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Preliminary design of transport systems for TRIUMF beam line I Tautz, M. F. Oct 31, 1968

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PRELIMINARY DESIGN OF TRANSPORT SYSTEMS FOR TRIUMF BEAM LINE I M. F. Tautz TRI-68-8 Physics Department University of Victoria October 1968 TABLE OF CONTID~TS 1. Introduction 2. Preliminary Extraction System 3. Identity Section Transport between Targets 4. Transport from Last Target to Neutron Irradiation Facility Appendix I - Calculation of Effect of Targets on Beam Appendix II - Tables and Figures - 1 -1. Introduction: This report deals with the design of a beam transport system for beam line I of the proposed "TRIUMF" cyclotron1• The general nature of the design requirements can be understood by examining Fig. 1. We see that the beam is to undergo dispersionless extraction and then to be focussed on up to three pion production targets located along the beam line before the neutron facility. The first target T1 will be at a distance of about 15 to 20 meters from the accelerator exit. The transmitted beam is again focussed on the second pion production target T2 approxim-ately 13 meters away and then on the third target T3 situated about another 13.0 meters down the beam line. The systems have been designed to accommodate thin targets at * T1 and T2 and either thin or thick targets at T3 • Finally this beam, which will have a large emittance due to its interaction with the targets, must be transported to the neutron irradiation facility. In this report three systems are described. Systems I-68~ and I-68-6 satisfy the above criteria with the neutron facility being at position A in Fig. 1. The essential difference between these two systems is the distance to the first target position. The target T1 shown * A "thin target" is 2 gm/cm2 of carbon, a "thick target" 20 gm/cm2 of carbon. - 2 -in Fig. 1 is at distance of 15.0 meters from the cyclotron exit for system I-68-4 and 19.5 meters for system I-68-6. The system I-68-5 is the same as I-68-4 except that the location of the neutron irradiation facility is at point B in Fig. 1. Although the presently planned position of the neutron facility is at A, the position B was considered and for completeness the design parameters for that trans-port system have been included in this report. A complete list of the drift lengths and magnet parameters for these systems is given in tables 1, 2, 3. These designs should be considered as first approximation systems since no calculations have been made of the focussing properties of the cyclotron fringe field and the combination magnet has not been included. In fact, a unit transformation matrix from the stripping foil to the first bending magnet of the extraction system has been assumed. When the fringe field calculations are available, the focussing properties can be accommodated by small adjustments in the first part of the transport system. The extraction system, and the rest of the design should be relatively unaffected. The design momentum for the three systems was taken to be the maximum design output beam of the acceler-ator 1.09 Gev/c, corresponding to 500. Mev protons. The systems will accept beams of other momentum by suitably - 3 -* scaling the magnet parameters (the positions of the elements need not be altered). However, since the foc-ussing properties of the fringe field will be a function of beam energy, the extraction system will have to be rematched separately for each energy. The design has included flexibility in the choice of target locations. This will permit the position of the targets to be chosen for optimum second pion beam of various types for the three experimental areas. 2. Preliminary Extraction System: As stated in the introduction the extraction system is incomplete since calculations for the first few elements (from the stripping foil through the combination magnet) have not been included. The present system consists of a 30° dispersionless bending system followed by a quad-rupole triplet which focusses the beam on the first target. The design £or the bending system was based on that given 2 by A. C. Paul • It consists of five quadrupoles situated between two 15°, constant field bending magnets. Other designs with fewer quadrupoles were investigated but it was felt that the extra flexibility of the five quadrupole system would probably be necessary to accommodate the variation in properties of the fringe field of the acceler-* Magnetic fields of the elements should be scaled in the same ratio as the momenta. - 4-ator magnet if an achromatic system were to be required at all the extracted energies. It may be seen from the transformation matrix components for the horizontal plane, given in table 4, that the system is effectively achromatic (T13 = T23 = 0.0) at any point after the second bending magnet, element 13. The quadrupole triplet was adjusted to produce a double waist at the location of the first target. This target position has not been fixed so that two designs were looked at covering the possible limits. In the first system, I-68-4, the target T1 was placed close to the entrance to experimental area Ia at about 15.0 meters from the cyclotron exit. For the other system, I-68-6, this distance is 19.5 meters. Although only a few cases were run it was felt there would be no problems in matching to target positions intermediate to the above ones. The phase space emittance used for the beam coming out of the cyclotron was taken from the TRIUMF Proposal and Cost Estimate.3 Reproducing the calculations given there, the estimated phase space area at 500. Mev for particles exiting the stripping foil is A= .064 rr in. mr. = .01616 ~em. rad 100 and hence the beam emittance is approximately E = A= .01616 em. rr rad 100 - 5 -The estimated maximum value of particle dis-I placement xm and slope xm is given for the horizontal plane as We assume this x = .11 em. m x~ = • 59 mr. initial ellipse is ax = 0.0 ~X = Xm = • 11 em. I • 59 Xm mr. upright and thus = 4-.73 em. rad/100 Yx = 1/~x = .211 rad/100 em. Similarly for the vertical plane the estimates given are and we obtain Ym = .28 em. y~ = .23 em. ay = 0.0 ~Y = 30.96 em. rad/100 y = .032 rad Y 100/cm. The beam envelopes shown in Fig. 2 for systems I-68-4- and I-68-6 were computed using the above values as input ellipse coefficients. In these figures the plotted - 6 -points occur at the exit of each element and they have been joined by straight lines. These envelopes are for a monochromatic beam, i.e. the relative momentum spread in the beam ~ is zero. However, the transformation matrix components giving the dispersion effect on position and slope, T13 and T23 respectively, (shown in table 4) for points between the bending magnets are small. For a momentum deviation of ± 5% the change in particle displace-ment due to the dispersion effects is less than .5 em. i.e. L'lxmax :; T13 ~ :; ( -78.3 em) C± • 005) = + . 