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Design and calibration of a precise ion energy control system for a Van De Graaff electrostatic accelerator.. 1952

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DESIGN AND CALIBRATION OF A PRECISE ION ENERGY CONTROL SYSTEM FOR A VAN DE GRAAFF ELECTROSTATIC ACCELERATOR AND ITS USE IN THE STUDY OF RESONANT REACTIONS IN SOME LIGHT ELEMENTS. by David Andrew Aaronson A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n PHYSICS We accept this thesis as conforming to the standard required from candidates for the, degree of Doctor of Philosophy i n Physics. Members of the Department of Physics T H E , U N I V E R S I T Y 0,F B R I T I S H C O L U M B I A December, 1952. ABSTRACT A precise energy control system has been constructed for the U.B.C. e l e c t r o s t a t i c accelerator. Over the past s i x months i t has provided analyzed beams of protons as large as ̂  microamperes on a target with an energy homo- geneity of 0.1%. In the system adopted, the accelerated pos i t i v e ions are analyzed by a 90° d e f l e c t i o n magnet provided with entrance and exit s l i t s to define the beam path. The magnetic f i e l d i s s t a b i l i z e d to a few parts i n 1 0 0 , 0 0 0 , and controlled by a nuclear magnetic resonance method. A f r a c t i o n of the emergent beam f a l l s on two insulated s l i t s ' ^ " s n i f f e r s " , connected to a d i f f e r e n t i a l amplifier, the output of which varies as the beam impinges more on one than the other. Thus an error signal i s obtained according to the s h i f t i n energy and hence p o s i t i o n of the beam, which i s used to modulate a reverse beam of electrons sent up the d i f - f e r e n t i a l pumping tube of the generator. This beam loads the generator so as to maintain i t s voltage, and hence the energy of the ions, constant. The main central part of the beam passes through the s l i t s onto the target mounted beyond. One-dial control over a range of 20 KeV i s achieved by simply tuning the o s c i l l a t o r c o n t r o l l i n g the frequency of the nuclear magnetic resonance fluxmeter head. The energy of the ions can be varied i n steps as f i n e as 0 . 2 KeY i n 1,000 KeV. The generator's voltage scale (the generating v o l t - meter) and energy scale (the magnetic f i e l d of the analyzing magnet) have been calibrated r e l a t i v e to the currently accepted standard value of Herb, Snowdon, and Sala of O.8735 MeV for the strong F 1^(p, c* V ) 0 l 6 resonance and checked with the 0.3^0*+ MeV resonance occurring i n the same reaction. Additional c a l i b r a t i o n points were obtained using mass 2 and 3 beams. The complete gamma ray e x c i t a t i o n curve for the re- actions from bombarded with protons has been taken up to 2 MeV and new resonances found at 1.62 and 1.8^ MeV. The 1 .355, 1.381 MeV doublet was resolved with a peak to trough value of 9/1 which i s excellent confirmation of the homogeneity of the proton beam. The resonances i n the N-^Cp, <A>^)C 1 2 reaction have also been investigated and background yields from various target backing materials measured up to 2 MeV. THE UNIVERSITY OF BRITISH COLUMBIA F a c u l t y o f Graduate S t u d i e s PROGRAMME OF T H E F I N A L ORAL E X A M I N A T I O N FOR T H E D E G R E E OF DOCTOR OF P H I L O S O P H Y D A V I D ANDREW AARONSON B.Sc. (Western Ontario) 1949 M.A. ( B r i t . Col.) 1950 TUESDAY, DECEMBER 16th, 1952, at 3:00 P.M. IN ROOM 301, PHYSICS BUILDING of COMMITTEE IN CHARGE Dean H. F. Angus, Chairman Professor J . B. Warren Professor C. A. Barnes Professor E. Leimanis Professor F. Noakes Professor J . Halpern Professor E. Signori Professor W. B. Coulthard Professor G. M. Shrum GRADUATE STUDIES F i e l d o f Study: P h y s i c s . X-Rays and Crystal Structure -- Professor J . B. Warren Nuclear Physics -- Professor K. C. Mann Quantum Mechanics -- Professor G. M. Volkoff Electromagnetic Theory -- Professor W. Opechowski Special R e l a t i v i t y --Professor W. Opechowski Advanced Quantum Mechanics -- Professor W. Opechowski Electronics -- Professor A. van der Z i e l Advanced Electronics -- Professor A. van der Z i e l Theory of Measurements -- Professor A. M. Crooker S t a t i s t i c a l Theory of Matter -- Professor A. J . Dekker Chemical Physics -- Professor A. J . Dekker Other S t u d i e s : , D i f f e r e n t i a l Equations -- Professor T. E. Hull Advanced D i f f e r e n t i a l Equations -- Professor T. E. H u l l Design of E l e c t r i c a l Machinery -- Dean H. J . MacLeod Operational Methods in Engineering -- Professor W. B. Coulthard Advanced C i r c u i t Analysis -- Professor W. B. Coulthard T H E S I S DESIGN AND CALIBRATION OF A PRECISE ION ENERGY CONTROL SYSTEM FOR A VAN DE GRAAFF ELECTROSTATIC ACCELERATOR AND ITS USE IN THE STUDY OF RESONANT REACTIONS IN SOME LIGHT ELEMENTS A precise energy c o n t r o l system has been constructed f o r the U.B.C. e l e c t r o s t a t i c accelerator. Over the past s i x months, i t has provided analyzed beams of protons as large as 4% microamperes on a target with an energy homogeneity of 0.1%. In the system adopted, the accelerated positive ions are analyzed by a 90° de f l e c t i o n magnet provided with entrance and e x i t s l i t s to define the beam path. The magnetic f i e l d i s s t a b i l i z e d to a few parts in 100,000, and controlled by a nuclear magnetic resonance method. A frac t i o n of the emergent beam f a l l s on two insulated s l i t s , " s n i f f e r s , " connected to a d i f f e r e n t i a l amplifier, the output of which varies as the beam impinges more on one than the other. Thus an error signal i s obtained according to the s h i f t i n energy and.hence p o s i t i o n of the beam, which i s used to modulate a reverse beam of electrons sent up the d i f f e r e n t i a l pumping tube of the generator. This beam loads the generator so as to maintain i t s voltage, and hence the energy of the ions, constant. The main central part of the beam passes through the s l i t s onto the target mounted beyond. One-dial control over a range of 20 KeV i s achieved by simply tuning the o s c i l l a t o r c o n t r o l l i n g the frequency of the nuclear magnetic resonance fluxmeter head. The energy of the ions can be varied i n steps as fi n e as 0.2 KeV i n 1,000 KeV. The generator's voltage s c a l e (the generating voltmeter) and energy scale (the magnetic f i e l d of the analyzing magnet) have been calibrated r e l a t i v e to the currently accepted standard value of Herb, Snowdon, and Sala of 0.8735 MeV for the strong F 1 9 (p,°<.lf)016 reson- ance and checked with the 0.3404 MeV resonance occurring i n the same reaction. A d d i t i o n a l c a l i b r a t i o n points were obtained using mass 2 and 3 beams. The complete gamma ray ex c i t a t i o n curve f o r the reactions from bombarded with protons has been taken up to 2 MeV and flew reson- ances found at 1.62 and 1.84 MeV. The 1.355, 1.381 MeV doublet was resolved with a peak to trough value of 9/1, which i s excellent con- firmation of the homogeneity of the proton beam. The resonances i n the N ^ (p,°^tf)C^ reaction have also been i n v e s t i g a t e d and background y i e l d s from v a r i o u s t a r g e t backing materials measured up to 2 MeV. PAPERS PRESENTED BEFORE LEARNED SOCIETIES 1. Crystal Controlled Frequency Divider from 150 kc/s to 60 c/s. Presented before the Institute of Radio Engineers, London, Ontario, chapter, 1949. MEMBERSHIP IN LEARNED SOCIETIES 1. Student member, Canadian Association of Physicists, 1947/52. 2. Student member, Institute of Radio Engineers, 1946-52. 