 9 4 8 0 - 0 . 9 2 0 5 9 4 8 0 - 0 . 0 0 0 0 0 0 0 0 - 0 . 0 8 5 9 9 8 0 6 - 0 . 0 8 5 9 9 8 0 6 - 0 . 0 0 0 0 0 0 0 0 o 0 . 6 0 9 3 1 7 0 6 0 . 6 0 9 3 1 7 0 6 0 . 0 0 0 0 0 0 0 0 0 . 8 3 8 1 0 5 0 7 0 . 8 3 8 1 0 5 0 7 0 . 0 0 0 0 0 0 0 0 0 . 1 1 0 8 0 3 3 4 0 . 1 1 0 8 0 3 3 4 0 . 0 0 0 0 0 0 0 0 © o S H I M S AT 3 E X C E E D E D LOWER L I M I T . S E T EQUAL TO 0 . 0 , T H I S L I M I T . * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * o o o 0 . . . o o I O i o ; ° i o ! o i i o : O i o o o o o o o o o o o o o o o o o o o !o o o © o o o o o ***r****999z*9tf*fZ*z$$s#*zz**s«z$$z$$#z%$z*$***#z*if#Rf:pETITION NUMBER = 7 **zzt**$*ir***tr***zzz%$22$z*s***z***$2szs*$2$*t**z* **** OVERALL FIELD WEIGHT = O.OOIOOOO **** **** OVERALL FOCUSING WEIGHT = 0.0100000 **** DETERMINANT = 0.1D 11*(10** 01 O o o o o o o o o o o o o o o o o o o o o o CONDITION NUMBER = 0.50 01 SHIM NUMBERS 1 FOR INSIDE OF POLE PIECE 0 . 0 0 / ? 2 3 4 5 6 7 0 . 0 0 . 0 - 0 . 4 3 - 0 . 1 7 - 0 . 2 7 - 0 . 2 8 - -s 8 9 10 11 12 13 - 0 . 0 1 0 . 2 9 0 . 2 9 0 . 2 2 - 0 . 0 3 - 0 . 0 9 14 15 16 17 18 19 - 0 . 2 1 ' - 0 . 2 8 - 0 . 1 2 0 . 1 6 0 . 1 7 0 . 0 1 -20 21 - 0 . 0 2 - 0 . 0 9 - — . ... . — . . . . . - - -- • • - • - • - — ... . - - • . ' - -• - -- - -o r \ o SHIM NUMBERS FOR OUTSIDE OF POLE PIECE O o s r 1 0.0 o 2 3 _, 0.0 0.0 ' -0.45 . . . . . _ G o 5 6 -0.23 -0.37 O 7 -0.06 o 8 9 10 0.27 0.28 0.04 - • -G o 11 12 -0.09 -0.17 G 13 -0.13 o 14 15 16 0.03 0.18 0.22 • • - - - - - - • - • G o 17 0.01 O • o G !o O i jo O o o © o o o o o o o o o o o o ' . . . . . . . o o - o LIMITS ON INSIDE SHIM NUMBERS SHIM MINIMUM MAXIMUM 7 8 9 10 11 12 13 14 15 16 17 18 "19 20 21 0.0 0.0 0.0 - 6.43000 - 0 . 7 0 0 0 0 -0.93500 -0.93500 -0.93500 -0.93500 "0.93500 -0.93500 -0.93500 -0.93500 -0.93500 -0.93 500 -0.93500 - 0 . 9 3 5 0 0 -0.93500 -0.93500 -0.93500 -0.93 500 0.93500 0.93500 0.93500 0.93500 0.93500 0.93500 0.93500 0.93500 0.93500 0.93500 0.93500 0.93500 0.93500 0 .93500 0.93500 0.93500 0 . 9 3 5 0 0 0.93500 0.93500 0.93500 0.93500 ; -J . -TO' o < LIMITS ON OUTSIDE SHIM NUMBERS > o o SHIM MINIMUM MAXIMUM o s J ? 1 0.0 0.93500 o 2 0.0 0.93500 f -, 3 0.0 0.93500 4 -0.56000 0.93500 o o 5 -0.72000 0.93500 6 -0.93 500 0.93500 7 -0.93500 0.93500 o 8 -0.93500 0.93500 o • 9 -0.93500 0.93500 o 10 -0.93500 0.93500 o 11 -0.93500 0.93500 12 -0.93500 0.93500 o 13 -0.93500 0.93500 14 -0.93 500 0.93500 o 15 ' -0.93500 0.93500 16 -0.93500 0.93500 o o 17 -0.93500 0.93500 o _ . . . . . . . . . . . o . !o o I ! ° . . . . . . . . . o o o o o o o o o o o e . _ _ _ o Q o ... . _ . _ . . . . . o © o © o / RADIUS WEIGHT PRESENT MINUS DESIRED FIELD INITIALLY UNWEIGHTED ERROR AFTER FINAL ITERATION WEIGHTED ERROR AFTER FINAL ITERATION I 7 5 . 0 1 .000 - 5 3 . 0 0 0 - 5 3 . 3 1 0 4 0 * - 0 . 0 5 3 3 1 * / f 80.0 1 .000 - 5 3 . 0 0 0 * - 5 0 . 1 2 0 5 9 * -0. 0 5 0 1 2 * \ 85.0 1.000 - 4 7 . 0 0 0 * . - 4 2 . 0 6 3 7 3 * - 0 . 0 4 2 0 6 * 90.0 1 .000 - 4 0 . 0 0 0 * - 3 1 . 7 7 7 8 1 * . - 0 . 0 3 1 7 8 * 95.0 1 .000 - 3 5 . 0 0 0 - 2 3 . 7 3 6 5 4 * . - 0 . 0 2 3 7 4 * 100.0 1 .000 - 3 3 . 0 0 0 * - 1 2 . 4 8 5 4 4 * . - 0 . 0 1 2 4 9 * 105.0 1 .000 - 3 6 . 0 0 0 * . 0.33799 0.00034 110.0 1 .000 - 4 1 . 0 0 0 * 5.12301 . * 0.00512 . * 115.0 1.000 - 4 3 . 0 0 0 * , 3.39337 0.00339 120.0 1 .000 - 4 0 . 0 0 0 « - 0 . 3 8 0 3 4 * - 0 . 0 0 0 3 8 * _ 125.0 1.000 - 3 6 . 0 0 0 - 1 . 0 0 8 1 6 * - 0 . 0 0 1 0 1 * 130.0 1.000 - 3 3 . 0 0 0 # - 1 . 0 5 6 7 4 * - 0 . 0 0 1 0 6 * 135.0 1 .oOo -32 .000 * , - 0 . 2 4 3 5 3 * - 0 . 0 0 0 2 4 * 140.0 1 .000 - 3 2 . 0 0 0 # - 1 . 1 3 9 7 7 * - 0 . 0 0 1 1 4 * 145.0 1 .000 - 3 2 . 0 0 0 * - 1 . 6 5 8 3 6 * - 0 . 0 0 1 6 6 * 150.0 1 .000 - 3 3 . 0 0 0 * - 4 . 4 4 3 2 9 * - 0 . 0 0 4 4 4 * 1 5 5 . 0 ' 1.000 - 2 9 . 0 0 0 * . - 1 . 9 6 3 3 6 * - 0 . 0 0 1 9 6 * 160.0 l .ooo - 2 5 . 0 0 0 # - 0 . 4 6 3 5 1 * - 0 . 0 0 0 4 6 * 165.0 1 .000 - 2 1 . 0 0 0 - 1 . 6 6 9 2 4 * -0.00167 * 170.0 1 .000 - 1 5 . 0 0 0 * - 2 . 0 8 7 1 8 * - 0 . 0 0 2 0 9 * 175.0 1 .000 - 1 0 . 0 0 0 * . - 2 . 2 5 8 1 2 * - 0 . 0 0 2 2 6 * 180.0 1 .000 - 4 . 0 0 0 - 0 . 4 6 4 2 7 * - 0 . 0 0 0 4 6 # 185.0 " 1 . 0 0 0 1 .000 * 0.30297 . » " 0.00030 .* 190.0 1 .000 7.000 * 0.77871 .* 0.00078 .* 195.0 1.000 13.000 * 1.14414 .* 0.00114 .* 2 0 0 . 0 1 .000 2 0 . 0 0 0 * 2.96538 .» 0.00297 .* 205.0 l.ooo 2 4 . 0 0 0 * 3.57871 .* 0.00358 .* 210.0 1 .000 2 5 . 0 0 0 * 2.87496 .* 0.00287 .* 215.0 1 .000 2 5 . 0 0 0 * " " 1.87066 .* 0.00187 .* 220.0 1 .000 2 3 . 0 0 0 * 0.93120 .* 0.00093 .# 2 2 5 . 0 1 .000 2 0 . 0 0 0 * 1.76517 .* 0.00177 .* 2 3 0 . 0 1 .000 17.000 * 3.10734 .# 0.00311 .* 2 3 5 . 0 1 .000 11.000 s 2.20911 .* 0.00221 .* 240.0 1 .000 3.000 * - 0 . 8 6 8 9 4 * - 0 . 0 0 0 8 7 * 2 4 5 . 0 1 .000 - 3 . 0 0 0 - 1 . 0 8 5 3 9 * - 0 . 0 0 1 0 9 * 250.0 1 .000 - 8 . 0 0 0 * - 0 . 6 5 0 9 2 * - 0 . 0 0 0 6 5 * 2 5 5 . 0 1 .000 - 1 3 . 0 0 0 * , - 1 . 0 4 6 6 9 * - 0 . 0 0 1 0 5 * 260.0 1 .000 - 1 6 . 0 0 0 # - 0 . 2 0 0 6 2 * - 0 . 0 0 0 2 0 * 2 6 5 . 0 1 .000 - 1 8 . 0 0 0 # - 0 . 3 3 0 2 4 • * - 0 . 0 0 0 3 3 * 270.0 1 .000 - 2 0 . 0 0 0 * - 2 . 0 8 8 7 8 * - 0 . 0 0 2 0 9 * 2 7 5 . 0 " 1.000 -21 .000" # - 4 . 1 3 2 0 5 * - 0 . 0 0 4 1 3 * 2 8 0 . 0 1 .000 - 1 7 . 0 0 0 * - 2 . 1 1 7 3 2 * -0.00212 * 2 8 5 . 0 1 .000 -11 .000 * - 2 . 0 6 4 1 0 * - 0 . 0 0 2 0 6 * 290.0 1 .000 - 1 . 0 0 0 - 1 . 2 6 7 8 6 * - 0 . 0 0 1 2 7 * 295.0 1.000 10.000 * 1.09381 0.00109 300 .0 1 .000 22 .000 * 9.32256 . * 0.00932 • * 3 0 5 . 0 1 .000 2 1 . 0 0 0 * 1 1 . 3 3 8 8 5 * 0.01134 * 310.0 1 .000 - 6 . 0 0 0 * - 1 1 . 11876 * . - 0 . 0 1 1 1 2 * 315.0 1 .000 - 3 0 . 0 0 0 * - 3 0 . 9 9 5 6 4 * . - 0 . 0 3 1 0 0 * 3 2 0 . 0 1 .000 4 4 . 0 0 0 * 4 3 . 8 3 3 5 3 . * 0.04383 . * RMS ERRORS 1 5 . 6 4 9 1 5 0.01565 ,_-I-D-: O PRESENT MINUS UNWEIGHTED ERROR WEIGHTED ERROR DESIRED FOCUSING AFTER FINAL AFTER FINAL RADIUS WEIGHT INITIALLY ITERATION ITERATION - 75.0 1.000 0.040 . * 0.03836 . * 0.00038 ? 80.0 1 .000 0.010 0.00706 * 0.00007 * \ 85.0 1.000 -0.005 * -0.01374 * -0.00014 90.0 1.000 -0.010 » -0.03260 *. -0.00033 *. 95.0 1.000 0.005 * -0.04071 *. -0.00041 *. 100.0 1.000 0.025 -0.03820 *. -0.00038 *. 105.0 1 .000 0.045 . * -0.01095 * -0.00011 * 110.0 1 .000 0.045 . * 0.02639 .* 0.00026 .* 115.0 1 .000 0.005 * 0.01673 .* 0.00017 .* 120.0 1 .000 -0.010 * 0.01819 •* 0.00018 .* 125.0 1 .000 -0.015 * 0.00411 * 0.00004 * 130.0 l.ooo -0.005 * 0.00815 * 0.00008 » 135.0 1 .000 0.010 .* 0.01009 * 0.00010 * 140 .0 1 .000 0.020 .* 0.02262 .* 0.00023 .# 145.0 1.000 0.015 .* 0.01696 .* 0.00017 .* 150.0 1 .000 0.005 * 0.01249 . * 0.00012 .# 155.0 1 .000 -0.005 * 0.01215 .* 0.00012 160.0 1 .000 -0.010 0.02843 0.00028 .* 165.0 1.000 -0.010 * 0.04153 . * 0.00042 . * 170.0 1.000 0.0 . * 0.04836 0.00048 . * 175.0 1.000 0.005 * 0.03951 . * 0.00040 180.0 1 .000 0.015 .# 0.04399 • *. _ 0.00044 . * 185.0 1.000 0.015 .