391 em. p It is evident then, that the maximum beam displacement will always be less than 5.0 em. which is the upper limit for passage through 4 inch aperture quadrupoles and that in many places 3 inch quadrupoles will pass the -primary beam. The ellipse coefficients at the position of the first target, after element 21, can be read off tables 5, 6, 7, 8. These results are summarized below. System Plane a ~[ cm/rad] xm[cm] x'[ rad J 100 m 100 I-68-4 hor. 0.0 .283 .068 .239 vert. 0.0 .249 .063 .255 I-68-6 hor. 0.003 1.000 .127 .127 vert. 0.003 1 .001 .127 .127 The emittance in all cases above is equal to the input value .01616 em. rad. 100 - 7 -For both systems a double waist is produced at the first target location. For system I-68-6 the phase space ellipses in both planes are identical. Also the maximum particle slope is smaller than for system I-68-4 and allows for easier transport of the beam through the next section of the system. System I-68-6 seems to be preferable to system I-68-4 if the target position of the former, which is farther along the beam line, can be accommodated. The waist size for either plane is quite small and consideration of local heating in these targets may necessitate producing a more diffuse beam at T1 and T2• 3. Identity Section Transport between Targets 3.1 System Requirements As mentioned previously, the positions of the three pion production targets (labeled T1 , T2 and T3 in Fig. 1 ) have not been fixed. If we assume each target is to lie in front of one of the experimental areas Ia, Ib, and to the left of its center, then we can estimate from Fig. 1 the maximum and minimum distances between targets that will be required. For targets T1 , T2 dmax = 1 7. 0 m. dmin = 6.4 m. and for targets T2 , T3 dmax = 18.0 m. d i = 7.4 m. m n Ic - 8 -It is apparent that the transport system connect-ing these targets should have: i) a system length of 6.0 to 18.0 meters, ii) a system "acceptance" large enough to accommodate a beam which has traversed two thin targets. We shall show that four quadrupole "identity sections" satisfy the above criteria. In addition, these systems have the following useful features: 1. the total system length is on easily adjusted parameter; 2. the phase space ellipse representing the beam is left invariant so that the rest of the transport system (before T1 , after T3) is not affected if changes are made to the relative spacing of the targets; 3. the field gradients for each quadrupole are the same. 3.2 Description of the Identity Sections The theory for such identity sections has been discussed by Tautz4• These systems have a transformation matrix equal to -I where I is the unit matrix. They consist of four quadrupole magnets of equal strength, alternately focussing and defocussing. A representative system is shown below: - 9 -+g -g +g -g -·-·-~1 ~ ~ 1 ~ ~1 ~ I ~1--l .f- 11 ~"""'- ~ 13 1~ 1,~ .. " "" D 11 , 12 , 13 , ~' 15' are the system drift lengths. They must satisfy g is the quadrupole field gradient and 1 the quadrupole effective length. The g-values are equal in magnitude and alternate in sign. A formula can be derived which relates the value of g to the total system length D, the effective length 1 and the central drift length 13. It is convenient to define the dimensionless quantities 0 < -t = 13/D J5 < -l ~ t r = 15111 d = 1/D Then a system of a given length is uniquely determined when the three ratios l, r, and d are specified. - 10 -We shall examine three identity sections with D = 6.0, 13.1 and 18.0 meters. For each of these systems we have taken r = 1 and d has been chosen such that 1 = .4 meters. The t-value is different for each system and is chosen to satisfy criteria which are discussed in the next section. 3.3 13.1 meter Identitv Section It has been found4 that the quadrupole field gradient g for these identity sections is a minimum when l= t. The system acceptance is the same for both the hori-zontal and vertical planes and also has a minimum at~= t. When a large acceptance is required it may be desirable to choose a system with a gradient greater than the minimum value. This is the case with the 13.1 meter section. The beam emittance is increased due to multiple scattering in the two thin targets and in order to transport the beam, with four inch aperture quadrupoles, it is necessary to choose a system with t > t. The characteristics of the system used are given in Fig. 3. The gradient required, for 500 Mev protons, is 702 gauss (minimum gradient is 410 gauss) with em em -f = .431. This is the largest-{ -value which could be used while leaving a reasonable minimum distance (.3 meters) between magnet edges. The beam envelopes given in Fig. 3 are for no targets, one thin target and two thin targets in the line. The phase space ellipses representing the input - 11 -beam i.e. for the no target case were taken from the ellipse tracking output for systems I-68-4 and I-68-6 given in tables 5 to 8 and the calculation of the change in the phase space ellipses due to target scattering is described in Appendix I. In Fig. 3 we see that the beam envelopes for system I-68-6 are substantially better than those for system I-68-4 as the maximum beam displacement, in either plane, is reduced from 4.6 em to 3.5 em. 3.4 6.0 meter Identity Section The characteristics of a 6.0 meter identity section are shown in Fig. 4. The t' -value for this system was not increased from t since the minimum gradient for this system was already high (1021 gauss) and the beam envelope trace em was satisfactory for 4 inch aperture quadrupoles. From the curves we see that the maximum beam displacement in either plane is 2.4 em. The input beam was taken from the ellipse tracking output for system I-68-4. As for the 13.1 meter system, an improvement is obtained if one assumes the input beam is taken from the output of system I-68-6 (maximum beam displacement becomes 2.0 em). 