3. Engineering pupil, Association of Professional Engineers, 1947-52. ACKNOWLEDGEMENT. The author wishes to express his sincere thanks to Prof. J.B. Warren who has constantly guided and encouraged him i n a l l his work at the Unive r s i t y of B r i t i s h Columbia. Thanks are also due to Dr. C.A. Barnes for invaluable help i n nuclear physics and to Prof. W.B. Coulthard for the many helpful discussions on regulator systems. He i s very g r a t e f u l to the members of the Van de Graaff group of the Unive r s i t y of B r i t i s h Columbia, both s t a f f and research students, without whose generous help, t h i s work could not have been done. The author would l i k e to express his appreciation of the awards of a Bursary and Studentships made to him by the National Research Council without which i t would have been impossible f o r him to pursue his s c i e n t i f i c carreer to thi s stage. Thanks are due to the Defence Research Board f o r their f i n a n c i a l a i d i n carrying out t h i s research work. Table of Contents.. Page Introduction i Part I The Van de Graaff Accelerator and S t a b i l i z i n g Equipment. I. Acceleration of a Beam of P o s i t i v e Ions. 1 I I . _ The Energy Selector and Analyzing Magnet. 3 1. Introduction 3 2 . Proton Magnetic Resonance Absorption . 5 3 . Proton Magnetic Resonance Fluxmeter and F i e l d S t a b i l i z e r 0 10 (a) Magnetic Current Regulator 10 (b) Error Signal from the Fluxmeter 11 (c) Fluxmeter r - f Head 12 (d) r - f Head Power Supply 13 (e) Fluxmeter Signal Amplifier and Phase Sensitive R e c t i f i e r 13 (f) Fluxmeter Regulator Chassis ih (g) Attenuator Interconnecting Network 15 (h) Operation and Performance of Flux Regulator 16 ( i ) Engineering Features of the Magnet - S t a b i l i z e r 17 (j) Accuracy and S t a b i l i t y 19 *f.. Vacuum Deflection Box ; 20 I I I . The Spray Current S t a b i l i z e r . 21 IV. S t a b i l i z e r for 2 M i l l i o n V o l t s . 2h 1. Need for the S t a b i l i z e r 2h 2 . Modulated Reverse Electron Beam Voltage S t a b i l i z e r 25 Theory of Operation 26 The Insulated S l i t s ("Sniffers"): 29 -5. D i f f e r e n t i a l Amplifier 30 6 . Reverse Electron Gun 30 I: V.- Voltage S t a b i l i t y and Control. 33 1. Placing the S t a b i l i z e d Beam on the Target 3*+ 2 . One-dial Adjustment 35 VI. Homogeneity of the Beam and Energy Resolution 1. Beam Homogeneity 2 . Energy Resolution VII* Future Operation of the Accelerator 38 Part II Voltage and Energy C a l i b r a t i o n VIII. Measurement of High d-c Voltage *+5 1. Measuring One M i l l i o n Volts h5 2 . The Generating Voltmeter k-6 IX. Absolute Measurement of Energy of Heavy Charged P a r t i c l e s h7 1. Magnetic Deflection >+7 2 . E l e c t r o s t a t i c Deflection kS 3 . Other Methods ^9 X. The Importance of Accurate Energy C a l i b r a t i o n f o r Nuclear Physics 50 XI. Absolute Voltage and Energy C a l i b r a t i o n 5*+ XII. C a l i b r a t i o n of the U.B.C. Van de Graaff Accelerator 55 1. Preparation of Targets 56 2 . S l i t s and Target Box Assembly 57 3 . Counting Equipment 60 h. Checking the Counting Equipment 6 l 5. The Ca l i b r a t i o n Curves and Determination of k 6 l 6 . Calculations and Preliminary Results 63 7. F i n a l Calibration:' , Nov. 1952 68 8 . C a l i b r a t i o n of Generating Voltmeter 70 XIII. Summary of Results on C a l i b r a t i o n 70 1. Reproducibility and Absolute C a l i b r a t i o n 70 2 . Possible Sources of Error i n Absolute Energy Measurements 72 Part III Determination of Some Nuclear Exci t a t i o n Functions XIV. Resonant Reactions 73 XV. The Breit-Wigner One-Level Dispersion Formula 7*+ 1. Reaction Cross Section and Yie l d 7*+ 2 . Application of the Dispersion Formula to Show the Peak Y i e l d f o r a Thin Target Resonance Curve Occurs at E - Eg - f § /2 77 3 . Relative Yie l d of Thick and Thin Targets 78 ( p , o l V ) Resonant • Reactions 79 XVI. Limits of Energy Resolution 80 1. Doppler Limit to Energy Resolution 80 2 . P r a c t i c a l Limits -to Energy Resolution 80 XVII. The Proton Bombardment of Fluorine 82, 1. TP-ray.