* 0.05902 0.00059 . * 190.0 1 .000 0.015 . * 0.07515 * 0.00075 * 195.0 1 .000 0.020 . * 0.07632 . * 0.00076 . * 200.0 1 .000- 0.035 . * 0.07631 . * 0.00076 205.0 1 .000 0.065 . * 0.09633 0.00096 * 210.0 i .ooo 0.100 . * 0.11643 * 0.00116 . * 215.0 1.000 0.125 •. * 0.12397 * 0.00124 . » 220 .0 1 .000 0.125 * 0.10583 0.00106 * 225.0 1.000 0. 135 :. * 0.09909 » 0.00099' * 230.0 1 .000 0.155 * 0. 10978 0.00110 . * 235.0 1.000 0.175 * 0.12677 * 0.00127 . * 240.0 1.000 0.170 .. * 0. 11603 0.00116 . * 245.0 1.000 0.160 * 0. 10238 . * 0.00102 . * 250.0 1 .000 0.140 * 0.08492 * 0.00085 . * 255.0. 1.000 0.130 0.08278 0.00083 260.0 1 .000 0.130 . * 0.10046 . * 0.00100 * 265.0 1 .000 0.120 0. 10899 0.00109 * 270.0 1 .000 0. 100 .. * 0.10980 * 0.00110 275.0""" 1.000 0.055 :. * 0.05520 :. * 0.00055 280.0 1 .000 -0.010 0.02592 .* 0.00026 285.0 1 .000 -0.050 *. 0.01073 0.00011 290.0 1.000 -0.030 *. 0.06279 . * 0.00063 . * 295.0 1.000 0.010 :. * 0.09818 :. * 0.00098 * 300.0 1 .000 0.090 :. * 0.12 394 . * : • 0.00124 * 305.0 1.000 0.310 :. * 0.28566' :. * 0.00286 " . " * 310.0 1 .000 0.545 :. * 0.48395 * 0.00484 . * 315.0 1 .000 0.320 :. * 0.29269 * 0.00293 :. * 320.0 1.000 0.125 :. * 0.12793 * : 0.00128 RMS ERRORS .. ... 0.11382 . 0.00114 _ . . STOP 0 EXECUTION TERMINATED J c O o o o o o . o o o o i o : O i o 1 o o o O : o - 116 -D.2 L i s t i n g o f TRIMFIT and input data The computer program TRIMFIT was designed to p r e d i c t the best com-b i n a t i o n of a p a r t i c u l a r change in the e x c i t a t i o n o f the main c o i l and a p a r t i c u l a r set o f t r i m c o i l cu r ren ts in order to repa i r measured e r r o r s in the average f i e l d as a f u n c t i o n o f r a d i u s . The computer f i l e s t ha t were used in running TRIMFIT are g iven in t h i s s e c t i o n . a) E (1,422) conta ins the code f o r the program TRIMFIT. b) F (100,199) conta ins the program which generates the changes in the average f i e l d caused by the t r i m c o i l s . I t s use is i l l u s t r a t e d in the sample TRIMFIT run included in t h i s s e c t i o n . c) F(200,299) g ives the average f i e l d changes caused by a change in the main c o i l e x c i t a t i o n of one amp- turn . d) F ( l , 3 8 ) conta ins two isochronous f i e l d s w i t h a d i f f e r e n t 500 MeV r a d i u s . The f i r s t 19 l i n e s con ta in a f i e l d w i t h the 500 MeV radius at 311 i n . , whereas the l a s t 19 l i n e s g ive a f i e l d w i t h t h i s radius a t 307 i n . e) A t y p i c a l TRIMFIT run is then g i v e n . Before the TRIMFIT code is a c t u a l l y en te red , the small computer program shown in the output is used to help set up the TRIMFIT input g r i d s . o o o o o o o o o o o o © © © © © ILIS 6(1,422) 1 IMPLICIT P.EAL*8(A-H,0-Z)  2 REAL*8 MNDIVR 3 DIMENSION BI (200),BE I 200),BTR(200,70),WT(200),CM INI 70) ,CMAX(70) _. -_-4_ _ ... l,A(70.,70).,AINVaO,J.0),C.(JJJJ.,U(JO!.,l.(X<l)-,aBXW(200)_,ja.U0) . _• . 5 2 , i-iCCIIL ( 70 ) ,NCOIL (70 ) ,T6TKl 200,70) 6 COMMON/P/A , C D , BTR, B I , DBI W,WT, CM I N, CMA X , DR , CUWA I T , DET , COND i RT , 7 Iftt.CWAIT,JR, I , NT ,MC ,NT1 ,NRM IN, NRMAX, MC FREE, L IM , I EL AG , LGPLOT  8 CUMMDN/C/TRDIVR,MNDIVR,SCALE 9 COMMON/MAT E X P/JE XP 10 1000..F0RMAT(.2I5,4.F10.5,4I5/4F10...5,3.1.5) __ 11 1005 FORMAT(1215) 12 1010 FORMAT(3 F10.5) 13 1015 FORMAT I BF10 .5 )  14 1030 F0RMATI2F1O.5) 15 1040 FORMAT(/////1 TRIM COIL 1,15,' IS BELOW ITS MINIMUM CURRENT:-1 ,F10 . . 16 . ._. 1.5,' SO SET . A T ZERO , 101 '****«• ) )_ 17 1050 FORMAT!/////1 TRIM COIL 1,15,' IS ABUVE ITS MAXIMUM C U R R E N T F 1 0 . 18 15,' SO SET AT MAXIMUM ',10(•*****•)) 19 1060 FURMAT(///// 1 LIMIT ON ITERATIONS REACHED, WITH COIL', 15,' STILL 0 20 1UTSIDE CURRENT LIMITS ',10(•*****•)) 21 1U70 FORMAT(//////' EXECUTION COMPLETED') 22 ._ .1080 FURHAT (/////• MATRIX DETERMINANT IS Z ERO _' ,JOJ.1 ***** 1 ) ).. 2 3 READ (5, 1000) JR ,NT , RM IM ,Ht'.AX , OR , COWAI T , L IM, MAT R I X , KPR I NT , M C F R E " E , 24 1TKUIVR,MNDIVR,SCALE,RELWT,LGPLOT,ITER,NPARLL 25 lFINPARLL.LE.O) GO TO 7  26 READ(5,1005)((MCuIL(J),NCUIL(J)),J=1,NPARLL) 27 C LIM = MAXIMUM NUMBER OF CYCLES PERMITTED 28 C PUT MATRIX. = 1 TO PRINT OUT. MATH IX .A AND VECTOR. D . EVERY. CYCLE . 29 C OTHERWISE POT MATRIX = 0 30 C KPRINT = 0,1 OR 2 FOR DIFFERENT PRINT OPTIONS 31 C HCFB£B=1 IF MAIN COIL CURRENT IS Til BE A FREE VARIABLE  32 7 I.T1=NT + 1 3 3 ,MC=NT _._ .34 . READ(7,1015) ( R T ( J ) , J = 1,NT) ._ . . .. . . . . 35 READ(7,1015) (IBTRIJ,N),J=1,JR),N=1,NT) 36 C BTR(J,N) IS THE CONTRIBUTION TO THE AVERAGE FIELO AT 3 7 C RADIOS J DUE Tfl ONE A M P IN THE N 1 TH TRIM COIL  38 IF (MCFKEE)2,2,1 39 1 MC=MT1 40 _ ._R£ADJ..7._,.1.015.)_.( BTRUR , N C. _).,. I R = 1., JR) .. ._ 41 C BTR(IP.,NC) IS THE "INCREMENTAL MAIN CUIL FIELD" 42 2 REALMS,1010) I B I ( I R ) , BE ( I R ) , WT ( IR ) , I ft= 1, JR ) 43 CALL UNITS  44 C BI(IR) IS THE DESIRED ISOCHRONOUS AVERAGE FIELD AT RADIUS IR 45 C BE(IR) IS THE ACTUAL AVERAGE FIELD DUE TO THE MAIN COIL ALONE 46. . .;c AT THE POT SETTING CHOSEN . . 47 C WT(IR) IS THE RADIAL WEIGHTING USED IN THE LEAST SQUARES FIT, 48 C AND MAY BE SET PROPUkTIOMAL TO TORN DENSITY AT THAT POINT 49 MRMAX=M 1N0 ( JP., ID INT ( ( KM AX/PR ) +U. 5 ) )  50 NRMIN=IDI NT((RHIN/DR1+0.5) 51 4 IF(LIM) 6,6,5 .. . .52 .5 R'E AH (5 ,1030) . (.CM IN (.I.T.) , CM AX ( I T ) , I XH 1 ».N.T ) 53 C CHIN A N D CMAX ARE THE LIMITS O N THE TRIM COIL CURRENTS 54 C NOW CALCULATE THE MnTRIX A AND CALCULATE A PROVISIONAL SET OF 5 5 C TRIM COIL CURP.Fr.'TS C U T )  O O O o O o o o o o o o o o o o o o 56 6 IF(NPARLL.LE.O) GO TO' 8 57 DO 21 IR=NRHI.N,NRMAX 5 8 DO 21 J=1,NT 59 21 TBTRIIR,J)= 6TRIIK,J) 60 00 22 I 1=1,NPARLL 61 JJ=MCUIL(I I) -< 62 :-'.K = i'JCOIL ( I I ) 63 DO 22 L=NKMIN,NRMAX b'<___ _ DO 22 J = J J , K K . . . ' . O 65 DO 25 K = J.J,KK 66 I!: (K.EO.J ) GO TO 25 67 THTK ( L , . l ) =THTR( L , Jl+BTKl L, K)  6 8 25 CONTINUE 69 22 TBTRIL,J)=TBTR(L,J)/INCUIL( I Il-MCOIL( I I ) + l) 70 . .. DO 26 IR=NRMIN,NRMAX . _ . _ . .. . . . 71 DO 2 6 J=1,NT 72 26 BTR(IR,J)=TeTR(Ii;,J) 73 8 Oli 17 N = 1,MC  74 Mi. )=N 75 C I(M) 15 A "SUB If-i-.bX" AND 13 USE'. TO EXCLUDE FROM THE CALCULATIUM 76 _ ._C__ANY CURRENTS WHOSE VALUES HAVE BEEN FIXED AT CM IN OR CMAX. __ _ _ . _ _ . ._ _ 77 DO 15 H=N,NC 78 A(N,M)=0. 79 DO 111 1 R = NRM I M , NRM AX  80 10 4(M,«)-.A(N,rt)+ftTRI IK ,M|*ftTR< IR , M)*WTl IR) 8 1 15 A ( M , N ) = A ( N , H ) 82 _ 17 A(i.,N)=A(N,N>+CI. WAIT __ _ __ . . . '83 " IF IMCFREE.EO.O.) GO TO 18 * 84 AINC,NC)=A(NC,NC)- I RELWT*RELWT -1.)*CUWAIT/(RELWT*RELWT) 8 5 18 CONTINUE  86 DU 20 IR=NRMIN,NRMAX 87 20 DB IW(IR)=WT(IR)*(BI( IRl-BE(IR)) 88 IFLAG = 1 'B9 30 DO 40 N = l , N C ' " " - - - - - -90 C(I(N))=0. 9). !i(N)=0.  