3.5 18.0 meter Identity Section The characteristics of an 18.0 meter identity system are given in Fig. 5. As for the 13.1 meter system a large ~-value (.433) was chosen in order to keep the beam envelope small. We see from the envelope curves that for maximum beam - 12 -displacement to be less than 5.0 em. With two thin targets in the line it is necessary to use the input beam taken from system I-68-6. In this case the maximum beam displace-ment is 4.6 em and the system is just barely satisfactory. 4. Beam Transport From Last Target to Neutron Facility The beam leaving target T3 has a large angular spread due to its interaction with the upstream targets. A system is needed that can transport this beam using quad-rupoles with reasonable apertures. A quadrupole triplet was found which will "flip" the large emittance phase space ellipse into a position favourable for transport. The sit-uation is described in the diagram below. Before triplet In either plane the phase space ellipse describing beam leaving target T3 is approximately upright, with large maximum slope due to target scattering. x' After triplet Ellipse has been "flipped" (in both planes) approx-imately to position shown. It can now drift long dist-ances with small maximum displacement. x' - 13 -As a numerical example we examine the beam exiting from target T3 of system I-68-6. With a 24 gm/cm2 equivalent target in the line the computer tracking program gives a ~[cm/rad] ~[em] x~[ffl] 100 - the ellipse after T3 [hor. o.o .1415 • 21 1 .49 vert. 0.0 .1415 0 21 1.49 - the ellipse after triplet thor. .82 22.7 2.67 .152 vert. .84 22.2 2.65 .155 The beam emittance is .315 [em rad] 100 The drift distance to the nearest waist in the horizontal plane is then dx = + ~ = ~ = +(.82)(22.7) = 11.13 meters Y 1+a2 1 + (.82) 2 and similarly for the vertical plane dy = 10.93 meters. The beam can drift approximately 22.0 me't;ers from the exit of the triplet before the maximum particle excursion returns to its starting values c-- 2. 68 em) 0 The curves in Figs. 6 and 7 show the effect of this triplet on the beam envelope for systems I-68-4 and I-68-6 respectively. We see that even for one thick and two thin targets in the line the maximum beam displacement in either plane does not exceed 4 em. - 14 -If it were found necessary to use 6" quadrupole * apertures here, the pole tip field for the strong central magnet of the triplet would be 1.571 k gauss 3 x 2.54 em_ 12.0 k gauss em which is feasible. Another point of concern is the length of the first drift space after the thick target T3. There must be room enough here to include adequate shielding for the first quadrupole, but this drift cannot be very long since the beam size is rapidly increasing and soon exceeds the quad-aperture. This drift length has been set at 1.0 meter as this gives satisfactory transport of the beam and, it is hoped, enough space for target shielding. Calculations show that it could be increased to about 1.25 meters using the current design (with a 24.0 gm_ equivalent carbon target). cm2 The final section of the transport systems I-68-4 and I-68-6 is a triplet which has been adjusted to produce a double waist at the neutron target when there is the equiv-alent of 1 thick and 2 thin targets in the line. In this case the computer finds the phase space ellipses at the neutron target to be as follows: * Our target calculations are optimistic, as stated in Appendix I. Also "thicker" targets might be considered. • system plane a ~ E xm[dm] '[rad] xm 100 I-68-4 hor. o.ooo 5.00 .243 1 .1 0 .22 vert. 0.001 5.00 .239 1.09 .22 I-68-6 hor. 0.004 5.00 • 3151 1 .26 .25 : vert. -0.001 5.00 • 3151 1 .26 .25 System I-68-5 ":t; ~. _\...,. ) ~ . . :~ >~ ~:: Syste~~ i;.;6:a·~5 i& .the 'S'ame as I-68-4 except that the " . ~ . ;;: .. r.,.,. ~ '\~ •tl' ~ neutron irradiation facility has been moved to a position in line with the experimental areas (position Bin Fig. 1). The magnet parameters and beam envelope curves for the last section of this system are given in Fig. 8. If dispersion effects are considered the maximum particle displacement for points between the bending magnets is increased and the quad-rupoles there would possibly need 6 inch apertures • - 16 -1. J. B. Warren, L. P. Robertson and J. J. Burgerjon, 1967. Interim Report on Reappraisal of Beams, Building arid Site, Internal Report No. I-67-1. 2. Paul, A. C. 1964, U.C.L.A. Report P-65 • . 3. Vogt, E. W. and J. J. Burgerjon, editors, 1966. TRIUMF Proposal and Cost Estimate. 4. Tautz, M. F. 1968. 5. Yale Internal Report, Y-12, Appendix L. 6. Steffen, K. G. 1964. High Energy Beam Optic~ (Interscience, New York). ( • - 17-Acknowledgements The author wishes to thank Dr. L. P. Robertson for his guidance during the progress of the work and his assistance in the preparation of the report. The author also wishes to thank Dr. R. M. Pearce and Dr. D. E. Lobb whose comments regarding this report were much appreciated • .. _ .-··--~- I-1 APPENDIX I. Calculation of Effect of Targets on Beam The effects of multiple coulomb scattering have been calculated using the following equations. The mean square projected scattering angle is given by6 2 <92> = 1 (~1. ~\ ..i.. 2 \P~c) x 0 where p = particle momentum (MeV/c) ~c = particle velocity xo = radiation length (~:2) t = target thickness ~:2) and the mean square deflection due to scattering is * If the initial phase space ellipse is upright, the approximate change in the ellipse can be computed by increasing the initial maximum beam displacement xmo by <x2>t and the initial maximum beam slope x~0 by <e 2>t i.e. X = m xmo + <x2>t .1_ I I <e2>2 X = xmo + m * The phase space area occupied by the beam after target scattering is not in general elliptical. I-2 If we assume the ellipse stays upright we obtain the ellipse parameters after the target scattering as a = o.o X X + <x2>t ~ m mo = -, = <e2>t ' xm xmo + Tables 9, 10, 11 show the output from the computer program "Target" which carries out the calculations described above. The phase space ellipse parameters after scattering off carbon 2 targets of thicknesses 1.0 to 30.0 gm/ cm are given. The input ellipses were taken to be those found at the first target location for systems I-68-4 and I-68-6. The following key may be helpful when reading these tables. 