- Excitation Function 82 2 . New Resonances at 1.62 and 1,8k MeV 83 XVIII. The Proton Bombardment of N 1^ 8h Appendix 86 References 89 LIST OF ILLUSTRATIONS. figure Facing P, 1 Prototype of U.B.C..Van de Graaff Generator 1 2 1 Analyzing Magnet h 3 Magnetization Curve k : k Fluxmeter r - f Head k 5 Block Diagram of Flux Control Equipment 1G 6 90° Deflection Graph 11 7 Fluxmeter (Proton Resonance): r - f Head C i r c u i t 12 8 Fluxmeter (Proton Resonance) Signal 13 Amplifier and Phase Sensitive R e c t i f i e r 9 Compensating Network 13 10 500 C/S O s c i l l a t o r 15 11 Interconnection of Flux and Current Error Signals • 16 12 Total Error Signal 16 13 Spray Current S t a b i l i z e r and Graph 21 I 1* Cathode Follower as Current S t a b i l i z e r 22 15 S t a b i l i z i n g System of Accelerator Block Diagrams 22 16 S t a b i l i z i n g System of Accelerator 25 17 Reverse Electron Gun and Curves 26 18 Spray Current and Accelerator Voltage 33 19 S l i t s and Target Box Assembly 57 20 "V"-Ray Counting Equipment Block Diagram 60 21 C a l i b r a t i o n Curves at 0 .8735 MeV, Sept. 1952 61 Figure Facing Page 22 Generating Voltmeter C a l i b r a t i o n , September, 1952 70 23 Fluorine ""J^-Ray Ex c i t a t i o n Function 82 21+ Fluorine O^^O^ MeV Resonance 83 25 Fluorine 1.355 and I . 3 8 I MeV Resonances 83 26 Fluorine 1 .62 , 1.69 and 1.8^ MeV Resonances 83 27 Fluorine 1.8^ MeV Resonance 83 28 Fluorine 0 .8735 MeV Resonance with a Mass 2 Beam 83 29 Fluorine 0.8735 MeV Resonance Curves, November, 1952 C a l i b r a t i o n 83 30 Nitrogen V - R a y Resonance, O.898 MeV 8h 31 Nitrogen If-Ray Resonances, 0.1+29 and 1.21 MeV 8h i Introduction. The E l e c t r o s t a t i c Generator i n Nuclear Physics. The Van de Graaff e l e c t r o s t a t i c generator 1 i s a machine for providing a constant source of d-c p o t e n t i a l of several m i l l i o n v o l t s which i s free from r i p p l e and stable to better than 1%, An important precise tool for Nuclear Physics research i s obtained by f i t t i n g a suitable vacuum tube to the generator f o r acceleration of p o s i t i v e ions or negative electrons for use as bombarding p a r t i c l e s . The whole assembly of d-c generator, vacuum accelerating tube, and the a u x i l l i a r y apparatus needed to provide the source of ions as well as a selection and control of t h e i r energy, i s c a l l e d the " e l e c t r o s t a t i c accelerator". The e l e c t r o s t a t i c accelerator i s the most suitable machine available at present f o r investigating the energy l e v e l s i n the l i g h t elements for i t alone can provide a very constant but r e a d i l y variable accelerating p o t e n t i a l . I t i s the object of t h i s thesis to describe how the e l e c t r o - s t a t i c accelerator of the University of B r i t i s h Columbia was s t a b i l i z e d to i t 0.1$, calibrated with respect to an absolute voltage and energy scale, and then used i n the investigation of (p,<*V ) resonances i n some l i g h t n u c l e i . Figure 1. Prototype of U.B.C. Van de Graaff Generator to face page 1, Bart I The Van de Graaff Accelerator and Stabilizing Equipment I. Acceleration of a Beam of Positive Ions The Van de Graaff generator provides a high voltage for the acceleration of ions.. Figure 1, shows a cut-away- view of the prototype of the 1.3.C. machine. Positive charge, which i s sprayed from a high voltage set on to a long end- less insulating belt, i s carried up into the inside of a large hollow metal electrode where i t i s