92 DO 40 1K=NRMIN,NRMAX 93 40 0(N)=D(Nl+DBIW(IR>*BTR(IR,I(N)) 94. DO 50 N=1,NC _. _ _ , _ _ .._ . _ 95 Dl I 50 M=1,NC 96 50 AINV(N,f-M=Air.!,M> 97 C A L L 0 T NV RT ( A I N V , NC , 7 0 , UE T , COND )  9 8 I F ( D E T . H Q . O ) W R I T E ( 6 , 1 0 S C ) 9 9 6 0 D O 7 0 N = 1 , N C 1 0 0 D O 7 0 M = l , N C . . 1 0 l ' 7 0 " "C ( I I N ) ) = C ( I ( N ) I +AINV (I. , M ) V D ( M ) 1 0 2 I F I I T E R . L E . O ) G O T O 7 5 1 0 3 C A L L 0 H E B Y ( N R M I N , N R M A X , H C , I , I T E R , C , W T , B T R , D B I W ) 104 GO T O 6 105 75 CUNTINUE 106 CALL PR I NT ( 2 AT R I X_) . 107 IF(LIM) 210,210,80 108 C SEE IF AMY CURRENTS ARE OUTSIDE THEIR LIMITS. 109 C IF SO FIND THE COIL FURTHEST OUT, NUMBER IKILL, AND SET IT TO IT'S LIMIT 110 80 KILL=0 111 CM=0. 112. I.O = NC-MCFREE 113" " NEXT=NC-1 114 00 100 N=1,ND 115 F,(l=nARS (C 1 I (N ) ) l-CMAX ( I (N ) ) o o Q 116 IF (CD-CM) 100,100,90 117 90 Cri=(".n 118 KILL=N 119 100 CUNTINUF. 120 IF (KILL) 110,110,150 121 110 CM = 0. 122 DO 130 N=1,N0 123 C:: = CMIW ( I (N ) )-DABS(C ( MM) ) ) _124 . . .IF (CD-CM.) j.30,i3u, 1.2.0 125 120 CH=CD 126 KILI.=N 127 130 CONTINUE 128 IF (KILL) 210,210,140 129 140 I KILL = I (KILL) ..130 . . ._.! F ( I F L A G . GE . I. I M ). .GO.TO. 200 131 C(IKILL1=0. 132 WRITE(6,1040) IKILL,CM IN(IKILL) 133 GO TO 170  134 150 IK I L I. = I (KILL) 135 IF < IFLAG.GE.LIM> GOTO 200 136 . C(IKILL)=DSH;N(CiiAX( I.KI.LL).,_C( IKILL ).) 137 WRITEI6,1050) IK i LL,CMAX( IKILL) 138 DO 160 IR-MRMIM,NRMAX 139 1 6 0 U D I W ( IR ) =DK 1W( I I . ) — C 1 IKI LL ) ~ - B T K I IR , 1 KI LL ) * W T ( I R ) 140 170 UL) lftu N=K ILL, NEXT 141 I (N) = l (M + l ) ..142 C RE LAB El. T N O P X I ( ) _ 143 C ELIMINATE ROW ANO COLUMN "IKILL" FROM MATRIX A 144 DU 180 M=1,NC 145 180 A(N,M)=A ( M + l ,H I  146 DO 190 N=l< ILL , NEXT 147 DO 190 M=l,NEXT 1.4 H ... . 190_A(M,M)=A(M,M+1) .. 149 NC = NF XT 150 IFLAC-=IFLAG+1 151 C RETURN TO LEAST SQUARES FITTING, WITH C(IKILL) AS A FIXED VARIABLE 152 GO TO 30 153 200 WRITE(6,1060) IKILL 154.. . 210 CONTINUE 155 CALL PKINT(KPRINT,0) 156 WRITE(6,1070) 157 STUB 156 END 159 SUBROUTINE PR I NT(KPRINT,MAT) .160 ..IMPLICIT .RE*X*8(A=U,rjL=Z.) 161 REALS8 LINED,LINEG 162 DI MENS ION BI(200),BE(200),BTR(200,70),WT(200),CM IN(70),CMAX(70), 163 1A (70,70 ) ,C (70).,D (70) ,D2 (70) ,D3(70) , I (70) , DBIWI 200) , DBFW I 200) , 164 2I1BF (200 ) .LINED (71) ,YD( 200) ,RT( 70) , DBFV( 200) ,OBUHPS ( 20U) ,OTSUM( 200) 165 3 ,«RTOT ( 200 1 , 0 LIM MY ( 200 ) , L I NCG ( 101) 166 . ... ._ COMMON / P/ A, C , Ll, BTR , B .1, OB I W_, WJ.jXUI N» CMAX ,.QR, CU HA I T , DE T, C GND , EX., 167 1SE,CWAIT,JR,I,NT,NC,MT1,NRMIN,NRMAX,MCFREE,LIM,IFLAG,LGPLOT 168 C 0 MM 0 N/M A T G X P/J E XP 169 1000 FORMAT('ILIMITS ON TRIM COIL CURRENTS (AMP TURNS) 1///  170 l'COIL MINIMUM MAX I MUM 1 / / ( I 5,6X,2F10.5) ) 171 1020 FORMAT( 11'/25X,'PRESENT MINUS',22X,'UNWEIGHTED ERROR 1,20X, ,172 1'WEIGHTED ERROR 1 / 2 5 X , 1 D E S I R E Li_ F I EL.!._' , 22X,'AFTER F I MA L 1 , 25 X_,.__ . 173 2'AFTER FINAL'/4X,'RADIUS',5X, 'WEIGHT' ,4X, ' INITIALLY' ,26X, 174 3' ITERATION 1,27X, ' ITERATION'//) 175 1010 FORMAT (' 1 '////// 101 ' ) , 'RtPETI TI LIN NUMBER ',I3,3X,  ( 176 H 0 ( ' * * * * * ' ) / / / / ' * * * * * * * * * * WEIGHT ON CURRENT IS ',E9.2, \ 177 2 i * * * * * * * * * * i / / / i DETERMINANT IS 1,E8. 1, 1 #(10** 1, 14 , ' ) '// 178 3'CONOITION NUMBER IS ',68.1) 179 10 30 FORMAT( ' 1 ' ,2X , 'COIL',9X,'COIL RADIUS 1,9X, 1 AMP-TURNS',26X, 180 I 1 8 1 l'BASE TEN LOG OF COIL CURRENTS'//49X,'-2 ****** -1 ******* 0', / ( 1 8 7 3' TRIM R M S ' , 2 3 X , F 1 0 . 3 , 7 X , 7 1 A 1 ) \ 183 1040 FORMAT(4X,12,10X.F7.1,10X,F10.3,7X.71A1) 164 1050 FORMA.T_( 2X , 1 MAIN,CO1 L„..22X., F 1 C _ . 3 ,_7X , 7 1A 1) _ . 185 _ " 1060 FORMAT! '1 VECTOR D MATRIX A ' / / i 186 10 70 FORMAT(F1U.5,10X ,1IF 10.5/(20X,11F10.5) ) 187 1UH0 FORMAT( 11 K.S. MATRIX EQUATION L.S. MATRIX EQUATION', 183 111X,'DIFFERENCE'//(4X,F15.8,8X,F15.8,10X.F15.8)) 189 1090 FORMAT{//20X, 'AVE. BUM P AftEA' ,6X,F10.5) 190 1100 FORMAT./60X, ' P A R T I A L SUM OVER ' . 2 OX , 'PARTIAL SUM_TO '/4X , ' RAD I US.' , 191 15X,'WEIGHT',4X,'NU. RUMP S', 26X , 1 LAST BUMP ' , 2 7X , 1 PRE S EI .T RADIUS'//) 192 1110 FORMAT( '1 ' , 15X, * PHASE SLIP ANALYSIS - LOOKING AT SUM OF ', 193 1'UNWEIGHTEO FIELD ERROR X RADIUS X DELTA RADIUS'/) 194 1120 FORMAT( '1>/2X,'COIL',2X,'COIL RADIUS' ,2 X,'AMP-TURNS *,25X,'COIL 1 , 195 1 ' CURRENTS IN UNITS OF HUNDREDS OF A M P - T U R N S ' / / 3 0 X , 1 0 ' , I X , 1 7 ( ' * ' ) , 196 21X, ' 1 ',1X,17( '*' ) ,IX,'2' ,IX,17( '*' ),IX,•3' ,IX,17! •*• ),IX,'4' ,1X, 197 317('* 1 ),IX, '5'/' TRIM RMS',10X,F9.3,2X,101A 1) 198 1130 FOKMATI3X,I2,4X,F7.1,3X,Fv.3,2X,101Al) 199 1140 FURMAT(IX, 1 MA IM C O IL ' ,9X,F9.3) 200 DATs DOT,STAR,PLUS,BE LOW,BLANK/'.','*1 ,' + ','-' , ' •/ 201 K=KPRIM7+1 20 2 DO 5 N = l , 7 1 203 5 Lii.ED(i<)=BL . ' .NI. 204 G O TO (10,30,60),K 205 10 IF (LIM) 30,30,20 20 6 20 WRITE(6, 1000) (IT ,CM IN(IT ) ,CMAX( IT),IT=1,NT) 207 30 WRITE(6,1020) 20 3 OS! 50 I K = ! . K . « I M , N R M A A 209 Bi.=0. 210 01) 40 N = ] ,NC 211 40 BR=BR+C(I ( N))*BTR(IR,I (N ) )*WT(IR) 212 DBF 11 (IR ) =DB IW ( IR )-BR 213 DBF ( IR )=DBFU( IR ) /',:T ( I R ) 214 50 DBF V ( IR ) =DBFW( I R ) /DSt.RT (WT t I R ) ) 215 CALL EKKOR(NRMIN,NRHAX,UR,WT,DSF,OBFV,BI,Dc) 216 ASIGN=DABS(DBF(NRMIN))/DBF(NRHIM) 217 BUMPS=1. 218 A INT=0. 219 RTOT=0. 220 TSUM=0. 2 2 1 DO 52 IR=NRi"iIN,NRMAX 222 KR=IR*[JR 223 O'l SUM ( ) R ) =0. 224 DUMMY(1R)=0. 225 AINT=AINT + DK*DABS( DBF (IK) ) * R R 226 227 RTOT=RT0T+DBF(IK)*DR*RR BS IG N = 0 A 8 S(DBF( IR) )/DBF( IR) - • - - " 228 IF(BSIGN.NE.ASIGN) QTSUM<IR-1 )=TSUH 229 TSUM = TSUM+DBF ( IR ) * L ) R * R R 230 IF(BSIGN.EO.ASIGN) GU TO 51 231 BUMPS=BUMPS+1. .232 2 33 AS IGN =B S I G N TSUM=DBF(IR)*OR*RR ..... 234 51 QBUMPS(IR)=BUMPS I 235 IF ( I R. EO. NRM AX ) IjTSUKI I R ) =TSUM -236 52 QRTUT ( I R ) =RTOT 237 AINT=AINT/BUMPS 238 WRITE(6,1110) 239 WRITE 16,1100) 240 CALL ERR0R(NRMIN,NRHAX,0R,HT,0TSUM,QRTOT,0BUMPS,DUMMY) 241 WRITE(6,1090) A1 NT 242 RETURN 243 60 WRITE(6,1010) IFLAG,CWAIT,DET,JEXPtCOND .244 7.0. .IF (MAT )91.i 91,81 , . . . O 245 81 WRITE(6,1060) 246 00 90 N=1,NC,5 247 90 WKITE(6,1070) 01N ) , (A(N,M),H =1,NC,5 )  240 91 IF(IFLAG.GT.l) GO TO 100 249 00 96 N=1,NC 250 ._ .. 92._ 03 (N)=0. .. , . . _ .. _. 251 U2(N)=0. • . 252 UU 95 M=1,NC 253 95 02 l.N ) =02 IN ) + A(N,M )*C ( 1 (M ) )  254 96 03(N)=02(N)-0(N) 2 5 5 WR I T E I 6 ,10 8 0 ) (f) ( N ) , D2 ( N ) , 03 ( N ) , H= 1, NC ) 256 .... .10p_ SQC = 0. 257 NM=NT+MCFREE 258 DO 61 N=1,NT 259 61 S0C=SOC+ (C IN )**2 )  260 R,-|SC = DSf.)RT ( SOC/NT ) 261 IF(LC-PLOT.NE.l) GO TO 02 .262. .__DUM = PLUG10(RMSC). 263 IF1DUM.GT.5.) DUH=5. 2 64 KPD=(DUM-:-2. )*10. + 1. 265 L IMEP ( KPD ) = S T A R 2 6 6 U R I T E ( 6 , 1 0 3 0 ) R M S C , L I N E D 2 6 7 L I N E D ( K P D ) = B L A N K 2 6 8 . D O 8 0 ...1 = 1 , N N 2 6 9 L I N E D ( 1 ) = D 0 T 2 7 0 L I N E D ! 1 1 ) = D ( J T 2 7 1 L I N E 0 ( 2 1 ) = S T A R  272 L I NED ( 31 ) = i)OT 273 LINED(41)= P 0 T 274 _ „ LINEI.X51 ) =D0T . 