2 THICKNESS = target thickness [gm/cm ] D.SM = change in slope, <e 2>t in [rad/100] DXM = change in particle displacement, <x2>t [em] ALPHA ) ) = phase space ellipse parameters, a, ~' e, BETA ) ) where notation is the same as used in Steffen7. EMITTANCE ) XMAX = maximum particle displacement in beam in [em] SMAX = maximum particle slope in beam [~~g] I-3 In this report a "thin" target means a 2.0 gm2 em carbon target and a "thick" target means a 20.0 gm2 carbon em target. Beam envelope calculations based on the output from "target" are optimistic in that they correspond to approxi-mately 68% (one standard deviation) transmission of the beam. Also no account has been made for nuclear scattering effects. Similar calculations were made for a few target materials other than carbon. The materials considered are listed below. Target material Density ID!L Radiation length- ·~ cm3 em carbon 2.25 42.4 berYllium 1. 84 63.7 copper 8.96 12.0 tungsten 19.3 6.9 We summarize the results obtained in the following table. carbon -target thickness gm2 em 2.0 (1 thin) 4.0 (2 thin) 20.0 (1 thick) 22.0 (1 thick, 1 thin) 24.0 (1 thick, 2 thin) -39 • 56 1. 25 1 • 31 1.37 approximate target thickness to give same <e 2>t as for carbon: · [gm/cm2] berY'll::tum conner tung_sten 3.0 6.0 1.0 30.0 6.0 3.5 6.5 3-9 7.0 4.0 APPENDIX II Tables and Figures · Table 1. Tables System I-68-4 System I-68-5 System I-68-6 II-'t Table 2. Table 3. Table 4. Transformation Matrix Components for Horizontal Plane, System I-68-4. Table 5. Table 6. Table 7. Table 8. Ellipse Tracking for System I-68-4 - Horizontal Plane - No Targets in Line Ellipse Tracking for System I-68-4 - Vertical Plane - No Targets in Line Ellipse Tracking for System I-68-6 - Horizontal Plane - No Targets in Line Ellipse Tracking for System I-68-6 - Vertical Plane - No Targets in Line Table 9. "Target" Calculations for System I-68-4 - Horizontal Plane Table 10. - "Target"· Calculations for System I-68-4 - Vertical Plane Table l1. - "Target" Calculations for System I.-68-6 - Horizontal or Vertical Plane. II-2 t· Figures Fig. 1 • - Plan View of Beam Line I Fig. 2. - 30° Dispersionless Bending System Fig. 3. - 13. 1 Meter Identity Section Fig. 4. - 6.0 Meter Identity Section Fig. 5. - 18.0 Meter Identity Section Fig. 6. - Transport to Neutron Facility (I-68-4) Fig. 7- - Transport to Neutron Facility (I-68-6) Fig. 8. - Transport to Neutron Facility (I-68-5). I I C Y C L OIT R 0 N I I I OUTER COIL RA I 8.94 I\ I \ I \ I \ I \ I \ . I \ I \ I \ FIG. I PLAN VIEW OF BEAM LINE J:. .. RIMENTAL AREAS --. 2.1 f--I a Ic 10.6 10.6 10.6 SYSTEM I-68-4: 30° DISPERSIONLESS BEND, STRAIGHT BEAM LINE TO NEUTRON FACILITY AT A. SYSTEM I- 68-5: SAME AS I -68-4 EXCEPT FOR 60° BEND WITH NEUTRON FACILITY AT B. SCALE - I em. = 4 .24 meters. ALL DIMENSIONS SHOWN IN METERS Tr. T2,T3 REPRESENT PION PRODUCTION TARGETS . 1.0 ·o Two Systems are shown: up to element 16 they are identical, after element 16 --- system I-68-4 ------- system I-68-6 Bending Magnet Ef.Length(m) Field(Kgauss) 1 .643 -14.81 13 .643 -14.81 - both magnets deflect beam by 15° - field index = 0 - normal entry and exit FIG. 2 - 30° DISPERSIONLESS BENDING SYSTEM (up to the first target) Approximate Beam Envelopes . .... __ _ · 5.Cf 10.0 ~· DISTANCE ( m.) . Quadrupole Ef.Length(m) Field Gradient(gauss) · em 15.0 3 .432 5 .432 7 .406 9 .432 11 .432 16 18 20 system I-68-4 · .406 16' 18' 20' ~ .. .406 .406 system I-68-6 .406 .406 .406 -, ......... ... _~ ... _ ...... -------517.3 377.2 398.6 377.2 -517.3 558.7 -730.4 507.3 502.2 -462.4 154.1 -------------------------------------~----_t 4 ~~­Ua::2 -w 1-z w 2 w (.) <t .....J > 0 Q.._j C/)-a:: -o2 a I ~ 4 r-- -- - ---------- ·-----------· .. --·---··---------------------- -----··---·- ------ ··- - ···--- ·------- - ·----·-·-- ---- -, All quadr upole magnets have e f fect i ve length = .4 meters field gradient = 702 gauss/em FIG. 3 - 13.1 METER IDENTITY SECTION ( t = .431 ) ------- system I-68-4 ------- system I-68-6 Approximate Beam Envelopes (for 0, 1 , 2 thi n targets in upstream beam) --------------- -- ·-------------+ ~--2.725--~ 0 2 - --- - -------- - ----··--------+ 1+--------.5.45 _______ ...,. .3 4 6 METRES 8 H--- 2. 725--_..,. 10 l2 ·--------·--·~-----~· ... - -------· ---All quadrupole magnets have --- system I-68-4 - effective length = .4 meters field gradient = 945.9 gauss/em system I-68-6 not shown FIG. 4 - 6.0 METER IDENTITY SECTION ( t = .25 ) ·! /.4-1 2.0f-! .,,.L . s.: ;;MJ, 0 i ..c ! ~55m---? + Approximate Beam Envelopes (for 0, 1, 2 thin targets in upstream beam) -------·~---~,~-~--------·-•>·~~-----~· - + _, .1.1 ~ 1.1 .... "' ... 1.1 -::· •' " ... . ~ / ..... I ~ J I l t ! -f ! J ~ l ' -i l l .55~ t l L-.--------------------_,;.-~-------~--ll'..._........ ___ .... _~~~-------------~----..... .,_..__.1 DISTANCE IN METERS 1-- 2.0 z w ~ w u <t ....J ;,., u.. (/) -Q ~ 2. ~ 0 ....c 6 .. • ~------------·-------·-------·--·" ..... _ .. ... --···-.. ---···-----··---------·---All quadrupole magnets have effective length = .4 meters field gradient = 702.gauss/cm FIG. 5 - 18.0 METER IDENTITY SECTION ( t = .461 ) ------- -~ -.. __ _ system I-68-4 ------ system I-68-6 - - - - · --- - - - .. h _ ..,..- - --- --------- -------------------::__- ------------------.____ - - - --------------·-· -----------..... -----··--·----·-----·-- -- -----·-- ------ -- ---.. ......... .._, -.. .__ ---~ --.... -- ._ ..._________ .__. --. -- ------- - -- ---..._ --.. -- ----- --. --. -- .__ ---. -....... -- -----·-------- ----------------+ + I l ~====~~3~.9~5m~====~~==============~7~.Q9~==============~~~3-.