removed. This charge, which spreads to the outside surface of the electrode, raises i t to a very high potential of equilibrium value determined by the balance of charge carried up and the load on the generator. A long vacuum tube, f i t t e d with an ion source and focussing system at the top end, reaches from inside the hollow metal electrode to ground where i t connects with a vacuum box containing a target. The ions are injected into the vacuum tube, are focussed and accelerated by the high potential with respect to ground and strike the target with a high velocity. The generator voltage i s coarsely adjusted by varying the spray current from the high voltage set. The University of British Columbia Van de Graaff i s a vertical pressurized machine designed for a potential of four million volts. It uses an electrodeless, radio fre- quency type of ion source which provides a source of a l - most mono energetic atomic ions (up to 75% of H ^ i n a total current of up to 50 /v amps,homogeneous in energy within 100 electron volts, (eV)), with low gas consumption (about 0.15 c.c. per minute at 760 mm. of mercury) and good fo- cussing. The ion source-together with pressure bottles of hydrogen and deuterium, palladium thimbles, power supplies:, controls and monitoring meters ise f i t t e d i n the confining space of the polished top terminal (about 3i" feet diameter and 3i" feet h i g h ) T h e r e are two vacuum columns,. 16 feet long, one of which is used for differential pumping while the other i s the main accelerating tube used for the pos- i t i v e ion beam. Four large o i l diffusion pumps maintain a vacuum of 2 X 10~̂ mm. of mercury or less during normal operation with a beam of positive ions. The insulating column supporting the top terminal and equipment is made up of 6h aluminum equipotential plates, each spaced by three 2 7/8 inch porcelain spacers. Sections of conducting rubber join each plate to the metal electrodes of the two vacuum tubes. In addition there is a *+50 megohm resistor linking each pair of plates to h provide a .constant load of 2.8*+ X 10 megohms for the machine. The f i r s t equipotential plate up from ground is however returned to a negative potential of 1200 volts to suppress secondary electrons emitted from the grounded inner surfaces of the bottom of the vacuum tubes. The main parts of the machine (figure 1.) are enclosed in a large steel pressure tank which is pumped up with to face p.3 dry nitrogen (plus freon 12) to a pressure of 75 to 100 pounds per square inch to i n h i b i t corona. The pressure tank i s provided with a number of glass viewing ports as well as a periscope for viewing meters i n the top electrode. The accelerator w i l l of course accelerate any type of ions produced by the source, but for most investigations, atomic ions of hydrogen - protons - or of deuterium - deuterons - are required. For some purposes a source of helium ions would be useful but the r - f type source tends to produce He ions, not alpha p a r t i c l e s with two charges:. II.-The Energy Selector and Analyzing Magnet. 1. Introduction. The accelerated beam of ionized hydrogen contains the following ions: H - protons, (mass 1 ) , HH"*" - si n g l y charged hydrogen molecules, (mass 2 ) , HHH"*~ - (mass 3 ) . A large 90° analyzing magnet provided with a vacuum box between i t s pole faces was used to focus and separate the d i f f e r e n t mass components. This magnet, weighing over seven tons, required a current-of about ^5 amperes at 250 v o l t s d-c to provide a f i e l d of about 20,000 gauss over i t s 16 inch square.pole faces through i t s one inch a i r gap. A degenerative electronic current s t a b i l i z e r , b u i l t Figure 3 MAGNETIZATION C U R V E RUBICON S E T T I N G , V(VOLTS): V" 0 0 5 0 8 I 0 0-5 1 0 1-5 2 0 2-5 20 18 16 CO CO 3 < o - J X o Q bJ 14 12 10 8 o Z CD < 2 1 1 i 1 1 / O / / - - / - / o / f - / / © / - / o / - / — r e/ / — 7° O -/ 0 li 1 o INCREASING C U R R E N T DECREASING 1 i 1 i 1 i 1 i 80 70 6 0 CD Is- Is- I© o u o. cs V. o 40 30 UJ Z X 20 10 10 20 30 4 0 50 MAGNET C U R R E N T , l (AMPS) by the author^, held the f i e l d constant to a few parts i n 1 0 , 0 0 0 . Figure 2 i s a photograph of the magnet. The magnetization curve i s shown i n figure 3 . •'•he hysteresis loop was too narrow to show up, about 0 . 