275 LINED(61)=DOT 276 LI NED(71)=DOT 277 YD ( J ) =DABS ( C ( J ) ) 273 YD(J)=DL0G10(YD(J)) 279 IF(YD(.) ) .LT.-2. ) YD(J)=-2. 280 _ 1 F (Y.O(J.) .GT.5 . ) YIMJ ) =5... . 2 81 KPI.)=( YD ( J ) +2 . )*10. + 1. 282 LINEn(KPD)=PLUS 203 IF(C(J).LT.O.) L1NEU(KPD)=BEL0W 284 IF(J.EU.NN.AND.MCFREE.EU.1) GO TO 76 205 WRITE (6 ,1040) J , RT ( J ) , C ( ,1) , L I NED 286 . . GO TO 78 . _ . _ . _.. 287 76 WRITE(6,1050) C1J),LINED 288 78 CONTINUE 289 80 LINED1KP0)=BLANK  290 RETURN 291 82 iFlRMSC.GT.500.) RMSC=5U0. 292 ..DO 140 .M = l , 101.. _ 293 140 LINED(N)=BLANK 294 KPI)=(RMSC/5. 1+1. 295 I- INFG (KPD ) =STAR  .296 WRITE (6 ,1120) RMSC,LINEG 29V 1. I NE G ( K PD ) = RL ANK 298 00 180 J=1,NN 299 LINER (l)=Dt.T 300 LINEG(21)=l)f)T < 301 LINEG(41)=DlTT 302 LINEG(61)=DOT 303 LINEG(81)=D0T 30'. LlNEG(101)=nnT 30 5 Y0(J)=DABS(C(J)) 306 IF(Y0(J) .GT.500.) YD(J)=500. • 307 KP0=(Y0(J)/5.>+1. 303 LINEG(KPU)=PLUS 309 IF (C (J ) .LT.O. ) LINEG(KP(D=BELOW 310 IFU.EQ.NN.ANO . MC FREE . E <1. 1,1. GO TO J.7.6 _ .._ 311 WRITE(6,1130) J , R T ( J ) , C ( J ),LINEG 312 GO TO 178 313 176 WR1TE(6,1140) C(J) 314 178 CONTI HOE 315 180 LIMEG(KPD)=BLANK 316 RETURN "317 END 318 SUB ROUT I ME E RROR 1 N I'.M IN , NRMAX , OR , C , OB F , OB F W , BAVO , BA VA ) 319 IMPL IC IT REAL*8 ( A-H,0-7_) 320 REAL * 8 L I.'. E A , L I N E B , L I i. E C 321 I) I MEMS ION C (200) ,DBF ( 200) , DBF'.. ( 200) , BAVOI 200) , BAVA ( 200) ,L INEA(21), 32 2 1L1NER (21 )_,L Ii-iEC .( 2 1) ,YA( 200 ) 323 DATA MOT , STAR. , BLANK, E D G E / 1 > 1 ',':'/ 324 10 FliRMAT(3X,F7.1,3X,F7.3,3X,F8.3,5X,21Al,lX,F9.4,5X,21Al, 1X.F9.4, 325 15 X , 2 1A 1 ) 326 15 FORMAT(/3X, 'RMS VALUES',45X,F9.5,27X,F9.5) 327 DHINA=0. 32 8 DMINB=0. . _ _ . _ -. _ 329 DMINC=0. 330 DMAXA=0. 331 I.MAXB=0. 332 DMA XC =0 . 333 S0W=O. 334 SU=0. . . . .. . .. . ... . . 335 DEN OM = i. R M A X-N R MIN +1 336 00 100 IR=NRMIN,NRMAX 337 S0W = SOW + DBFW(IR)*DBFWI IR) 33 8 100 S(0 = SQ+QBF ( IR )*0BF ( IR ) 339 R M S B W = D S Q R T ( S 0 W / U E N 0 M ) 340 _ KMSB=DSORT(SO/OENDM) 34 f DU 110 J=l,21 342 L INEA(J)=6LANK 343 LINEBIJ)=BLANK 344 110 L I NEC ( J ) =F.LAMK 345 OO 120 J=NI'<MIN,NRMAX 346 . YA(J)_='8AVD(J)-P-AVA(J) . , . 347 " IF(YA(J).GT.OMAXA) DMAXA=YA(J) 340 IF(YA(J).LT.DM IN A) DMINA=YA(J) 349 IF (DBF ( J ) .GT.DMAXP) DM AX B = DBF 1 .)) 350 IF ( DBF ( J ) .LT .DMINB) DM I NB = DBF ( .1 ) 351 IF (DOFW( J ) .GT.DMAXC ) l.l>1AXC = 0I.F W ( J ) 352 1.2.0 IF(OBFW(J).LT.DM INC) DMINC = DBFW(J) 3 53 KIA = - 2 0 . * 0 M IN A / ( D M A X A- D M I N A ) + 1. 3 54 KZB=-20.*UMINB/(OMAX B-DMIN B)+1. 355 KZC=-20.*0MINC/(DM AX C-OMINC) + 1. -' 356 DO 130 ,I=H|PHIN.NRMAX 357 LINEA(1) = E D G F 358 LINER(1)=EDGE 359 L INEC(1)=EDGE 3 60 LINEA(21)=EDGE . 361 L1NEB(21)=EDGE / 362 LINEC(21)=E0GL= N 363 LINEA(K ZA)=00T . .364 LINFB(K/B)=D0T 365 L INEC (KZC)=DOT 366 KPA=20.*<YA(J1-DMINAI/(DMAXA-DMINA)+1. 367 KPB=20 .S(DBF IJ)-DM I MB)/(DMAXB-DMINB) + 1. 3 68 K PC = 20.*(DBFW(J) - D M INC)/(OHAXC-DMINC) + 1. 369 L INEA (KPA)= S TAR 3 7 0 . . . L INE B (K PB) = S T AR . . . . _. . . .. ... . ... . ... 371 L INEC(KPC)= STAR 372 RAD=J*DR 373 WRITE (6 , 10 ) RAD . C ( J ) , Y A ( .1 ) , L I ME A, DB F ( J I , L I ME B , DBFW ( J ) , L INEC 374 LINEA(KPA)=BLANK 375 LINEB (KP 1:1) =BLANK _ . . 376 .130 L INEC (KPC) =BLANK . .... ._ ... . . . . . . 3 7 7 WRITE (6,15) R,-iSb,RMSBW 3 78 RETURN 379 E N D 3 80 SubKOU'flNE UNITS 38 1 IHP L I C I T R EA L *8(A-H,0-Z ) 3 82 R I T A L * K MND I V R _ . . . - ... 3 83 Mil-1 EN S I U N B 1 ( 2 0 0 ) , B E ! 20u ) , BTR ( 200, 701 , WT( 200 ) , CHIN* 70 ) , C M A X ( 70 ) , 3 84 1 A ( 7 0 , 7 0 ) , A I H V ( 7 0 , 7 0 ) , C ( 7 0 ) ,D ( 7 0 ) , I ( 7 0 ) , D B I V M 200),RT(70) 3 85 COMMON/P/A,C , D , B T R , B I ,DBIW,WT,CM IN,CMAX,DR,CUWAIT,DET,COND,RT, 3 86 1BE,CWAIT,UR,I,NT,NC,NT 1,NRM IN,NRMAX,MCFREE,LIM,I FLAG,LGPLOT 3 87 Cul-il-iON/C/TRD IVR, M N D IVR , SCALE . 3 88 DU 10 J«1,MT . . _ _ _ _„ .... . ._ 389 0 0 10 L=1,JR 3 90 10 B T R ( 1 . , J ) = B T R ( L , J ) / (TROIVK*SCALE> 391 IFIMCFREE.EO.U) GO TO 30 3 92 DO 20 L=1,JR 393 20 B T R ( L , N T + 1 ) = B T R ( L ,NT+1)/(MND IVR*SCALE) 394 30. ..CONTINUE. .. . ... . 395 CWAIT=CUWAIT 396 CUWAIT=CUHAIT/(TRDIVR*SCALE*TRDIVR*SCALE) 397 RETURN 398 END 399 SUB ROUT INE CHEBY(NRHIN,NRMAX,NC,I,ITER,C,WT,BTR,DBIW) 400.. Ii.RI IT. I T RFAI *8(A-H.O-7 ) . . . . . . . . 401 DIMENSION C(70),WT(200) ,B T R (200,70),DBIWI200), I (70),DBFWf 200) 402 D A T A I M I T / I / 40 3 I I H T = I N I T * 2 404 0 0 50 I R = N R M I N , N R M A X 40 5 BR = 0 . . . 406 DU 40 N = l ,NC - . .... .... ... 407 40 B R = BR+C ( I ( N ) ) * B T R ( I p. , I (N ) )*WT ( IR) 408 DuFW(Ik)=UBIW(IR1 -BK 409 50 DBF1/,1 ( IR ) =DBFW ( IR ) /WT ( IR ) 410 D ENOM =NRMAX-N RMIM+1 411 SUl! =0 . .4-12 413 DO 100 II!=NKM IN , NRMAX 414 SQW=SOW+DBFW(IR)vD6FW(IR) I 415 100 SU=SO+WT(IR)*WT( IR) 3U3~ u < ' 416 RM3fi..'=DS(.RT ( SQ'.!/DENOM ) 417 RMS8=DSQRT(SO/DENOM) 418 ' DU 110 IR=MRMIN,NRMAX 419 110 WT(IR1= ((DABS(DBFW(IR))>**INIT)*RMSB/RMSBW 420 ITER = ITER-1 42) RETURN o ; o o 422 END END OF FILE o i o SCOP *SKIP o o o o 1 1 O ; o . . . . ... O ; o O ; ° o :j o I o 1 - - - - - • • - -- - . . . . . . .... . . . ... . . . o © o a . . . . . . . . . . _ . . o o o © © _.. ... ._ ... - - o o o o o o o o o s o o o SLIS F(100,199) 100  DIMENSION BTKI300.60),RT160) 101 F (X)=0.3 55*(EXP (-ABS(X/( B*C) ) ) )* ( TANHl X/B)-D) 102 READ(5,1000) NR,NT,RMIN,DR .103. READ (5 ..11.00) .1 RI11 ) , I.= 1 ,.NT > 104 1000 F0RMAT(2I5,2F10.5) 105 1100 FORMATI8F10.5) _LQ6 DO 10 1=1.NT  10 7 108 .109 . . 109.025 C 110 111  R=RT(I) 6=3.6+390.0/R C=0.147*R-4.2 C=.124*R D=O.59-O.O0128*R DO 10 J=I,NR  112 113 113.025 114 115 116 X = RM IN + I J - l >*DR BTR(J,I)=F(X-R) .WRITE (7,1100) (RT.U.) > 1 = 11 NT) WRITE(7,1100) ((BTR(J.I),J=1,NR),I=1,NT) STOP END END OF FILE SCOP *SKIP 126 -O 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 O O O O m m o i ^ i M m co ro O r - o> o xi o-* rvj LA ' O N '3 s 1 CM c\j t\j CM CM 0 0 o o.o- o co -o o <t -n co r- r-j o x m x 3D i n . vO m LTi LA oi f - ^ fM' CM CM CM) f\J CM O O O O O O H K I T - 0 N CT1 CC' J - <J- CM CM IT. i A . 0 t— C" . v CM CM CM CM CM (TI O O Q O C : O CM 0 \ CM CM O c o * O o r - m c r x-i n ' C i co •—1 ; CM CM iMi rM CM cn O o cj O O O O O O O O O • O CO 3 O 1 1—l \ r-i -o 1— " CM' r - r-1 o -j- c •c m o r - <JJ CM CM CM CM : M r n 0 c c l o c c 0 0 q o c i 0 0 o o o c LL O • o • LO CM 1 co r-i m r- m o •O : A m —1 LP -4_ C 1 m i cn CT" i n r~ ••O- •—< >o CM cn 4* i n I A %o o o •; 0 0 0 -a CM <- CO CM J - CO O 0 r-, i n cn i n c r 0 CM CD >r :<"v O r-H m i 0 -0 —: r~ m vj- s+| m i n -0 r- CO", O O O O 0 0 O 0 O i f > f O O - ^ H 3 vf IT. CP t \ ' NO r e cc 01 ' j - i n o i n cr* m cn - r - j - <j- m -c o o c . o c i cc -J- m <? -x so cr cr- i r . o r-i CM «C 'm m 0 - i i <T v t •4" i n *0 O O o ! O O O H m r - ' cc i n i p m 1—it—i 0 CM r - r- c <_'•> O : X -4' rn rn <(• i n 0 0 0 0 0 : •C -3* -O CC CM CM CM --O r— O Cr a ; —t i r , t-i m o ^- L> p-, cti r n cr m rn. - t . j - i n m o c • o c —1 :<•) •„*>, O O £ O C cn ~ ''C cc CM sO o -0 ff' -•j- cc cn r - CM cn m <r -t m u | O O O O s f c~' O • 0 0 0 0 0 • co a> o r-i CM D O C ^ (M CM CM, CM r\, • 0 CM m o t-J CM o r-, 33 m LC\ ^ h 2 0 0 0 cn f—' O O 3 I M o r -cn CP >C ' 0 N m ^j* i n LL c^ : CM CM O O O O 0 O Q Q O @ O © © o © © © © SLIS F.1.38) 1 0. 