-95~----~ ·- ·-- -J .DISTANCE IN METERS • ,..-----~---------------------------------------------------~ -E v ;:: z..o -z UJ ~ w u .ct ....J ~ U1 Cl ·l z.o ~ a ....c 4. All quadrupoles have effective length = .4 meters FIG. 7 - TRANSPORT TO NEUTRON FACILITY ( for system I-68-6, Table 3 ) Approximate Beam Envelopes (for 0, 1 thick, 1 thick and 2 thin targets) -------==--==-=--=---=-:=-- --··-·-·----------·--41 ~1 45 A1 Quadrupole 41 43 45 47 49 51 49 51 J.o-1-t.zi..{ir-1-----·-----------------:-.---·-----12.0 --·- --- -----------··- --------1-l 0 .12.jc * Field Gradient . (gauss) em 1160.5 -1571.4 786.7 199.6 ..;.551.9 376.4 1--------------- - - - ---- ---- -··-· ------ ·-- --·--- -- ·- -··--· --- ----------·---------·-----------·-·--·---'-·· -----''-- - ---·· DISTANCE IN METERS 4. r E u -4. ---·-·------·-------- · ··- -------------------------------. All quadrupoles have effective length = .4 meters Bending Magnet Field Quadrupole 8 lO.OKgauss 20 10.0 - angle of bend 15° - normal entry and exit FIG. 8- TRANSPORT TO NEUTRON FACILITY (for system I-68-5, Table 2) Approximate Beam Envelopes (for 0, 1 thick and 1 thin targets) ----D ISTANC E IN MET eRS 2 4 6 10 12 14 16 18 22 24 26 · gauss Field Gradient( ) 1160.5 -1571.4 786.7 -225.6 41.3 301.2 -422.7 166.9 -160.8 588 . 4 -556.9 em I .·-0 .. INITIAL SYSTEM PARA~ETERS UNITS System I-68-4 l .. E t\.GI .. H~.ME I .E.R 5 ...... ;. ..... ~· ··· ···-········--··--- ··· ····· · ·-·-····· .. --···-·----.. -·--·-·-- ·~--- ---··· .. ·---··-···---··--·· -····-··-·--··--·-------··-----·-·----·-·------·······-·· .. ··-----··----.. ----·--------·;-·--FIELD GRADIENl-GAUSS/CM FIELD-KILOGAUSS ANGLE-DEGREES ARTICLE REST ENERGY 938.200 MEV MOMENTUM 1.09004 GEV/C 1 BENDING MAGNET EF LENGTH 0.6426 FIELD ~14.81400 • mm m Et\I.RANC.E ... ANGLE .. ··· ·······--·· ··-·----~-O .•. O ..... ______ f...Xl.T.._ANGL£ Q.O BENDING ANGLE · ~-15. 00000 2 DRIFT SPACE LENGTH 0.3048 ... liE.LD ... J]i.Q.fX_,,_~-· .. Q .• O ......... --·· 3 QUADRUPOLE- DH 4 DRIFT SPACE EF LENGTH LENGTH 0.4318 FIELD GRADIENT -517.34277 0.3048 14 15 .. 16 17 18 19 ; LENGTH EF LENGTH L ENGT 1-1 .. ....... .EEL.EN.G.IJ:L ..... . LENGTH EF LENGTH LENGTH EF LENGTH • 2.7250 FIELD GRADIENT 398.60693 .FlELD .JiRA.O.l.ENI.. _______ 3.JJ.l.78.96. FIELD GRADIENT -517.34277 -14.81400 . BENDING ANGLE -15.00000 FIElD INDEX o.o 0.4064 FIELD GRADIENT 702.36890 · 8-!l8~2 FIELD " GRAOIENT ··· :.;·702~3789l 5.4500 0.4064 FIELD GRADIENT 702.38696 0.3000 w • F l EL.P. ....... G..P.. A D.J EN T ..... -._ .. 1..Q.Z .!!..~§.~2.Q. FIELD GRADIENT FIELD GRADIENT -702.37891 702.38696 QlJADRUPOLE-DH EF LENGTH 0.4064 FIELD GRADIENT -702 • . 38477 DRIFT SPACE LENGTH 2.7250 ORIFT SPACE LENGTH 1.0000 ··· c;:UAORUPOL . E,;.;;FH ···· ····EF LENGTH ........ 0~4064 .. FIELD GRAOIENr·-· .. 1T60·;··si489 .. DRIFT SPACE LENGTH 0.2000 QUADRUPOL E-DH EF LENGTH O. 4064 FIELD GR~ lENT -1571.36377 DRIFT SPACE LENGTH 0.2000 • 46 DRIFT SPACE LENGTH 16.5000 ·47 QUADRUPOLE-FH EF LENGTH 0.4064 FIELD GRADIENT 232.15099 48 DRIFT SPACE LENGTH 0.5310 · .... 49 "QUAORUPOLE.;;;;DH ·······EFLENGTH o;4064 . . FTELOGRAOI"ENT····· .. ;;;;·497;·-s5T76 .. 50 DRIFT SPACE LENGTH 0.4070 51 QUADRUPOlE-FH EF LENGTH 0.4064 FIELD GRADIENT 290.81299 52 DRifT SPACE LENGTH 5.5200 UNITS LENGTH-METERS Table 2. System I-68-5 ) ........ ..... ~. l~t8~~-~-tEt~~Is. ~~- ~~ 5<.:.~ --- ... ........... as ·· th~!!~:!e~~d:!:~::~~w:~: - ~;!t:~~~68-4) · · ANGLE-DEGREES DESIG~ ENERGY 500.CO MEV PARTICLE REST ENERGY q38.256 MEV M M T M .09007 GEV C . 1 ORIF T SPACE LENG H 2 Q~AORUPOLE-FH EF lENGTH FIELD GRADIENT 1160.51489 3 DRIFT SPACE lENGTH . . . ... . ~ g~~~~U~~~t£PtL ... f~·N bt~G.I h .. .. f I .. E.=.~ ..  O ...... G.~ .A .. P. .. I .. ~.N .. I _ -=-t5._7_t~.Ifl..liJ. .. 6 QUADRUPOLE-FH EF lENGTH FIELD GRADIENT 786.73584 7 DRIFT SPACE lENGTH 8 BENDING MAGNET EF LENGTH -10.00000 • BENDING ANGLE -30.00000 FIELD lNOEK 0.0 DRIFT SPACE LE~GTH 3.0000 CUAORUPOLE-DH EF LENGTH 0.4064 FIELD GRADIENT -225.63399 DRIFT SPACE lENGTH 0.8050 QUAORUPOLE.::;;FH ... EF TENGTH ·············· ·o~4064 -FTFLD .. GRAUTENT···-----·-4r~3T79.''1 .. DRIFT SPACE lENGTH 3.0000 QUADRUPOLE-FH EF LENGTH 0.4064 FIELD GRADIENT 301.20581 DRIFT SPACE LENGTH 3.0000 17 DRIFT SPACE LENGTH 18 CLADRUPOLE-FH EF LENGT~ 19 DRIFT SPACE LENGTH • 0.8080 0.4064 3.0000 F I El 0 GRAD lENT 166.972 99 ······ .... .... .. .. 20 BENDING MAGNET EF .. LENGTH ·· T~9o3·s FTFLU ........ ·------·-------·;;;;;ro~·oonuo · E_N TRANCE ANGLE 0.0 EXIT ANGLE 0.0 'BE.NUT.NG' ···AN'GCE···--;;;;:'3 ·n~-o·onn·ry · · FIF.LO INDEX 0.0 21 DRIFT SPACE lENGTH 1.5210 22 CUADRUPOLE-DH EF lENGTH 0.4064 FIELD GRADIENT -160.79900 .. .. }~ ~uA5~u~~t~~FH ~~Nt FN·c· THo! .·4 ~o~6 ?'4Y FIELD GRADIENT 588.37085 25 DRifT SPACE LENGTH C.2900 ~- -~ · 8~t~-~lJ~BktEOIJ ......... f~N~f~G.JtL ........ .. Z:~~-8~ .. fJJ~.R ... Gg~QJE:. _NI ......... ::.?..?6. 8 84 77 . .. . .... .......................... ...... ................................................................................................... ..................................................... .. . .................................................... ................................ , _____________________________________________________________________ _ ................................ ....... .. ...................................................................... ...................... .............................................................................................................................................................................................................. _ ................. "······-··································- ·····-·"-··--·············-..... ............................................................................................ .... ............................. ......................................................................................................................... . - - -----· -------·- --- .. ·-·· ·-- --- ·- .......... ___ ____ ---..---0 • INITIAL ~YST~M PAkAMEf~~S U~llS l E 1\ G T H- ;1.1 E T [ ~~ S F lEU! Ci{ACI i :'JJ-,.,G/u.JSS/CJ"l .. FlELD-KILCGl~USS ANGLE-CEGREES DESIGt\ ENERGY 500.00 MEV ENERGY (BB. 256 MCME~TUM 1.09007 GEV/C 1 bENDING MAGNET EF LENGTH Ef\TRAI\iCE ANGLE ..... ........ 