2 amperes wide at 15 amperes and about 200 gauss high at h kilogauss. The analyzing magnet separates ions of different charg to mass ratio and of different energy. Thus i f a parallel beam of ions of energy eV - i mv2 (II.1) are incident on the entrance s l i t , then they w i l l be de- flected through 90° and pass through the exit s l i t i f their radius of curvature is of value ^ fixed by the positions of-the s l i t s , where: H e v - mv2, (II . 2 ) r and (using c.g.s. units) H i s the magnetic f i e l d strength between the pole faces in e.ra.u. , e i s the charge of the ion in e.s.u. , m i s the mass of the ion, v is the velocity of the ion,, c i s the velocity of light, ^ i s the radius of the path of the ion, V i s the potential through which the ion was accelerated. Combining equations (II.1) and (II.2) gives the relation- ship between the accelerating voltage, V, charge-to-mass ratio, e/m and the momentum of the particles, H ^ 5. V r e H 2 £ 2 . (II.3) 2 m c 2 In addition, the well known focussing properties of a • , i 90° magnet allow maximum beam on the target with exact d e f i n i t i o n of p and hence of beam energy. Since e/m i s constant for each mass component, and since ^ may be f i x e d by entrance and exit s l i t s on the magnet box, ions of energy eV - E only w i l l be focussed at the ex i t s l i t i n a f i e l d of constant H. However, from equation (II. 3 ) , i t can be e a s i l y seen that f o r a given curvature, A E - AJ -2AH (11*1+) E V ' " H so that a highly s t a b i l i z e d f i e l d i s needed to maintain the emergent ion beam homogeneous i n energy, E. For t h i s purpose a proton magnetic resonance fluxmeter was b u i l t fo r f i e l d measurement, s t a b i l i z a t i o n and co n t r o l . 2 . Proton Magnetic Resonance Absorption. As a consequence of quantum mechanics, a l l i s o l a t e d nuclear systems possess a t o t a l angular momentum I quantized i n i n t e g r a l or h a l f - i n t e g r a l values, i n units of h/2 TT (j£"). Experiment shows that for even mass number (A) n u c l e i , I i s i n t e g r a l ( 0 , 1 , 2 . . . . . ) and for odd A n u c l e i , I i s h a l f i n t e g r a l ( i , 3 / 2 , . . . . ) . I t i s also found that a l l n u c l e i having an even number of protons (Z) and an even number of neutrons (N) have I - ©. Associated with this t o t a l angular momentum, which may be loosely c a l l e d nuclear spin, i s a nuclear magnetic moment 6 . which is again of course, zero for even Zj, even N nuclei. Y " > the gyromagnetic ratio, the ratio of the magnetic moment to the angular momentum, has been measured quite accurately for a large number of nuclei. When nuclei are placed i n a strong magnetic f i e l d , H, they may orient themselves in different quantized d i - rections with respect to the f i e l d because of their magnetic moment. Each position defines a quantum mechanical state possessing a certain energy and there are (214-1). possible S. states. The energy of these states i s E - E G +• Mj ME (II.6) where Mj i s the projection of the vector I on the axis of the magnetic f i e l d H. For transitions between adjacent levels, 4 Mj 1 and no others are allowed by selection rules. Therefore the energy difference between these states is AE EL. -^y"H . (II.7) If, now an oscillating magnetic f i e