3.0289 3.0306 3.0323 3.03395 3 .03602 3.03911 3 .05116 3.06719 3.09003 3.12069 ,03757 ,03833 ,05302 ,06993 , 09'. 14 .12584 03968 03991 05 5_16_ 07290 09793 13093 3.04193 3.04258 ,3.05728_ 3.07 60 3 3.10226 3.13589 3.04353 3.04513 _3_. 05949 3.07932 3. 10679 3. 14148 3.04350 3.04745 ..3.06178 . 3.08277 3.11142 3.14741 ,04160 .04947 ,06445 ,08605 ,11608 ,15344 9 10. 11 12 13 3.15953 3.20593 3 .26199-3.33441 3.42036 3 .52424 3.16543 3.21320 3.2V 099. 3.34655 3.43381 3.54017 3. 17 1.83 3.22041 3.2S062 3 .35829' 3.44821 3 .5574 8 3.17843 3. 22803 3.29117 3. 37036-3.46179 3.57529 3.18483 3.23630 .3.30142 3.38256 3.47652 3.592S2 3.19174 3.24378 3 .31259. 3.39509 3.49117 3.61173 1987S 25239 32369 . 40849 50717 3.63034 14 15 16 17" 18 19 3 .64 979 3 . HO 112 .3 .98595 '4.20992 4 .49719 4.79151 3.67045 3.82529 4.01486 4.24634 4.54223 4.84367 ,6.8938 ,85098 ,04657_ .28 316 .59125 3.71149 3.87565 4.07812 4.32 337 4.6 37 20 3.73363 3.90211 4.10838. 4.36251' 4.67744 3.75449 3.93014 4.14234 4 . 'h026 8 4.71429 3.77831 3.95767 4.17598 4.45007 4.75002 20 21 22 23 24 25 2.99621 2 .99902 3.01053 3 .02579 3.04760 2.99772 2.99820 3.01229 3.02840 3.05153 2.99977 2.99971 3.01433 3.03124 3.05514 .9890 2 3.00196 3.00229 3.01635 3.03422 3.05929 ,9913 2. 3.00350 3.00476 3.01845 3.03737 3.06363 9926 2 3.00344 3.00699 3.02062 3.04067 3.06806 .9942 3.00153 3.00892 3.02317 3.04378 3.07251 26 27 23 29 30 31 ,07691 ,11406 ,15837 ,21185 " ,28103 ,36296 3.08185 3.11974 3. 1.6531 3.22045 3.29263 3 .37576 3.O0671 3.12581 3. 17218. 3.22984 3.30384 3.38947 09145 13212 17944 23973 31535 40237 3.09679 3.13822 3.18735 3.24953 3.32697 3.41638 3.10246 3.14482 3.19445. 3.26021 3.33891 3.43030 3.10824 3.15155 3.20260 3.27081 3.35169 3.44552 32 33 34 3 5 36 37 3 .46178 3.58091 3 .72396. 3.89785 4.10 707 4.37340 3 .47689 3 .60049 .3,74 6 74 3.92494 4.14096 4.41482 3.49334 3.6 1836 3.77 100 3.95470 4.17513 4.45990 3.510 27 3.63931 3.79419 3.98 42 3 4.21251 4.50186 3.52689 3.66027 3.81910 4.01243 4.24873 4.538 11 3.54484 3.67992 3.. 84549, 4.04417 4.28584 4.57089 3.56247 3.70245 ,3.87132. 4.07552 4.32981 4.60241 38 END OF FILE 4.63933 4.68623 SCOP *SKIP xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx 17:54 :14 11-19-70 UNIVERSITY OF 9 C COMPUTING CENTRE MTS(ANIZO) RES NO. 774388 o « « « » « « . « • » « * « » * • * * » * THIS JOB SUBMITTED THROUGH FRONT DESK READER * « * » » * * » » * * * * * * « * * * « $SIG TRLF T=100 P=60 PRIC=H *«l AST SIGMON WAS: 17 :52 :43 11-19-70  USER " T R L f " SIGNED ON AT 1 7 : 5 4 : 1 6 ON 11-19-70 *RIN *FOR TRAN SCAROS=F( 100,199 I SFHNCH = -H -EXECUTION BEGINS . . FORTRAN IV G COMPILER MA IN 11- 15-70 17.54 :21 PAGE 0 0 0 1 0 0 0 1 0 0 0 2 0003 ooo DIPENSICN BTf t (300 , 6 O I , R T ( 6 0 > F ( X ) = 0 . 35 5 * ( E X P ( - A B S ( X / ( B * C I > 11 *< TANH ( X /B >-D> R F - D ( 5 , 1 0 0 0 > NR.NT,RMIN,DR R S . O t ? - . 1 1 0 0 1 ( R T ( H , I = 1 . N T )  O 0 0 0 5 0 0 0 6 0 0 0 7 , 0 0 0 8 0 0 0 ° ooio 1000 FORMAT! 21 5 , 2 F 1 0 . 5 I 1100 F Q R K A T I 8 F 1 0 . 5 ) 00 10 _I_=1.,.NT R=R T ( I I B = 3 . 6 + 3 9 0 . 0 / R C = 0 . 1 4 7 * R - 4 . 2 0 0 1 1 . 0 0 1 2 0 0 1 3 0 0 1 4 0 0 1 5 C = . 1 2 4 * R 0 = 0 . 5 9 - 0 . O 0 1 2 8 » R DO 10. J = l ,NR X=RMIN'<-( J - l ) *0R 10 R T f M J , I ) = F ( X - R ( MR I TE( 7 . 1 1 0 0 1 (RT( I I .1 =1 ,NT) 0 0 1 6 0 0 1 7 0 0 1 8 WRITE ( 7 , 1 1 0 0 ) I ( B T R U , I ) . J= 1 , N R > , I = 1.NT> STOP END TCTAL ."EMORY REQUIREMENTS 011EBA BYTES COMPILE TIME 1.0 SECCNDS O O : I o i i O ! o O O O E X E C U T I O N T E R M I N A T E D U O o o o c o o «RUN -B 5 * « S 0 U R C E » 7 = - T R A T E X E C U T I O N BEG INS S T O P 0 E X E C U T I O N T E R M I N A T E D J R I I N * F C R T R A N S C A R C S = * S C U P C E * S P U N C H = - A E X E C U T I O N B E G I N S . . _ _ i.O i i i " j e ! ° i o I I © I o ' o o n.oc O o o o Q o o o o o o. o ( J o o F O R T R A N I V G C O M P I L E R M A I N 1 1 - 1 9 - 7 0 1 7 : 5 4 : 3 8 PAGE 0 0 0 1 0 0 0 1 0 0 0 ? 0 0 0 3 0 0 0 4 O I C E N S I C N H A V E ( 1 5 0 ) . W A N T ! 1 5 0 1 , WT( 1 5 0 1 , F ( 1 5 0 1 D I M E N S I O N C M I N ( I O O ) , C M A X ( 1 0 0 ) , M C 0 1 L ( 1 0 0 ) , N C C I L ( 1 0 0 ) R E A L M N O I V R J R = 1 2 P  0 0 0 5 0 0 0 f t 0 0 0 7 0 0 0 8 0 0 0 ° 0 0 1 0 N T = 3 6 RM I N = 12 . 5 _ R M A X = 3 ] 5_,_ L G P L O T = 0 I T E R = 0 N P A R L I = 0 0 0 1 1 0R = 2 . 5 0 0 1 2 C U W A I T = . 0 0 1 0 0 1 3 L l r > = 0 0 0 1 4 M A T R I X = 0 0 0 1 5 K P R I N T = 0 C 0 1 6 MC- F KE E = 1 0 0 1 7 T R D I V R = 2 0 0 1 8 P N D I V R = 1 2 o o i " ; S C A l . E = ? 0 , _ . _ 0 0 2 0 R E l W T = ? C 0 0 0 2 1 WR I T F ( 4 , 1 0 ) J R , N T , R M I N , R M A X » O R , C U W A I T I T P O I V K . M N O t V R , S C A L E . R E L X T . L G P L O T , I T E R L I M , M A T R I X , K P R I N T , M C F R E E , . N P A R L L 0 0 2 2 1 0 F O R M A T ( 2 I 5 , 4 F 1 0 . 5 , 4 I 5 / 4 F 1 0 . 5 . 3 I 5 ) 0 0 2 3 R E A D ( 5 , 2 0 ) ( H A V E ( I ) , 1 = 1 , 1 2 8 ) 0 0 ? 4 R E A D ! S ? O I ( W A N T U 1 , 1 = 1 , 1 2 8 1 0 0 2 5 0 0 4 3 1 = 1 , 1 2 8 0 C 2 6 K AVE ( I ) =HAVF. ( I ) * 1 0 0 0 . * 5 . / 3 . 8 7 5 0 0 2 7 4 3 W A N T ( I ) = W A N T ( 1 ) * 1 0 0 0 . * 5 . 1 3 . 8 7 5 0 0 2 8 F I E L 0 = R A N O N ( 1 . 1 * . 4 1 6 6 7 0 0 2 9 W A N T ( 1 ) = W A N T ( 1 I * F I E L O 0 0 3 0 F ( l ) = F l F l . n 0 0 3 1 HO 4 1 1 = 3 , 1 2 8 , 2 0 0 3 2 F ! E L 0 = F I E L D + P A N D N I O . ) * . 4 1 6 6 7 0 0 3 3 4 1 F ( I 1= F I EL D 0 0 3 4 DO 4 2 1 = 2 , 1 2 6 , 2 0 0 3 5 4 2 F ( I ) = ( F ( [ - 1 I + F I U l ) 1 / 2 . 0 0 3 6 0 0 4 5 1 = 2 . 1 2 7 C C 3 7 4 5 W A N T ( I 1 = W A N T ( I ) * f ( I ) 0 0 3 8 0 0 4 0 1 = 1 , 1 2 8 0 0 3 9 W T ( I 1=2 . 5 * 1 / 3 2 0 . 0 0 4 0 4 0 K R I T E ( 4 , 5 0 1 H A V E ( I 1 , W A N T ( I I , W T ( I ) 0 0 4 1 RE A C ( 7 , 1 1 0 1 ( C M A X( I ) , 1 = 1 , N T ) 0 0 4 2 n o F T P M A T ( R F 1 0 . 5 ) 0 0 4 3 DO 4 7 1 = 1 , N T 0 0 4 4 CM I N I 1 ) = 0 . 0 0 4 5 CMAX ( I l = C A X ( 1 1 0 0 4 6 4 7 W R I T F ( 4 , 5 l ) C K I N( I I , C M A X ( I ) 0 0 4 7 5 1 F O R M A T I 2 F 1 0 . 5 ) 0 0 4 6 _ 2 0 _ F 0 P M A T I 7 F 1 1 . 5 ) 0 0 4 9 5 0 F O R ^ A T I 3 F 1 0 . 5 ) 0 0 5 0 END T O T A L MEMORY R E Q U I R E M E N T S 0 0 1 5 B 6 B Y T E S C C K P . I L E-_T_IME_=_ _1.8_SECaNDS_ Q E X E C U T I O N T E R M I N A T E D $ R U N - A 4 = - D R A T 5 = F ( I . 9 S ) 7 = » S 0 U R C E « E X E C U T I O N B E G I N S . . . S T C P C . _ _ E X E C U T I O N T E R M I N A T E D 2 4 0 . 