2 UIUFL SPACE ..... ....... LEi~GTH ....... . 3 WLAORLJP CJLE-DH EF LEI%TH 4 Dklf-T SPACE LEf\GTH 5 (;;LALJI<UPfJL F-FH l::F L ENGH· ) . . .. , ..7 (.;UADRUP ;JL f.-Hi E:F LEf-..JGTH 8 LiR IfT SP:\CE LI::NGTH S QLADRUPOLE-Fh EF LENGTH . . ... ...... ........... .. .  .. . ......... ...... .... . . System 1::68.::.6 .. . MEV 0.6426 FIElD -14.81400 0.0 EXITANGLE .· ... ~ . 0.0 ·- -~-BENDING ANGLE -15.00000 FIELD INDEX 0.0 . .... 0.3.04 .. 8 .... 0. 4 3 1 B F f E L 0 GR .f61 E· Nr·--::.-517·~-34271--0.3048 0.4318 FIELD GRADIENT 377.17896 o. 1-t 064 1.3208 0.4318 FIELD GRADIENT FIELD GRADIENT 3f18.60693 377.17896 ...... ...... ............ 10 .. DR1Fl SPACE ........ . LENGTJt . . . . .................. 0 .• ..30.:4.8 o. 1+ 3 18 FTt=Lo GRADIENT' · · ·=517~3'~2 ·7·7' 0.30'tF3 11 CLfiDRUPt:rU:-OH lF L FI\G T H 12 l H I f- T S PAC E L EN G T f' 13 BENDING ~AGNFT EF LENGT~ 0.6426 FIELD ~14.81400 14 1 5 16 .......... ................. 17 18 19 20 -. 22 23 24 ...................... 25 26 27 28 29 30 31 32 . ... .. 3.3 34 35 36 37 :..8 39 40 41 ...... ........ 42 43 44 4? 46 47 48 49 . 50 51 52 ., Q.O EXIT ANGLE 0.0 L Er\J <J TH L Ef,H ... TH EF LENGff-' .. .. LEI\ GJJ::L . . ............. . tf LtNClr LENGTH E:F L U\IG TH ' t~ T li L E i'J '~ TH EF L ENGl r LEI\Clf-··· EF .... LE L~ .. G.Lb .... . Lci\Jt;TH EF Ltr'-J(,TH LENGTH E F L E IIJ(, T H -' lj ' • BENDING ANGLE -15.00000 FIELD INDEX 0.0· FIELD GRADIENT 502.22485 · . .. FIECti··· .G.RAD.lE ·r;ry--····-=·4·6z·:··3·9Ttf5···· FIELD GRADIENT 154.12199 FIELD GRADIENT ..... f. ... l ... E .. l .  O .... G.R.A.P . l .. E ... N.I... . ... =.J.0.2 . ~ .. .3.I6.9.J ..... . FIELD GRADIENT 702.38696 FIELD GRADIENT -702.38477 FIELD GRADIENT ?02.36890 ··r ··r···E··L··n· .. GRADl .. E.Nr·····-··· :::.7'02 .. ; ·3·78'91' .. FfELD GRADIENT 702.38696 .. FJJ~.P G.~~QJ~NI ... .. JJ. 99.!?1~§9 FIELD GRADIENT -1571.36377 FIELD GRADIENT 786.73584 ~F LENGTH 0.4~64 FIELD GRADIENT 199.60599 L E N G Tt~ C • 7 2 4 0 ····· ·· ·· EtNhthC!Ifi .... ........... H:~ggf) .F I ELO GRAQ.! E NT _____ ::.?.?.J .. .. 9IQ95 EF LE~GTH 0.4064 FIELD GRADIENT L E 1\G Hi 5. 7 510 Table 4. System I-68-4 ~ ~ ~ ~ ~ ~ ~ ~-~- :~A~kf~:c9~~0NENI.S ...... .. 1 <;i ~-~· -· ·· ':.~~~;nfi~~- ~~~ -~?{{:j -- -~y~~~~~ ·lli - ~'!:':1!.~~-C:B:~? 1 C.96593 0.63525 -0.10545 0.96593 -8.36312 -25.88167 2 0.93319 0.92966 -0.10545 0.96593 -16.25185 -25.88167 ~--~~~~--~~~50 0.47966 1.69366 -30.13205 -39.82343 4 1.15903 2.00773 0.47966 1.69366 -42.27022 -39.82343 5 1.24924 2.52465 -0.06857 0.66189 -54.89461 -17.70447 6 1.15867 3.39888 -0.06857 0.66189 -78.27866 -17.70447 ······A·· · ·· · · ···· · -~· :·-~·t2-~! ············ ·1:· 1-~ -~--j·-~·-·· ······=·8: ··§-g-~ -~-t -·· · · ··· =·8:·-~-~-g -l -! ···· =~2: ·~~--~-~--~- - --·· · ··if:-t~~U:-----9 0.02188 1.64013 -0.63296 -1.74322 -42.26637 39.82391 10 -0.17105 1.10880 -0.63296 -1.74322 -30.12804 39.82391 • 4.17546 1.11159 -1.95228 =2.(f8206 -1.93125 -2.03227 -7.55315 1.6555b 1.14690 2.30703 -0.00532 -0.00284 2.25117 -0.09223 0.53630 -0.00548 0.00205 11.10011 -0.09223 0.53630 0.02842 0.00205 10.73412 -0.0760R -2.32161 0.02776 -0.00530 9~5Cl34 .;.;:c.0760B .;;.;:2.32161 o~02495 ·:;;;;o;oos3o -- ----··-·--··--·---··-·-··--· 9.61595 -0.15375 2.89623 0.02558 0.00849 10.79472 -0.15375 2.89623 0402904 0.00849 11.24084 -0.07128 -0.72499 0.03052 -0.00130 (matrix co111ponents ~iyen are (it • ------- ·-···- --··· ---- ---·-·-- ----- . I . 0 Table 5. System I-68-4 HORIZONTAL PLANE no targets in line Elll PSE ... TRACKING . .. .. ....... . ............... ....... . . ........ .......... ... .. ............. ..... ···-----···--·-······- ---·-------·----·-···--·--·-- -- ·--· EMITTANCE 0.01616 2 3 4 . 5 ..... . 6 7 8 10 11 12 ... 13 14 15 16 7 8 19 20 ..... 21 ....... . 22 23 24 5 6 27 28 .. 29 .. ····  .. .... .. . 30 31 32 33 35 36 37 38 39 40 41 43 44 45 .. 46 . 47 48 49 . 51 52 GAMMA 0.21142 • 0.13516 0.13516 ALPHA o.o • 0.29242 0.36061 0.42913 ········· 0.64893 0.62780 0.55634 0.56391 SMAX 0.05845 • 0.04674 0.04674 (values are at the end of the numbered element) 10 11 12 13 14 15 16 7 18 19 20 2L 22 23 24 25 26 27 28 29 30 31 32 33 43 44 45 46 47 48 49 51 52 . . 0.09748 o. 09748 • 0.59358 0.45944 • 0.44931 0.44931 0.04091 ············· ··a·; o·4oq·r ·· ···············-···········-···---·-··········-···· ···························-······  0.19287 0.19287 0.22987 • o. 03969 0.03969 (values are at the end of the numbered element) 0 • Table 7. HCFI d iJlAL PLM<L t Ll I t ~. i- l R A C K lr'J G System I-68-6 E~ITIANCE 0.01616 _ no targets in line GJ\i'vjl'v\,~ n.2lh2 1 1l .24St:5 ALPHA 0. (; C.Yi!0 4 L t n~ 4. -1?.() )0 4 • 1i '1 i) Lt ] 3 4 5 _____________ __ ___ 6 7 8 l) -ll 12 13 14 15 16 17 8 19 20 21 22 23 24 25 26 2 7 28 29 30 31 32 33 34 35 36 37 3'8 39 40 41 42 43 44 45 46 ........ ...... .... A7 48 49 50 52 ' L () : 3.586Y7 -1.75~47 1.13596 3.5 3 697 -2. 84678 2.5,812 2.7q5Ql -4.40791 7.30933 ______ 2. 7Y 5 ') 1 __ - 6 .. 111Itt ..... 13. 7.2 210 __ 2.7Y5 0 l -14.3~701 7~.104R7 10.055~1 26.?9?65 68. 8 482 4 LO.C55~1 16.05719 32.52570 0 .24275 2 .2410S 24.8 0 920 0.24275 1.33 92 7 11.50 816 0.99991 2 .9~ 3 14 9.72183 0.99991 ;).003 1-+0 1.00005 r).9999l -:::: _<?, ___ .I2l ~"'b 8.4•J649 l.-9 45t6 3. 7<J53t; --- ~~9i6td l.9~5 Bb 3.21163 5.81467 U.43117 -1.0 8 122 5.03052 0.41117 -3.43108 29.6?254 12.3Y095 17.00Y 86 t3.4 3 12 12.3rJCY5 1 .1.29251 llt.3401t9 1. 000 10 2.72847 8.443b9 1.0001 0 J .0032C 0 .999B6 1 • GCl C)l 0 ··:;_ 2 .1220i;· .. ..... B: 40875 l. C) 1+(>3 6 3. 7 '-J 6 1t 4 7. <;t f3 8 7 L.9463 h 3.212~4 5.81617 0.43112 -J.C8137 5.83174 tJ.4J 12.3'-ilfl6 12.Y;l86 l.U 002 b l. COC78 1. 00028 1.59536 1.59536 2.44d5f~ 2.448?8 0 .3060C J.jObJO . ······· 1. ,))J)<j t. :J2329 7.71436 7.-(1436 ? ') • '· '. t l. 65'dl0 :n.Jr> Ol5 DMAX 0.27647 c. 269fJ2 SMAX 0.05845 0.06354 0;.16548 0.16548 0.04308 ___ _o_. __ Q .. '.t_,l_Q_ft .... ______  ,. _____________ ,. o. 16374-0.16374 0.20250 • 0.19892 0.07032 o. 0 7032 ...... 0~12859 - - - --- --- - ········ o. 12859 0.35308 0.35308 (values are at the end of the numbered element) ) -- --- - - ----- ··- ·-- - - --··-···--- - -------------------T VEkllCl\L PL4 i'·JC Ellli~L TRACKING No targets in line - System I-68-6 E fY, l T lAI\.C L .... ...... ... . 