l d , Hj_, perpendicular to H is applied, transitions may be induced between neigh- boring states most strongly when the magnetic resonance relation holds true, i e . A E - • ' K w . f i y H , (II.8) where U J i s the frequency of the applied f i e l d E±ln the $ A H T " the work done to rotate the dipole t - -• - - ^ r I against a f i e l d H from the past to the Mx j next possible position i s H cose -juE Mj r-f range, and gives the Larmor precession frequency for the nuclear spin vector about H. These transitions w i l l occur not only by absorbing energy from the r - f f i e l d applied but also in stimulated emission. Since the tran- sition probability i s the same for each direction no ab- sorption of energy from the applied f i e l d would occur i f this was the only factor to be considered. ,However the thermal motions within the sample of nuclei set up fluctu- ating magnetic fields which can act upon the aligned magneti dipoles and sometimes change their orientation. This "spin-lattice" interaction does not affect states of higher and lower energy equally however; Boltzman stati s t i c s i n - dicate that a slight preponderance of dipoles w i l l exist in the lower states. Thus for protons for which I - f there are two states, parallel and anti parallel having an energy difference A E- - 2 ^ p H so that in< equi- librium, which takes place with a time constant T i , the "Relaxation Time", of from 10 to 100 seconds depending on the l a t t i c e conditions, the ratio of protons present in the two states i s : N' higher £ e , (II.9) • N lower where k i s Boltzmanh's constant and T is the absolute temper- ature. For room temperature with a f i e l d of 5 ,000 gauss, 4E/kT ^ 3 X 1 0 " 6 whence: N - N AE /-*- 2 M H lower higher - kT~ ~ kT ? " ' (11.10) N lower Thus the slightly larger population of the lower state 8 . w i l l result in a higher absorption than stimulated emission from the upper state. The extra energy so absorbed appears as heat energy in the l a t t i c e vibrations and motions. Consider protons in a sample of water. With no exter- nal magnetic f i e l d , the orientation of the protons w i l l be quite random. When a f i e l d , H, is applied the protons w i l l assume only two quantized positions with respect to the applied f i e l d ; s t a t i s t i c a l l y about half w i l l be align- ed parallel to the f i e l d and about half anti-parallel. The thermal motion of the nuclei brings about changes in their spin orientations so that there i s a slight excess of protons i n the lower energy state (parallel) according to Boltzmann's s t a t i s t i c s . There i s a characteristic time associated with this re-orientation process, the spin- la t t i c e time, T^, which for protons i n water (plus some ,MnCl2) i s of the order of 0.G1 seconds. The excess of protons in the lower energy state is about 7 per million in a f i e l d of 10 kilogauss. The magnetic resonance con- dition (II.8) may be satisfied i f the oscillating magnet- i c f i e l d , H-p i n the radio frequency (r-f) range (about ho Mc/s) is supplied by a small c o i l surrounding the water sample. H-j_ ,of the order of 5 gauss,may be obtained by applying about 0 .5 volts from a suitable oscillator to the r-f c o i l . The magnetic resonance absorption signal observed under the above conditions varies from a few microvolts to a m i l l i v o l t depending on H, the size of the sample, the value of T, and the homogeneity of H around the sample. 