2 4 0 . 3 6 0 . 3 6 0 . I N V A L I C COMMAND '. . _ I R O N F I 4 2 3 I 5 - - D R A T 7 = - T R A T + F ( 2 0 0 . 2 9 9 ) E X E C U T I O N B E G I N S 3 6 0 . 3 6 0 . 3 6 0 . 3 6 0 . o ! o ' nop . . O O o o o i o ; o I o o o '. o o o o * * • * « * « * « * » * * * * » * » » » * * » « * * * * * * * * * * * * • • • » * » • • • * « * » « R f ; p _ j | T I O N NUMBER 1 » » • * • * * » * * » « » • * * » « * • • * « * * » * » * * * « • * * * » » * » » * * • * * • * « * * * * * * * * * * * WEIGHT ON CURRENT IS 0 . 1 0 D - 0 2 * * * * * * * * * * D E T E R M I N A N T IS 0 . 6 C - 0 3 * I 1 0 * * - 1 5 0 ) C O N D I T I O N NUMBER I S O . J D C« f R . S . MATRIX EQUATION L . S . MATRIX EQUATION DIFFERENCE o • o 1.31771931 0.09920428 -0.12458344 0.C7969415 1.31771931 0.CS920428 -0.12459844 0.C7969415 -0.00000000 - 0 . OOOOOOOO 0.OOOOOOOO -0.00000000 J J o f 0.55494775 1 . 1 7964408 1 .88665744 0 . 55494775 1 .17964408 1 . H8665744 -c .oooocooo -0.00000000 -0.00000000 \ o 2.6303R879 3.37955613 4.C7819706 2.63038879 3.37955613 4. C 78 19706 - c . cooooooo -o.oooooooo -0.00000000 G o 4.65965638 5.C8403092 5. 29857322 4.6596563R 5.0 84 03 092 5.2SE57322 - 0 . oooocooo -0.00000000 -0.oooooooo t _ o 5 .24733140 5.10806456 4.59609830 5.2 47 33140 5. 1C806456 4.596C9830 0.00000000 0.00000000 0.cooooooo Q o 4.20574843 3.10734782 2 .37350788 4 .20574843 3. 1C734782 2.3735C788 o.oooooooo 0.oooooooo 0.cooooooo o c C.46338980 -0 .72859043 -3 .70233001 0.46333980 - 0 . 72858043 -3 .70233001 0.cooooooo 0.oooooooo c.oooocooo Q o - 5 . 53094026 -7 .62261323 _-9.57572483 -5.53094026 -7.62261323 -9.57572483 0 .oooooooo 0 . oooooooo o.oooooooo 0 o -11.73596329 -14 .12167811 -16.75947648 -11.73596329 - 1 4 . 1 2 1 6 7 8 1 ! - 1 6 . 7 5 9 4 7 6 4 e 0.00000000 0. OOOOOOOO 0.00000000 o o -19.68847617 - 2 2 . 9 3 529722 -26.52742234 - 1 9 . 68847617 -22.93529722 -26.52742234 0.OOOOOOOO C. OOOOOOOO 0.OOOOOOOO o © -30.49645146 -33.95756636 - 3 7 . 64533261 -30.49645146 -33.95756636 -37.64533261 c • cooooooo c.cooooooo 0.00000000 o -41.30986447 -44.05980960 . . ... .15 . 06744220 - 4 1 . 3C986447 -44.G59 80960 15.06744220 C.oooooooo 0.oooooooo -0.00000000 o © o © 0 © o o o © o © 0 © > o © o C O I L C O I L R A O I U S A M P - T U R N S C O I L C U R R E N T S I N U N I T S O F H U N D R E O S O F A M P - T U R N S T R I M R M S 1 1 4 . 0 0 * * * * * * * * * * * * * * * * * x * * * * * * * * * * * * * * * * * 2 * * * * * * * * * * * * * * * * * 3 * * * * * * * * * * * * * * * * * 4 < . * » * * » « * * » » » « » * * • 5 1 9 2 . 1 7 6 » 2 4 3 . 1 : 7 5 o 2 0 . 5 3 3 . 5 4 6 . 5 5 9 . 5 7 2 . 5 3 1 6 , - 1 2 3 . . . . . 1 . 9 4 , 2 , J _ 2 8 0 0 ? 3 6 4 0 _ 6 5 7 7 8 7 8 <} 1 0 9 8 . 5 ' 1 1 1 . 5 1 2 4 . 5 - 9 8 . 4 4 7 - 7 8 . 8 1 3 - 6 6 . 9 7 2 • • 1 1 1 2 1 3 1 3 7 . 5 1 5 0 . 5 1 6 3 . 5 - 1 6 7 . 6 7 C - 1 6 1 . 1 7 2 - 1 8 6 . 0 7 4 • -• 1 4 1 5 1 6 1 7 6 . 0 1 8 2 . 0 _ _ - 1 9 4 . 0 _ _ 2 9 . c.60 - 1 4 2 . 4 4 5 . - 4 0 . 5 6 4 - * 1 7 1 8 1 9 2 0 0 . 0 2 1 2 . 0 2 1 8 . 0 - 2 0 . 6 5 7 - 7 1 . 2 1 5 8 1 . 9 4 4 * 2 0 2 1 . 2 2 2 3 0 . 0 2 3 6 . 0 2 4 8 . 0 - 1 0 3 . 0 9 0 1 4 1 . 3 0 9 1 0 2 . 1 9 9 + 2 3 2 4 2 5 2 5 4 . 0 2 6 0 . 0 2 6 5 . 0 1 9 2 . 9 6 6 5 3 . 4 7 4 1 4 8 . 5 3 5 + • + • . * 2 6 2 7 - 2 8 2 7 0 . 0 2 7 5 . 0 2 8 0 . 0 1 9 4 . 5 8 4 - 5 . 6 5 3 4 3 6 . 7 6 9 • • • + * 2 9 3 0 3 1 2 8 5 . 0 2 9 0 . 0 2 9 5 . 0 1 1 7 . 0 1 8 2 7 5 . 6 9 5 2 9 5 . 9 3 5 + _ 3 2 3 3 . 3 4 3 0 0 . 0 3 0 4 . 0 3 0 8 . 0 1 4 5 . 7 0 6 4 1 6 . 8 1 8 _ 2 1 8 . 3 1 1 -+ + _ + 3 5 3 6 M A I N 3 1 2 . 0 3 1 6 . 0 C O I L 2 2 5 . 3 4 6 3 7 4 . 6 9 9 5 2 4 8 1 . 5 8 4 • + ... J o o o o o o o o c o o o o o PRESENT MINUS UNWEIGHTEO ERROR WEIGHTED ERROR OESIREC F I E L D AFTER FINAL AFTER F I N A L RADIUS WEIGHT I N I T I A L L Y ITERATION ITERATION > / 1 2 . 5 0 . 0 3 9 5 C . 4 9 7 * : - 1 . 1 0 3 0 * . : - 0 . 2 1 8 0 4 1 5 . 0 0 . 0 4 7 5 1 . 0 0 8 * - 0 . 1 3 4 4 * . : - 0 . 0 2 9 1 : 4. 17...5. 0 . 055 5 1 . 0 6 8 # : 0 . 1 1 0 7 .* 0 . 0 2 5 9 .4 2 0 . C 0 . 0 6 3 5 1 . 0 0 2 * 0 . 2 0 5 6 . 4 : 0 . 0 5 1 4 . 4 2 2 . 5 0 . 0 7 0 5 0 . 9 1 0 * - 0 . 0 8 7 1 4 . - 0 . 0 2 3 1 4. 2 5 . C 0. 078 5 1 . 1 7 6 * 0 . 0 1 3 7 : 4 0 . 0 0 3 8 4 2 7 . 5 0 . 0 8 6 5 1 . 4 3 9 4 0. 0982 .* 0 . 0 2 8 8 : .4 3 0 . C 0 . 0 9 4 5 1 . 4 2 1 * : 0 . 0 0 6 3 4 0 . C019 4 . . 3 2 . 5 0 . 1 0 2 . 5 1 . 3 6 4 . * - 0 . 1 0 8 9 4 - 0 . 0 3 4 7 4. 3 5 . 0 0 . 1 0 9 5 1 . 4 0 9 * 0 . 1 2 2 2 .* 0 . 0 4 04 .* 3 7 . 5 0. 117 5 1 . 4 6 3 •* 0 . 3 6 6 5 4 0 . 1 2 5 5 * 4 0 . 0 0 . 1 2 5 5 1 . 0 8 0 * 0. 1 3 5 7 .4 0 . 0 4 8 0 : . * 4 2 . 5 • 0 . 1 3 3 5 0 . 7 3 1 * - 0 . 1 5 1 3 4 - 0 . C 5 5 1 4 . 4 5 . 0 0 . 1 4 1 5 0 . 738 * - 0 . 0 9 4 9 4 - 0 . 0 3 5 6 4. 4 7 .5 . . 0 . 1 4 8 _ 5 0 . 7 3 2 . _ _. 4 - 0 . 1350 4 - 0 . 0 5 2 0 4 . 5 0 . C 0. 1 56 5 0 . 8 4 3 * - 0 . 0 7 5 8 4 - 0 . 0 2 9 9 4. 5 2 . 5 0 . 1 6 4 5 0 . 9 5 6 * - 0 . 1 01 7 * - 0 . 0 4 1 2 4. 5 5 . 0 0 . 1 7 2 51 . 2 2 7 * - 0 . 0 0 3 1 *. - 0 . 0 0 1 3 4 5 7 . 5 0 . 1 8 0 5 1 . 5 2 4 * 0 . 0 3 0 6 4 0 . 0 1 3 0 4 6 0 . 0 0 . 1 8 8 5 1 . 1 1 5 * 0 . 1 1 9 9 .4 0 . 0 5 1 9 . 4 6 2 . 5 0. 195 . _ . . .52. 3C 7 .. _ * 0 . 1 5 3 4 . .. ._*_.. 0 . 0678 . 4 6 5 . 0 0 . 2 0 3 5 2 . 5 9 8 * 0. 1301 .* 0 . 0 5 8 6 . 4 6 7 . 5 0 . 2 1 1 5 2 . 9 0 4 * 0 . 1 4 2 6 . 4 0 . 0 6 5 5 . 4 7 0 . 0 0 . 2 1 9 5 2 . 8 7 4 * - 0 . 1 4 0 6 4 - 0 . 0 6 5 7 4 . 7 2 . 5 0 . 2 2 7 5 2 . 8 4 4 * - 0 . 4 1 8 6 * - 0 . 1 9 9 2 4 7 5 . 0 0 . 234 5 3 . 4 1 7 * - 0 . 0 7 5 7 4 - 0 . 0 3 6 7 : 4. . . . . . 7 7 , 5 . 0 . 2 4 2 5 3 . 9 9 0 . . 4 0 . 2 6 0 8 . 4 0 . 1 2 8 4 4 8 0 . C 0 . 2 5 0 5 4 . 0 5 1 4 0 . 0 8 5 9 . 4 : 0 . 0 4 2 9 : . * 8 2 . 5 0 . 2 5 8 5 4 . 1 0 1 4 - 0 . 1 1 9 6 4 . - 0 . 0 6 0 7 4 . 8 5 . 0 0 . 2 6 6 5 4 . 4 8 3 4 0 . 0 0 7 3 4 0 . 0 0 3 8 8 7 . 5 0 . 273 5 4 . 890 4 0 . 1 4 5 5 .* Q . 0 7 6 1 : . * 9 0 . 0 0 . 28 1 5 5 . 0 0 2 4 : 0 . 0 2 5 1 4 0 . 0 1 3 3 — 9 2 . 5 0 . 2 8 9 5 5 . 1 33__ . 4 - 0 . 0 4 4 2 4. : . . . - 0 . 0 2 3 7 j_ 4 . 9 5 . C 0. 297 5 5 . 2 2 2 4 - 0 . 0 8 3 4 4 . - 0 . 0455 4 . 9 7 . 5 0 . 3 0 5 5 5 . 3 0 2 * - 0 . 0942 : 4 - 0 . 0 5 2 0 4 . 1 0 0 . 0 0. 31 3 5 5 . 4 8 8 4 0 . 0 6 3 0 4 : 0 . 0 3 5 2 : .* 1 0 2 . 5 0 . 3 20 5 5 . 6 8 7 4 : 0 . 1 5 5 4 . » o . o a B o 4 1 0 5 . 0 0 . 3 2 8 5 5 . 7 6 7 4 0 . 0 8 9 7 . 4 : 0 . 0 5 1 4 : . 4 _ 1 0 7 . 5 0 . .336. 5 5 . 849 , 4 - 0 . 0 5 8 0 4. - 0 . 0 3 3 6 4. 1 1 0 . 0 0 . 3 4 4 5 6 . 0 8 7 4 - 0 . 0 2 7 7 4. - 0 . 0 1 6 3 4. 1 1 2 . 5 0. 352 5 6 . 3 51 4 - 0 . 0 3 0 8 4. : - 0 . 0 1 8 3 : *. 1 1 5 . 0 0 . 3 5 9 5 6 . 522 4 : - 0 . 1 4 6 6 4 • - 0 . 0 8 7 9 4 1 1 7 . 5 0 . 3 6 7 5 6 . 7 3 4 4 - 0 . 3 5 6 1 : 4 : - 0 . 2 1 5 8 : 4 1 2 0 . 0 0. 375 5 7 . 554 4 0 . 0 2 6 2 4 0 . 0 1 6 1 : . 4 1 2 2 . 5 _. . . . 0 . 3 8 3 5 8 . 3 6 1 , 4 0 . 3332 4 : 0 . 2 0 6 2 4 1 2 5 . 0 0 . 3 9 1 5 8 . 7 9 3 4 0 . 3 0 3 8 * 0 . 1 8 9 9 : . 4 1 2 7 . 