0 ..... 0.16. L6 ..................... . 1 3 4 5 ........... ........ 6 . 7 8 9 GAMt'IA ALPHA 0.03231 J.O 0.03231 -0. 0 2 0 76 . - (' - ' \ 10.68793 10.68793 3.31174 ......... .3 •. 3 .LLI4 3.44606 3.44606 11.61152 11 0.03196 12 0.03196 13 0.03196 ...... 14 .. ........ 0 • 03.19.6. ... . 15 0.03196 16 10.77471 17 10.77471 18 2.42891 lS 2.42891 20 0.99tl56 21 0.99856 .... 2 2. ..... . .... ... ....... O ,t9~856 23 12.33906 24 . 12.33906 25 0.4284S 26 0.42849 27 1.95 ~3 28 1.95553 29 0.99846 3Q O.S9846 3 1 ...... ...... ... ........ ..... .. if~99846 32 12.33906 33 12.33906 34 0.42854 35 0.4 8S4 36 1.9551] 37 1.95513 38 J.99b37 39 ..... .. ..... ........... (1.9983 7 40 a.g9837 41 9.20494 42 ~.20444 43 .>. 54 44 5.15't14 45 C.3575C 46 0.357~0 4 r · · 4~2:ro2r 48 4.23021 4~ 10.05785 50 10.057A5 bETA 3 r) • 9 5 0 ~) I) 30.9633 '3 r 23.48979 14.84302 7.73220 .... 0 •. 4.05.19 0. 52 831 8.93293 16.80463 DMA·x···········  ·············-······-- sM Ax··········- --------- -------------·--··-···-·····----· ----o.7o721 o.02285 0.70737 0.02285 • 0.02936 (values are at the end of the numbered element) • __ __ _______ Table 9. ____ ..... ____ _____  - - --~--- -- ---- -----·- .. . ____ _ __ . _______ _ _ APPHLXI~ATE CALCUL~TIC~ CF F~ASE ~PAC~ ELLIPSES AFTER TRAVFRSING A TARGET __ fAR.G.El. MATER1AL~CARbCf\. _ ___ _ ___ .... __ _ ______ ____ _ ___ ____ __ _ l~CIG~~T FARTICL~ ~AS-C~ARCE NU. l.C0000 ------ ---- . __ _ __ __ __ _ .. t':Cf'~ El\ lU!V 109iJ .JUOOJ. Horizontal Plane vt::LlJCIT't/C 0.75210 input ellipse taken from .S.CALI ER ER. HAS -:-J{AJ: IA I I Lf\ LEl'iG I h . 1-t 2. 399 ~ 9 Syst~m .. .I-:6.6::9 _ __ ----------- --·· . -OENSlT~ 2.25CCC _ .H :.ICJ<I\E:SS IS"'- .... C.XfJ ALP!-:~ eEl A EMITTANCE . . . XMAX . . ... __ SMAX __ _ _ _ _ _ o.c o.o c.c 0. 0 0.2 d 700 0.01616 0.06810 0.23729 __ ____ lA.COOOO ... .. 0 ... 21864 _HC .• 00072 0.0 0.13339 O.C355C . . . O~C.b .8d2 ____ _ 0.51593 i.COOOO 0.394J5 C.OC~G~ C.C C.il1C7 C.04427 0.07012 0.63134 _______ 3.-LCOCC... C.4ti26l 0.00372 O.u O.O'J97c O.C517C 0.07lti2 .. . ... . G .. 7l99Q _ . ___ _ 4. 0 000Q 0.55727 C.CC572 C.C C.OS2Sl C.C5566 0.073 32 C.79456 . ... .... .5 .. CCCCC .C.623C5 . C.LC7SS O.C O.O ~H145 0.06547 0.07610 0......8.6..039-__ __ _  6.CUOOO 0.68252 0.01051 O.C C.Od546 0.07231 O.C78b1 0.91981 __ _ _ L.DOOOO .. __ Q.J3.12.L ___ __ ~.Dl32Lt 0.0 ... . .. .. . .. C .. C..B3ltl _ 0.07927 .. ... J1 .. Q.8.L3.!t. 0.97449 __ _ .. ___ ·--·-···---- .... . E.CCCOC 0.7881C C.016ld O.U O.OB21S 0.08642 0.08428 1.0253S ___ ____ 9.COOOO ____ Q.8359.L .. .... . C .. l..l.lS31 .G.C __ _ __ _ C.C814j .. C.09381 _ D .. LU74.l _ __ .L...il.L3-L-.2.u..O_ 1C.CCCCC C.88113 0.022tl O.C O.Odlll 0.10146 0.09071 1.11842 _____ lL .. .llil.O_G_O __ _ 0.92413 . ___ o_.l.i2tDS 0 •. 0 0.08llC. __ O._lOC13S __ __ C._G9~l9 _ ___ l..J..6l42 12.CCOCC C.S6522 C.C2S72 0.0 0.03135 0.11764 0.09783 1.20251 ·-·- · .. l.3_._o.o.a.oo ____ ___L.llO...~o.!t. ___ o . ...o335.2.. _ o. o . . o. o.a .Ld2 ____ ....ll .. l2.C.LC ..... . o .•.. l.O.l6.2 _ ___ _ ~. z 41 9 3 ---·--···· ··- - --· _ . __ ___ _ 14.00000 1.04256 C.03746 0.0 C.C3248 O.l351C 0.10556 1.27985 - - _l.5..........C.C c. c (. ______ .l........G.l.9.15 ____ _c_ .... .o!tl5. ~L -- . 0 .. 0 -·- 0 • 0 6 3 2 .s . --D • 14 4 3. 4 - ·-- -Q_ .... 10..9.6_lt --- 1 • "3 1 6 4 4 16.00000 1.11~54 C.C4576 0.0 0.0 8 423 O.l53S3 0.11386 1.35183 __ __ Ll .. LCO.CL. - .. 1... L'ulE5 ..... . C •.. 05 C~ L - c. .. c . - . -·- 0. 0 352 9_ H __ Q.l6381 .. --- - .0 . .....1.1822 _____ 1.....386 1 4 18.00000 1.1821? . 0.05461 G.O 0.08645 0.17418 O. 12271 1.41944 _ _lS_._CCOGC 1. 21 ~---.C~_522._ . ... .. 0 .• 0 ______ -·- ··· .. . L. • . ..C8.1 . .7L __ Q.._l.8_4..8..5. _____ ~732 1 .45184 2G.CCCCC 1.24610 0.06396 0.0 0.08902 O.l95frS 0.13206 1.48339 _ _ 21. QOO.O.O . ...c __ __ _L. 2 7 t. 8 1 ___ .!... 0.6..E..B. L . . 0 _._a ___ C.,_CS..C!t 2 _____ . 0 ... .20_7 3l ___ Q .... ..ll6.SL_ I .51 41 6 -- - - - ·· · ·· -·----22.COOOC 1.30692 0.0737e 0.0 0.09188 0.21910 0.14189 1.54421 __ 23......COD...O..O ... -L..33..62..9___ll. .... O.l...B..B1 ______ Q., 0 .... ___ __ . .. .C. 093..4L ___ {1...2.'ll2.f! ____ Q_._L4..6.9_7 ___ 1. 57 35 8 24.CCCCO 1. 36503 C.C€4C7 C.O 0.09497 0.24383 0.15217 1.60232 2 5. CO COQ_ _ _ l. 39 318 C. Q.B..93.a _ ___ .Q.._Q_ ____ _ _ ___ 0 .. 0.9.659 __ jl._25l: 11 _Q_. 1 5 74 8 1. 63047 26.00000 1.42077 C.G948C C.O C.09825 0.21910 0.16290 1.65806 _..2.L...f.:.C1l.C.Q_ _____ l .... .4.4:1.8!t. __ __ o_ ..lO 032 . . _ o. a ___ ____ ____ Q. 09.9..9..!t_ ____ fr...2ft3..8~---_o_· 1 6 84 2 1 • 6 a 513 28.00000 1.47441 0.1059~ 0.0 C.1016E 0.29791 0.17404 1.71169 _____ 2.9 .. LC.Q.C.C __ _ __j__.__5Q.C.5.L_ __ _ C .... l .ll6 L ______ C .. .o __ ·---· . ____ 0 .103..45._. ___ .0.....312~. 0 _____ 0....1.197 7 1 .73 779 30.00000 1.52615 0.1174Q C.O 0.10525 0.32729 0.18560 1.76344 ------------------- - · -----,, 1 ;i . i . . Table 10. .. _ . . -· ·- ···-- - --. - -·- ---·· -·-· APP~CXI~tTE CALCLLATIC~ CF P~A S E ~PACE ELLIFS ES AFTE R TRAVERSING A TA RGET ___ _l _~~t;;E T MAlEk IAL::::- CM{ 8 0N I~CICE~T FARTICLE ~AS-CrARGE ~ C . 1.CC CC C ~C~E~lU~ lCSC. CO OOO VELUCll~/C C.7?8CC _s_, A_lT_E {( ER. tA~-.R~. ~- J_~_I 1 CJ'\ __ 1 EN <,; T r 4 2. 39999 DENSITY 2.25000 ____ l_tjJ .. ~ K- ~_ E;SS CSM ___ _ _ CXtJ tl P H ~ o.c . o.c c.c ···- ··-··.·--·- - . -- - ·- -·--- ---- -· --Vertical Plane input ellipse taken from ... . ·--___ Sy~:~ ~~II! ~..=§.8-:::!±_ _____ _ EM ITTA f\C E XM A X . .. - --· --··---~~~~ 0.06 343 0.25475 - - - ------_ .. _ ... J.!..LC .~ .. ~ C ___ ____ C -. ?J 86'! _____ C .OO Q} 2 c.c u.u l: HA C.2 1-t<1CC 0 .12027 0.01616 0.03422 C.04247 0.04951 0.06415 0.53339 •..•. - --- - - .:c___:_;;.._c_.;.__ __ _ 2 . UOOOO 0.39405 C.OC2C2 - -· ·- - -~· -(~ OCC C.4_826J ·--- C. 0037 ~ 4.(000 0 0.~?721 0.00572 __ ____ ?_! _CCQCC _0.62 .302 ______ C. CC ISS 6.COOOO 0.68252 0.01051 _ _ 7. CO..Q.Q C ___ __ Q .• _J.} 7_?_Q _________ 9_!_CJ}.2 4 s.coccc c.7A810 o.o1618 __ --~-~_Q.Q_Q_Q_C _ _ Q._§ 3_~ 2_l ______ Q. _9l <; 31 1C.COOCC 0.88113 C.C226l _ _ _!_! ~_9..Q.Q_Q_9 ... .. Q. ... 32_41_~- -- · 0 ~ 0. 