5 0 . 398 5 9 . 2 2 4 4 : 0 . 2060 . 4 0 . 1 3 0 0 * 1 3 0 . 0 ' 0 . 4 0 6 5 9 . 4 2 7 4 - 0 . 1 2 2 2 : 4 : - 0 . 0 7 7 9 : 4 . 1 3 2 . 5 0 . 4 1 4 5 5 . 642 4 - 0 . 4 6 1 7 . 4 - 0 . 2 9 7 1 4 1 3 5 . 0 0 . 4 2 2 6 0 . 3 3 8 4 - 0 . 1 8 7 1 : 4 - 0 . 1 2 1 5 * 1 3 7 . 5 0.<t3 0_ 6 1 . 0 5 2 • 4 0 . 1 6 6 9 . 4 0 . 1094 4 1 4 0 . 0 • 0 . 4 3 8 6 1 . 5 3 3 4 : 0 . 3 3 1 7 4 0 . 2 1 9 4 • 4 142 . 5 0 . 4 4 5 6 2 . 0 4 3 4 : 0 . 3 5 6 0 4 : 0 . 2 3 7 5 : 4 1 4 5 . 0 0 . 4 5 3 6 2 . 2 1 6 4 : - 0 . 0 2 2 4 ». : - 0 . 0 1 5 0 4. '• J u o o o o o o o o o o o o •u D J XOTC" , 1 f 1 4 7 . 5 0 . 4 6 1 6 2 . 3 9 8 - 0 . 4 0 1 3 * - 0 . 2 7 2 4 * 1 5 0 . 0 0 . 4 6 9 6 2 . 9 9 2 - 0 . 2 5 2 8 : * • : - 0 . 1 7 3 1 1 5 2 . 5 0 . 4 7 7 6 3 . 5 F 2 * - 0 . 1 0 2 9 * - 0 . 0 7 1 0 : * 1 5 5 . 0 0 . 4 8 4 6 4 . 3 4 0 * : 0 . 1 2 0 1 . * 0 . 0 8 3 6 : * 1 5 7 . 5 0 . 4 9 2 6 5 . 0 9 0 * 0 . 2 2 8 6 . * : C . 1 6 0 4 : * 1 6 0 . 0 0 . 5 0 0 6 5 . 4 3 4 * - 0 . 0 1 8 4 * - 0 . 0 1 3 0 / > 1 6 2 . 5 0 . 5 0 8 6 5 . 7 3 8 * - 0 . 1 6 7 8 * - 0 . 1 1 9 6 * , 1 6 5 . 0 0 . 5 1 6 6 6 . 3 7 9 * 0 . 0 9 6 8 .* 0 . 0 6 9 5 : * _ _ 1 6 7 . 5 0 . 5 2 3 ._ 6 7 . 0 4 3 . . * : 0 . 2 4 3 8 . *_ C . 1 7 6 4 * 1 7 0 . 0 0 . 5 3 1 6 7 . 6 C 5 * 0 . 0 5 9 2 * : 0 . 0 4 3 1 * 1 7 2 . 5 0 . 5 3 9 6 8 . 2 2 3 * - 0 . 2 2 6 0 * - 0 . 1 6 5 9 * 1 7 5 . 0 0 . 5 4 7 6 9 . 2 5 0 * - 0 . 1 6 8 6 * - 0 . 1 2 4 7 * , 1 7 7 . 5 0 . 5 5 5 7 0 . 2 7 3 * - 0 . 0 3 4 5 * - 0 . 0 2 5 7 : * 1 B 0 . 0 0 . 5 6 3 7 1 . 0 2 7 » 0 . 0 1 5 0 0 . 0 1 1 2 _ 1 8 2 . 5 _ 0 . 5 7 0 7 1 . 7 7 0 * 0 . 2 5 1 6 „. * . C . 1 9 0 0 * 1 8 5 . 0 0 . 5 7 8 7 2 . 1 2 5 * 0 . 1 0 9 9 0 . 0 8 3 6 : * : 1 8 7 . 5 0 . 5 8 6 7 2 . 5 1 2 - 0 . 1 3 3 8 4 - 0 . 1 0 2 4 * 1 9 0 . 0 0 . 5 9 4 7 3 . 3 2 0 * - 0 . 0 6 1 7 * - 0 . 0 4 7 6 : * , 1 9 2 . 5 0 . 6 0 2 7 4 . 1 6 4 * 0 . 0 0 9 8 * 0 . 0 0 7 6 1 9 5 . 0 0 . 6 0 9 7 4 . 6 2 4 « - 0 . 0 9 0 4 • - C . 0 7 0 6 • 1 , 9 7 . 5 0 . 6 17 7 5 . 5 5 1 * _ - 0 . 1 6 3 7 » - 0 . 1 2 8 6 * 2 0 0 . 0 C . 6 2 5 7 6 . 6 7 2 ft 0 . 1 2 8 0 0 . 1 0 1 2 • 2 0 2 . 5 0 . 6 3 3 7 7 . 7 6 5 * 0 . 3 3 8 8 * 0 . 2 6 9 5 : 2 0 5 . 0 0 . 6 4 1 7 8 . 4 4 5 * 0 . 0 7 7 0 0 . 0 6 1 7 * 2 0 7 . 5 G. 6 4 8 7 5 . 1 2 9 * - 0 . 1 9 8 5 * - 0 . 1 5 9 8 * 2 1 0 . 0 0 . 6 5 6 8 0 . 0 6 6 * - 0 . 1 6 4 8 • - 0 . 1 3 3 5 . . 2 1 2 . 5 2 1 5 . 0 „ . 0 . 6 6 4 0 . 6 7 2 _ _ . . 8 1 . 0 4 3 • 8 2 . 3 0 1 if * , _ _ - 0 . 1 2 3 7 0 . 0 8 3 6 * - C . 1 0 0 8 0 . 0 6 8 5 .*_,., * 2 1 7 . 5 0 . 6 8 0 8 3 . 6 1 3 * 0 . 0 8 6 5 0 . 0 7 1 4 * 2 2 0 . 0 0 . 6 8 8 8 4 . 9 5 2 * 0 . 0 5 4 7 » 0 . 0 4 5 3 * 2 2 2 . 5 0 . 6 9 5 8 6 . 4 1 4 * 0 . 0 9 7 3 0 . 0 8 1 2 * 2 2 5 . 0 0 . 7 0 3 8 7 . 4 4 1 * - 0 . 0 9 4 7 - 0 . 0 7 9 4 • _ 2 2 7 . 5 . 0 . 7 1 1 _ _ 8 8 . 4 5 2 . * - 0 . 1 3 1 7 * - 0 . 1 1 10 * 2 3 0 . 0 0 . 7 1 9 8 9 . 6 2 9 * 0 . 0 1 3 2 * 0 . 0 1 1 2 2 3 2 . 5 0 . 7 2 7 9 0 . P 6 3 * 0 . 1 0 3 4 0 . 0 8 8 2 * 2 3 5 . 0 0 . 7 3 4 9 2 . 3 0 5 * 0 . 0 5 7 0 * 0 . 0 4 8 8 , * 2 3 7 . 5 0 . 7 4 2 9 3 . 8 6 7 * - 0 . 1 2 3 B : * - 0 . 1 0 6 7 2 4 0 . 0 0 . 7 5 0 9 5 . 5 3 5 * : - 0 . 1 6 8 2 : * - 0 . 1 4 5 7 * 2 4 2 . 5 _ 0 . 7 5 8 9 7.2 3 8 * - 0 . 0 6 7 8 : * - 0 . 0 5 9 0 * 2 4 5 . C 0 . 7 6 6 5 9 . 1 C 5 * 0 . 1 6 0 4 . * 0 . 1 4 0 3 * 2 4 7 . 5 0 . 7 7 3 I C O . 5 8 4 » 0 . 2 4 4 5 . * 0 . 2 1 5 0 * 2 5 0 . C 0 . 7 8 1 1 0 2 . 7 8 9 * 0 . 0 3 8 1 * 0 . 0 3 3 6 ,* 2 5 2 . 5 0 . 7 8 9 1 0 4 . 6 4 1 * : - 0 . 2 7 2 7 : * • - 0 . 2 4 2 3 * 2 5 5 . 0 0 . 7 9 7 1 0 7 . 0 7 4 * - 0 . 1 1 5 3 : • : - 0 . 1 0 2 9 * 2 5 7 , 5 0 . 8 0 5 1 0 9 . 5 5 4 * 0 . 2 4 5 3 . * 0 . 2 2 0 0 *__ 2 6 0 . 0 0 . 8 1 3 1 1 1 . 4 1 8 * 0 . 0 4 1 4 * 0 . 0 3 7 3 .* 2 6 2 . 5 C . 8 2 0 1 1 3 . 3 1 6 * - 0 . 1 2 4 2 : » • - 0 . 1 1 2 5 * 2 6 5 . 0 0 . 8 2 R 1 1 5 . 6 8 4 * : 0 . 0 0 0 5 * 0 . 0 0 0 5 2 6 7 . 5 0 . 8 3 6 1 1 8 . 1 4 1 * 0 . 0 1 7 1 * : 0 . 0 1 5 6 ,* 2 7 0 . 0 0 . 8 4 4 1 2 0 . 6 C 5 * - 0 . 0 1 7 8 : - 0 . 0 1 6 4 * 2 7 2 . 5 _ 0 . 8 5 2 1 2 3 . 1 5 6 * 0 . 0 6 5 5 « 0 . 0 6 0 5 , * 2 7 5 . 0 0 . 8 5 9 1 2 5 . 5 2 7 * 0 . 0 4 5 2 0 . 0 4 1 9 2 7 7 . 5 0 . 8 6 7 1 2 8 . 0 5 8 * : - 0 . 1 9 6 2 : * - 0 . 1 8 2 7 * 2 8 0 . 0 0 . 8 7 5 1 3 1 . 7 9 7 * 0 . 0 6 3 7 « : 0 . 0 5 9 6 2e2. 5 0 . 8 8 3 1 3 5 . 6 3 3 * 0 . 1 2 3 1 : 0 . 1 1 5 6 * 2 8 5 . 0 0 . 8 9 1 1 3 8 . 9 6 5 * - 0 . 0 5 7 0 : » - 0 . 0 5 3 f t * 2 8 7 . 5 0 . 8 9 R 1 4 2 . 4 5 7 * - 0 . 0 9 1 0 : # . . . - 0 . 0 8 6 3 . .. * 2 9 0 . 0 0 . 9 0 6 1 4 6 . 3 2 8 * : 0 . 0 8 9 9 0 . 0 8 5 5 * 2 9 2 . 5 0 . 9 1 4 1 5 0 . 3 2 0 * 0 . 0 2 4 5 * : 0 . 0 2 3 4 2 9 5 . 0 0 . 9 2 2 1 5 4 . 3 2 4 * - 0 . 1 1 3 1 * - 0 . 1 0 8 5 * o o o f 2 9 7 . 5 0 . 9 3 0 3 0 0 . 0 0 . 9 3 8 3 0 2 . 5 0 . 9 4 5 3 0 5 . 0 0 . 9 5 3 3 0 7 . 5 0 . 9 6 1 b 3 1 0 . 0 0 . 9 6 9 1 5 8 . 7 9 3 1 6 3 . 2 1 1 1 6 7 . 7 5 0 1 7 3 . 2 5 8 1 7 8 . 8 4 4 1 8 3 . 9 8 4 • * * * « * 0 . 0 5 U 0 . 1 3 6 6 : - 0 . 2 0 4 4 0 . 0 2 0 5 0 . 1 2 9 5 - 0 . 0 0 8 5 * * . * .* *. 0 . 0 4 9 3 0 . 1 3 2 3 - 0 . 1 9 8 8 C . 0 2 0 0 0 . 1 2 6 9 - 0 . 0 0 8 4 . * * * * \ J o ' 3 1 2 . 5 0 . 9 7 7 3 1 5 . 0 0 . 9 8 4 1 8 9 . 2 4 2 1 9 4 . 6 6 3 * - 0 . 1 4 9 3 * 0 . 1 0 1 2 * , : .» - 0 . 1 4 7 6 0 . 1 0 0 4 : * * R M S V A L U E S 0 . 1 8 8 5 2 0 . 1 1 0 8 3 o o o o c o o o G o O o O o O © O © O : © © ; o © ! © i o 1 ' O • © o , © o , o >- J o j P H A S E S L I P A N A L Y S I S L O O K I N G A T SUM OF U N W E I G H T E D F I E L D E R R O R X R A D I U S X D E L T A R A D I U S P A R T I A L SUM O V E R P A R T I A L SUM TO R A D I U S W E I G H T N O . B U M P S - L A S T BUMP P R E S E N T R A D I U S r 1 2 . 5 0 . 0 3 9 1 . 0 0 0 * 0 . 0 * - 3 4 . 4 6 8 9 * . \ 1 5 . 0 0 . 0 4 7 1 . 0 0 0 * : - 3 9 . 5 0 9 5 - 3 9 . 5 0 9 5 * . 1 7 . 5 0 . 0 5 5 2 . 0 0 0 * 0 . 0 : * : - 3 4 . 6 6 7 3 * . 2 0 . 0 0 . 0 6 3 2 . 0 0 0 * 1 5 . 1 2 1 0 . * - 2 4 . 3 8 8 5 * . : 2 2 . 5 0 . 0 7 0 3 . 0 0 0 - 4 . 8 9 8 9 * - 2 9 . 2 8 7 4 « . i 2 5 . 0 0 . 0 7 8 4 . 0 0 0 .* 0 . 0 - 2 8 . 4 3 1 1 * . 2 7 . 5 0 . 0 8 6 4 . 0 0 0 ,« 0 . 0 * - 2 1 . 6 7 8 6 * . 3 0 . 0 0 . 0 9 4 4 . 0 0 0 . * 8 . 0 7 9 3 - 2 1 . 2 0 8 1 3 2 . 5 0 . 1 0 2 5 . 0 0 0 - 8 . 8 4 4 3 * - 3 0 . 0 5 2 4 » . : 3 5 . 0 0 . 1 0 9 6 . 0 0 0 0 . 0 * - 1 9 . 3 6 2 2 * . '• 3 7 . 5 0 . 1 1 7 6 . 0 0 0 0 . 0 * 1 4 . 9 9 6 9 : * 4 0 . 0 0 . 1 2 5 6 . 0 0 0 5 8 . 6 2 2 7 . * 2 8 . 5 7 0 4 4 2 . 5 0 . 1 3 3 7 . 0 0 0 . * 0 . 0 * 1 2 . 4 9 7 1 * 4 5 . 0 0 . 1 4 1 _ 7 . 0 0 0 . * 0 . 0 * 1 . 8 1 8 3 • * : " ^ 4 7 . 5~ 0 . 1 4 8 7 . 0 0 0 0 . 0 * - 1 4 . 2 1 6 0 5 0 . 0 0 . 1 5 6 7 . 0 0 0 0 . 0 - 2 3 . 6 8 5 0 5 2 . 5 0 . 1 6 4 7 . 0 0 0 . » 0 . 0 - 3 7 . 0 3 7 1 5 5 . 0 0 . 1 7 2 7 . 0 0 0 - 6 6 . 0 3 3 7 * . - 3 7 . 4 6 3 3 * , 5 7 . 5 0 . 1 8 0 8 . 0 0 0 0 . 0 * - 3 3 . 0 6 8 1 * . : 6 0 . 0 0 . 1 8 8 8 . 0 0 0 * 0 . 0 * - 1 5 . 0 8 4 2 : *. 6 2 . 5 0 . 1 9 5 8 . 0 0 0 . * 0 . 0 : * 8 . 8 9 1 3 6 5 . 0 0 . 2 0 3 8 . 0 0 0 . * 0 . 0 : * 3 0 . 0 2 8 4 .* 6 7 . 5 0 . 2 1 1 8 . 0 0 0 . * 9 1 . 5 5 2 2 . * 5 4 . 0 8 8 9 * 7 0 . 0 0 . 2 1 9 9 . 0 0 0 . » 0 . 0 : * 2 9 . 4 8 8 3 . * 7 2 . 5 0 . 2 2 7 5 . 0 0 0 0 . 0 * - 4 6 . 3 8 3 0 * . 7 5 . 0 0 . 2 3 4 9 . 0 0 0 _ - 1 1 4 . 67_4_6__ - 6 0 . 5 8 5 7 * . 7 7 . 5 0 . 2 4 2 1 0 . 0 0 0 . * 0 . 0 : * : - 1 0 . 0 4 7 0 : *. 8 0 . 0 0 . 2 5 0 1 0 . 0 0 0 * 6 7 . 7 1 2 4 . * 7 . 1 2 6 7 8 2 . 5 0 . 2 5 8 1 1 . 0 0 0 . * - 2 4 . 6 6 4 3 - 1 7 . 5 3 7 6 8 5 . 0 0 . 2 6 6 1 2 . 0 0 0 * 0 . 0 * - 1 5 . 9 7 5 9 : *. 8 7 . 5 0 . 2 7 3 1 2 . 0 0 0 . * 0 . 0 : * 1 5 . 8 4 1 5 9 0 . 0 0 . 2 R 1 _ . 1 2 . 0 0 0 * 3 9 . 0 1 8 3 : . * : 2 1 . 4 8 0 7 9 2 . 5 0 . 2 8 9 1 3 . 0 0 0 . * 0 . 0 * 1 1 . 2 6 7 2 9 5 . 0 0 . 2 9 7 1 3 . 0 0 0 * 0 . 0 : * - 8 . 5 4 6 7 9 7 . 5 0 . 3 0 5 1 3 . 0 0 0 - 5 2 . 9 7 7 9 . - 3 1 . 4 9 7 2 : * . 1 0 0 . 0 0 . 3 1 3 1 4 . 0 0 0 0 . 0 ; * - 1 5 . 7 3 9 0 *. 1 0 2 . 5 0 . 3 2 0 1 4 . 0 0 0 . * 0 . 0 : * : 2 4 . 0 8 8 5 1 0 5 . 0 0 . 3 2 8 1 4 . 0 0 0 _ . * 7 9 . 1 3 9 1 * 4 7 . 6 4 1 8 . * 1 0 7 . 5 0 . 3 3 6 1 5 . 0 0 0 0 . 0 : * : 3 2 . 0 4 5 3 1 1 0 . 0 0 . 3 4 4 1 5 . 0 0 0 * 0 . 0 * : 2 4 . 4 2 0 6 : . * 1 1 2 . 5 0 . 3 5 2 1 5 . 0 0 0 . * 0 . 0 : * 1 5 . 7 5 7 5 1 1 5 . 0 0 . 3 5 9 1 5 . 0 0 0 0 . 0 : * : - 2 6 . 3 7 9 5 : * . 1 1 7 . 5 0 . 3 6 7 1 5 . COO . * - 1 7 8 . 6 3 0 0 * - 1 3 0 . 9 8 8 2 :* 1 2 0 . 0 0 . 3 7 5 1 6 . 0 0 0 * 0 . 0 : * : - 1 2 3 . 1 1 3 2 * 1 2 2 . 5 0 . 3 8 3 1 6 . 0 0 0 * 0 . 0 * - 2 1 . 0 7 3 0 1 2 5 . 0 0 . 3 9 1 1 6 . O C O 0 . 0 : * 7 3 . 8 7 2 9 * 1 2 7 . 5 0 . 3 9 8 1 6 . 0 0 0 . * 2 7 0 . 5 2 7 2 : . * : 1 3 9 . 5 3 9 0 . * 1 3 0 . 0 0 . 4 0 6 1 7 . 0 0 0 . * 0 . 0 * 9 9 . 8 1 8 8 * 1 3 2 . 5 0 . 4 1 4 1 7 . 0 0 0 * : 0 . 0 : * : - 5 3 . 1 0 6 9 * 1 3 5 . 0 0 . 4 2 2 1 7 . 0 0 0 - 2 5 5 . 7 9 0 6 :* - 1 1 6 . 2 5 1 6 . : * 1 3 7 . 5 0 . 4 3 0 1 8 . 0 0 0 : 0 . 0 : * - 5 8 . 8 7 5 4 * . 1 4 0 . 0 0 . 4 3 8 1 8 . 0 0 0 * 0 . 0 : * : 5 7 . 2 2 5 0 : . * ... 1 4 2 . 5 0 . 4 4 5 1 8 . OCO * 3 0 0 . 2 8 8 1 : . * : 1 8 4 . 0 3 6 4 . * ; o 1 4 5 . 0 1 4 7 . 5 1 5 0 . 0 1 5 2 . 5 1 5 5 . 0 0 . 4 5 3 0 . 4 6 1 0 . 4 6 9 0 . 4 7 7 0 . 4 8 4 1 9 . 0 0 0 1 9 . 0 0 0 1 9 . 0 0 0 1 9 . 0 0 0 2 0 . 0 0 0 0 . 0 0 . 0 0 . 0 - 2 9 0 . 0 8 2 0 0 . 0 1 3 6 . 5 4 4 7 r t 6 0 . o C. 5 0 0 2 1 . 0 0 0 o.o * 2 3 . 1 5 5 2 * s 1 6 2 . 5 0 . 5 0 8 2 1 . 0 0 0 - 7 5 . 5 2 7 5 • - 4 5 . 0 2 8 4 : • o . . . 1 6 5 . C 0 . 5 1 6 2 2 . 0 0 0 * : 0 . 0 * - 5 . 1 1 2 4 * 1 6 7 . 5 0 . 5 2 3 2 2 . O C O . * 0 . 0 9 6 . 9 8 2 5 * o 1 7 0 . 0 1 7 2 . 5 0 . 5 3 1 0 . 5 3 9 2 2 . 0 0 0 2 3 . 0 0 0 1 6 7 . 1 6 1 9 0 . 0 * * 1 2 2 . 1 3 3 5 2 4 . 6 9 0 5 * * 1 7 5 . 0 0 . 5 4 7 2 3 . 0 0 0 * 0 . 0 * - 4 9 . 0 7 8 4 : * o 1 7 7 . 5 0 . 5 5 5 2 3 . 0 0 0 . * - 1 8 6 . 5 0 0 6 * - 6 4 . 3 6 7 1 * . 1 8 0 . 0 . . . . 0 . 5 6 3 . _ 2 4 . O C O * 0 . 0 * - 5 7 . 6 3 5 3 : * . 1 8 2 . 5 0 . 5 7 0 2 4 . 0 0 0 0 . 0 5 7 . 1 6 3 5 * o 1 8 5 . 0 0 . 5 7 8 2 4 . 0 0 0 . * 1 7 2 . 3 6 8 9 • * 1 0 8 . 0 0 1 9 * 1 8 7 . 5 0 . 5 8 6 2 5 . 0 0 0 , * 0 . 0 * 4 5 . 2 7 3 6 * 1 9 0 . 0 0 . 5 9 4 2 5 . 0 0 0 ' . * - 9 2 . 0 4 0 4 * 1 5 . 9 6 1 5 19 2 . 5 0 . 6 0 2 2 6 . 0 0 0 4 . 7 3 0 3 * 2 0 . 6 9 1 8 : * o 1 9 5 . 0 0 . 6 0 9 2 7 . 0 0 0 * 0 . 0 * - 2 3 . 3 6 6 5 * 1 9 7 . 5 0 . 6 1 7 2 7 . 0 0 0 * - 1 2 4 . 8 8 6 6 * • - 1 0 4 . 1 9 4 8 * Q 2 0 0 . 0 2 0 2 . 5 0 . 6 2 5 0 . 6 3 3 2 8 . 0 0 0 2 6 . O C O * 0 . 0 0 . 0 « * - 4 0 . 1 7 3 9 1 3 1 . 3 1 9 5 * * 2 0 5 . 0 0 . 6 4 1 2 8 . C 0 C 2 7 4 . 9 9 2 9 * 1 7 0 . 7 Q 8 1 » o 2 0 7 . 5 0 . 6 4 8 2 9 . 0 0 0 * 0 . 0 * 6 7 . 8 3 2 0 * 2 1 0 . 0 _ 0 . 6 5 6 2 9 . 0 0 0 . * 0 . 0 * - 1 8 . 6 9 7 1 * 2 1 2 . 5 0 . 6 6 4 29.000 * - 2 5 5 . 2 2 7 4 * • . - 8 4 . 4 2 9 3 * o 2 1 5 . C 0 . 6 7 2 3 0 . COO * 0 . 0 * - 3 9 . 4 9 3 9 * 2 1 7 . 5 0 . 6 8 0 3 0 . 0 0 0 * 0 . 0 * 7 . 5 6 5 4 2 2 C . 0 0 . 6 8 8 3 0 . 0 0 0 . * 0 . 0 * 3 7 . 6 3 7 1 « 2 2 2 . 5 0 . 6 9 5 3 0 . 0 0 0 * 1 7 6 . 2 1 1 4 • * 9 1 . 7 8 2 2 * o 2 2 5 . 0 . 0 . 7 0 3 3 1 . 0 0 0 . _ * 0 . 0 * : 3 8 . 4 8 5 7 , * 2 2 7 . 5 0 . 7 1 1 3 1 . 0 0 0 . * - 1 2 R . 1 7 3 7 * • : - 3 6 . 3 9 1 5 • © 2 3 0 . 0 0 . 7 1 9 3 2 . 0 0 0 , * 0 . 0 * - 2 8 . 7 9 6 7 * 2 3 2 . 5 0 . 7 2 7 3 2 . 0 0 0 * 0 . 0 * 3 1 . 3 3 2 6 ,* 2 3 5 . 0 0 . 7 3 4 3 2 . 0 0 0 . * : 1 0 1 . 2 0 3 9 * 6 4 . 8 1 2 4 * © 2 3 7 . 5 2,4 0 . C 0 . 7 4 2 0 . 7 5 0 3 3 . 0 0 0 3 3 . 0 0 0 . * 0 . 0 0 . 0 * * : - 8 . 6 9 9 1 : - 1 0 9 . 6 2 C 7 * • * 2 4 2 . 5 0 . 7 5 8 3 3 . C O O . * - 2 1 5 . 51 7 4 * - 1 5 0 . 7 0 5 0 * 2 4 5 . C 0 . 7 6 6 3 4 . 0 0 0 . * 0 . 0 » : - 5 2 . 4 8 6 1 * 2 4 7 . 5 0 . 7 7 3 3 4 . 0 0 0 . * 0 . 0 * 9 8 . 8 0 4 2 * 2 5 0 . 0 0 . 7 8 1 3 4 . 0 0 0 , * 2 7 3 . 3 0 0 4 * : 1 2 2 . 5 9 5 4 , * © 2 5 2 . 5 2 5 5 . 0 _ 0 . 7 8 9 _ 0 , 7 9 7 3 5 . 000 3 5 . 0 0 0 * 0 . 0 - 2 4 5 . 6 5 3 1 * * - 4 9 . 5 7 7 8 : - 1 2 3 . 0 5 7 7 * * 2 5 7 . 5 0 . 8 0 5 3 6 . 0 0 0 * 0 . 0 3 4 . 8 4 9 6 • o 2 6 0 . 0 0 . 8 1 3 3 6 . 0 0 0 , * : 1 8 4 . 8 3 0 4 * 6 1 . 7 7 2 7 . * 2 6 2 . 5 C. 8 2 0 3 7 . 0 0 0 * - 8 1 . 5 1 1 3 * : - 1 9 . 7 3 8 6 : * 2 6 5 . 0 0 . 8 2 8 3 8 . OCO . * 0 . 0 * - 1 9 . 3 7 8 7 : * o 2 6 7 . 5 0 . 8 3 6 3 8 . 0 0 0 * 1 1 . 7 7 0 9 : - 7 . 9 6 7 7 * 2 7 C . 0 0 . 8 4 4 3 9 . OCO , * - 1 2 . 0 3 2 4 * : - 2 0 . 0 0 0 1 « 2 7 2 . 5 0 . 8 5 2 4 C . 0 0 C : 0 . 0 * 2 4 . 6 4 8 9 . * Q 2 7 5 . 0 0 . 8 5 9 4 0 . 0 0 0 7 5 . 7 5 5 5 * : 5 5 . 7 5 5 4 * 2 7 7 . 5 0 . 8 6 7 4 1 . 0 0 0 * : - 1 3 6 . 1 0 9 8 * • - 8 0 . 3 5 4 4 * Q 2 8 0 . 0 2 8 2 . 5 0 . 8 7 5 0 . 8 8 3 4 2 . 0 0 0 4 2 . 0 0 0 . * . * 0 . 0 : 1 3 1 . 4 9 9 7 * * : - 3 5 . 7 8 3 4 : 5 1 . 1 4 5 3 * * 2 8 5 . 0 0 . 8 9 1 _ . 4 3 . O C O * : 0 . 0 * 1 0 . 5 1 3 6 2 8 7 . 5 0 . 8 9 8 4 3 . 0 0 0 . * - 1 0 6 . 0 5 6 6 * : - 5 4 . 9 1 1 4 : * 2 9 0 . 0 0 . 9 0 6 4 4 . O C O . * : 0 . 0 1 0 . 2 3 3 9 O 2 9 2 . 5 0 . 9 1 4 4 4 . 0 0 0 * : B 3 . 0 3 1 6 • » : 2 8 . 1 2 0 2 J 1 7 5 . 9 3 4 2 2 7 . 9 7 1 2 - 6 6 . 8 1 9 7 - 1 0 6 . 0 4 5 6 - 5 9 . 5 1 7 5 3 0 . 4 9 9 1 u o c o Q o o o o o o o o o o o o 2 9 5 . 0 0 . 9 2 2 4 5 . 0 0 0 * : - 8 3 . 3 7 7 5 * . - 5 5 . 2 5 7 3 2 9 7 . 5 0 . 9 3 0 4 6 . 0 0 0 # : 0 . 0 * - 1 7 . 2 3 4 3 * . 3 0 0 . 0 0 . 9 3 8 4 6 . 0 0 0 « : 1 4 0 . 4 7 2 1 * 8 5 . 2 1 4 8 3 0 2 . 5 0 . 9 4 5 4 7 . 0 0 0 * : - 1 5 4 . 6 1 2 9 * . - 6 9 . 3 9 8 0 3 0 5 . 0 0 . 9 5 3 4 8 . 0 0 0 »: 0 . 0 * - 5 3 . 7 4 9 2 : * 3 0 7 . 5 0 . 9 6 1 4 8 . 0 0 0 *: 1 1 5 . 1 9 4 3 * 4 5 . 7 9 6 3 . * s 3 1 0 . 0 0 . 9 6 9 4 9 . 0 0 0 *: 0 . 0 * 3 9 . 1 8 3 3 . » 3 1 2 . 5 0 . 9 7 7 4 9 . 0 0 0 *: - 1 2 3 . 2 7 7 5 * - 7 7 . 4 8 1 2 * 3 1 5 . 0 „ _ _ _ 0 . 9 B 4 5 0 . 0 0 0 * 7 9 . 7 0 4 5 : 2 . 2 2 3 3 » RMS V A L U E S 9 4 . 9 0 9 7 2 6 3 . 3 0 6 5 7 O ' O , o o o , o ' o O ; O O O ' o: o o ! °! o o :o o , o o • o A V E . RUMP A R E A 1 2 2 . 3 0 8 8 8 E X E C U T I C N C C P P I E T E D S T O P 0 F X F C U T I 0 K T E R M I N A T E D * S I G 

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