2 §_Q ~.--c .c o.c o.o c.o C.lOCcS 0.091 0 7 O.Ob546 0.64 8B 1 0.06715 0.73737 --- ··--- --- --- · - ··---- ------· --·- - -- - -- -- -----0.0 8 516 0.05tl5 O.C6S15 0 . 3 12 0 3 0.08 1 3 7 0 .06270 0.07143 0. 8 77HO - . - ---· --- --- - ------ ----· 0.0 0.07B HS O.C6S3C O.C7394 C.93727 c • c c. c 1 7 3 c g ~ _oy_? 9 6. .. ___ _ ~L·_Q! 6 6 a o~·~9...:.9~1c..:.9..::6_· ___ _ 0.0 0.07634 O.C~3C3 0.07961 1.04286 o.c 0.07586 0.09024 0.(8274 1.09066 . -· ·· . -· · - ·-·--- ..• - - - - · ··- ·-····-------- -- .:::..=..:::._ _ _ _ _ _ c.c 0.07~75 0.09774 0.08605 1.13588 0.0 0.07594 0.10553 O.C8952 1.17889 ... ·-· ··- . ·- . ·•· ·-·-··-·--·-··-· -·-- -· ·-------·- -=-=-'-- ----------·-12.00000 o.9t~22 c.c2s12 o.o c.c7636 o .t1365 o.o9316 1.21998 _  13. __ CCQ_C_Q_. __ . t~ _  OQ4.~ '! _____ ... 9!_ Q 3~-~f . 0.0 0 .07(;98 ___ _ Q ~1?. 2 .~C __ ___ _ Q~_ 09695 1.25S3S 14.00000 1.042~6 C. C374t O.C C.C7777 0.13089 0 .10089 1.29731 ___ J 5 • _ _!:_9 c_~ ~ - -- 1._9_75! s.. ·--. _o .._<!._~ ~-~~-- o. c o. o1 s1 o u. 1~()Q ~--·- -9 • .1_ o ~~-I---~. 3 3 3_9-=.1 __ 16.(0000 1.11454 0.04576 0.0 C.07S75 0.14952 0.10920 1.36930 _____ ) __ 1 ~ !;_Q_9_Q 9 1. 1~ E ~ ,5 ____ C .._ C 5 C 12 0. 0 0. Od 09 0 0. 15~~~-- - _ Q __ !Jl }2_ 2. _ _ !__..__40 360 1 8 .00000 1.18215 0.05461 0.0 0.03215 0.16S61 0.11804 1.43f91 _ _.:1:;...;;9_;;; •. OOOO_Q _ _ _t!_~_l_4 5_? __ ~-Q~-~~..L_ i;.!...<L _ _____ .Q_!_ Q_834 E o .18 021 o. 12 265 1.46930 2C.CCOCC 1.2461G C.06396 0.0 0.08488 0.19119 0.12739 1.50085 _ ___ ) _1_. COO_QQ _____ ]._ ~-~J c_§_1 _ _ c;_!g68 8 !_ ___ Q_..__Q ______ _______ Q-._Q_8_~34 ___ ___ Q_..___?O 2 ~ 5 C. 1322 5 1. 5 3163 22.CCCCC 1.3069L C.0737~ C.C 0.08787 0.21429 0.13722 1.56167 2 3 • C O_Q_QO 1 • 3 3 6 2 9 0 • 0 78 8 7 O_.!_Q _ __ __ Q_. 0 8 9 4 4 0 • 2 2 t 4 2 0 • 14 2 3 1 1. 59 1 0 5 24.COOCC 1.36503 C.C84C1 C.O C.091C6 0~23893 0.14751 1.61979 25.CCCCC 1.39318 0.08938 o.o 0.09273 0.25183 0.15281 1.6~793 26.00000 1.42071 C.C~48C 0.0 0.09444 0.26512 0.15823 1.67553 27.CCCCC 1.447€4 C.1CC32 0.0 0.09618 0.27880 0.16375 1.70259 ·----- - - ---- --28.00000 1.47441 0.10594 o.o 0.09795 0.29288 0.16938 1.72916 _ :?_!}. CQQQQ_ ___ h _500 5C C.l1161 _ __ ()__! __ Q _____ _ __ ~....!- 09976 0.30735 9~_!._75_10 1. 7 5526 30.COOCC 1.52615 C.l174S 0.0 0.10159 0.32221 0.18093 1.7E091 --- ·-- - -- ---· - - ··--- - - --- ·- - - -- - -/ • • Table 11. AFFRCXIt-'~TE (ALCULAT lC~ lF Ft-ASE SPACL t:LL IPSES AfTER TRAVERSING A TARGET ··- 1 AK C El . NAJ . .ER lA.L~L.AR~GI\. l~CIC~NT FARTICLE t-AS-Ct-A~Gl ~C. 1.COODO Horizontal and Vertical Plane .... ·· ·-·· · -- · · ···--· · -··· ....... . ... l'. U-1£f~TL~ - l0'JO.J0000 -·· ... .... . ··- .. ·-· ··---···-·- ------------· VELOCITY/C C.75ECC input ellipse taken from .S..C A 1 ~1 £ R E R hAS-R A C 1 A I 1 CJ\ .u::: I\.C It. 't 2 • 3 '-} <..J 9 9 . I-68-6 --- -··--------DENSITY 2.2~0CC ... lh!C.K.I\.ESS LSJ\' ..CXt-' ALP HA tETA f:i"'ITTAr-.CE . XMAX .. _____ $.MAX.. _ _ __________ __ ____ ... U.C O.C 0.0 0 . 0 1.CCCOC 0 .01616 0.12712 0.12712 _______ l. (.CCC C. __ _ ( .27B61t ... ... L 0 COl2 0. 0 .. 0. 31506 0 .. C5 U:il . . . .O.l2.7..d.L ___ .0...._4..C._.5c.....7_....6'-:-___ _ C..COOCO 0.3S405 C.OC2C2 C.C C.247dC 0 . 06 731 0.12914 1 .52117 3.CCOCC C.4B2o1 . U.00372 0.0 0 .21458 'J.07'i78 0.1306.4 .. 0 .. .6..C9..13 _____ _  _ 4.COOGC 0.55727 0.0 0 ~7~ u.O C.lS41C C.O S C92 0 .1 32e4 C.6 8439 5.CCCCC C.t22C~ C.CC7SS 0.0 0.18011 0.10136 0.13512 _ 0 .. 75.017_ ·-·--- ----· -6.COOCO 0.682~2 0.01C51 0.0 0 .16YQS 0.11143 0.13763 0.8 0964 -· .. . 7 .•.. o.ouo o .. ... .c ..... .13.12.L ____ _ c. o 1.324 .... -· u. o . .. .. ... c .162.':t .. L __ _____ o .. l2.132 _______  o ... .l4.0.36 o. s.b!t3.2 __ _ B.COOOC C.7881C 0.01b1d U.J O.l565E 0.13115 0.14330 0.91522 .<;J......C.OOGC . . 0. tl3 5 '1 1 . C. C 15.3 L _. C. 0 C. 15 2C5 . C. 14101 .. -· 0.146.4.3 _ _ __ 0. .. 9 . .63..03 ____ _________ . ··- . 1C.CCOCC O.b81l~ C.022t1 C.C 0.14851 0.15097 0.14973 1.00825 ll ... GDO OO O.<J2413 . 0.02605 0.0 0.14574 . . . 0 •. 16LCc 0_.15.32.1 __ _1 ... .0512.5.. __________ ____ _ 12.CCCCC o.qt:22 C.C2~72 O.C C.14159 0.17133 0.156H5 1.09235 . __ ___ 1.3 ._LG.C LC _ _ 1 .... C 046{t ... ___ 0 .. 0.3.352 0 .. 0 __ 0._14 .l.S ~ _ .. ... 0 •. 181EC ____ . 0 .l6.0.tL.4_ ____ J.....Li.l.1fL._ 14.00000 1.04256 C.C3746 0.0 0.14C7C C.19(:~0 0.16458 1.16968 ____ 15. LC C..C..C._ . L • . C.J915 _ __ _ C ... 0 .415'1 ___ 0. C C .. 139 dL . .. __ Q .20345_ ... . .O .. . l.6.3..6.6_ _____ 1 ... .2.D...6.2..8.. 16.COOOO 1.11454 0.04576 0.0 C.13924 0.214!:1 C.ll2f8 1.24167 . __ _ l 7 .. C.CC.LL .. . . 1. 14 885 __ G •. 05..ClL. .... C .. Q D .1389_1. _____ 0_ .. 22615 _ .O ..... L7.L2..L. ____ .L...215.9L ___ __ ____ .. 1d.COOOO 1.18215 0.05461 0.0 O.l388C 0.23793 0.18173 1.30928 _ _lg_~o.a.o_ __ ...l..a..2.l.!t.55 __ _ .c ... ..a.5.S2.2.. __ __ c_. a _________ __c_._t3J3..a..s _______ .c .. z sao 1 __ Q .... 1Bo34 1. 34167 2C.CCCCC 1.2461t 0.06396 0.0 0.13915 0.26239 0.19108 1.37322 ___ Ll ... G.QOOC..__ L~2.76.dL _ ___ C....D.t...B.aL ____ .O .... D ___ .. . . ..0.13555 ___ 0 • .27.5.1J<.L . __ .0 • ..1..95.9~ __ ..1 ....4.0. ....... 39J....9~---· 2~.ccocc t.3C692 c.c737E c.c o.14o1o o.28811 o.2oo91 1.43404 __ _ 23 ... 0 0..0 QO ___ ..1....3.3 6 29 .... . __ Q ... .O .l.BB.~- ____ .O_.._Q __ _____ _.C .1_4_0.7 6._ . ___ 0 .. _3_0 .l!t5 __ _o_._2Q.5_9_9. _ _ __._I.._ • ..::x4_...b_.3=4"-2 _____ _____ _____ -··-·· ... 24.COOOO 1.36503 C.08407 0.0 C.l4154 0.31513 0.21119 1.49216 __25.a..ll.QCO 1.39318 C..OB938 O • ...Q _ _ ..Q.._14241 0 ..... 3...25.1.2_ _ _ 0.21650 1.52030 26.00000 1.42077 C.CG48C 0.0 0~14337 0.34351 0.22192 1.54789 ___ 2J.L.CL..CC _ _ l ..... ~4.1.8A _ _ C.....LG.C32. ___ ____ C. C ______ ., _____ Q ... l .44AL __ _ o_.._35.8.2..L _ _ Q • .22..1.!t!t._ ___ L.....5..L4L.:9u6"---- -- ····--- - -.. ··--2B.COOOO 1.47441 0.10594 0.0 0.14553 0.37326 0.23306 1.60153 _ __ 2..S ....... C.G.O C c ___ l .. ..5.GC..5.C __ _ .C .1.1l.O.l .. C • . C._ G. 146 7_L __ .0 .• 38 86.6.. ____ _ 0. 23.a.7_9 ____ _ 1 .. 6.2.1..6..2__ ___ _ _ __ ----- ···-30.COOOO 1.52615 C.l1749 0.0 0.14796 0.40442 0.24462 1.65328 - -- ---------· ------

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