9 . In practice, r - f power is supplied to a small c o i l containing the sample of protons. The strong magnetic f i e l d , H, applied to the sample i s modulated by a small pair of Helmholtz coils so as to sweep through the reson- ance condition many times (up to 500) per second. The net absorption of power by the nuclei from the r - f c o i l is detected as a lowering of the Q, of the oscillator c o i l (an increase in the effective series resistance of the coil) and may be displayed as a resonance signal after amplification on a cathode ray tube operated i n synchronism with the modulation frequency. By using the most recent value^ of ̂ fp for protons and substituting in (II.8 ) , the simple relation for measur- ing the magnetic f i e l d H in terms of the frequency fp i s obtained: H (kilogauss) - 0.23^865 f\ (Mc/s)±0.002^ ' p (11.11) A. suitable r-f power source, set- of modulation co i l s , amplifying and detecting equipment therefore constitutes a very precise fluxmeter. Fields as low as 11 gauss and as high as 12 kilogauss. have been measured with this method using proton samples. The lower limit i s set by the strength of the resonance signal obtained, which varies directly as 7 the square of H and the size of the sample . Since the signal strength decreases with inhoinogeneity in H, size of the sample is also a li m i t although water samples as large as one l i t e r have been used. The upper limit i s set by the d i f f i c u l t y of obtaining the r- f f i e l d excitation over a sufficiently large sample of protons in the presence Fig.5 BLOCK DIAGRAM OT COMPLETE PROTON RESONANCE FIELD CONTROL BgJIPMBHT m&gnet current regulator, d-e generators, etc, eleetro- aagnat proton reson- anee r-f head, modulation coils amplifier, phase sensitive r e c t i f i e r compensat-ing net-work 500 c/s oscillator cathode ray- oscilloscope attenuator 10, of a very strong magnetic f i e l d . The noise level i s set by the tubes in the detector and the f i r s t stage i n the amplifier. For protons, the S/N ratio i s sufficiently large to give signals adequate for use in stabilizing systems 8 without the need for low noise high gain amplifier . This i s not the case for other nuclei. Higher magnetic fields may be measured at lower fre- quencies (than that for protons) by using a nucleus such as L i ^ which has a larger gyromagnetic ratio than the proton. For example, in the same magnetic f i e l d , H, the ratio;. f L i - 0.388625 f_ (11.12) has been measured experimentally so that equation (11.11) 7 becomes, when using a sample containing L i ' nuclei: H(kilogauss) - 0 . 6 0 ^ 3 ^ 6 f L i(Mc/s). (11.13) This means that with suitable extra amplifying equipment, fields over 2-|- times as great could be measured at the same frequencies shownin (11.11), for protons. 3 . Proton Magnetic Resonance Fluxmeter and Field . Stabilizer. (a) Magnet Current Regulator.- Before the f i e l d of the magnet was s t a b i l - ized, i t s current was controlled by a degenerative regulator ci r c u i t . A standard manganin resistor inserted in the magnet current leads produced a voltage drop which was compared to the voltage of a standard c e l l (through a Rubicon potentiometer) by means of a Brown converter chopper. An error signal derived from this after amplification and detection was used to control the f i e l d current of two Figure 6 9 0 ° D E F L E C T I O N ( R A D I U S , p = 2\2 C M ) 11. constant speed d-c generators supplying the magnet current. The resulting magnetic f i e l d , up•to 16,000 gauss, was held to one part in 10,000 over short periods and to within a few parts in 10,000 over longer periods. (b) B r r o r Sjgpalffrom the Proton Magnetic Resonance Equipment. The proton resonance equipment provides a d-c error voltage proportional to the deviations of the magnetic f i e l d from the desired value H, as given above. The amplitude and polarity of this flux error voltage vary as the magnetic f i e l d i s below, equal to, or above the value H within the few gauss range of the proton re- sonance. The flux error voltage i s derived as follows. An a-c signal i s f i r s t obtained by modulating the magnetic f i e l d by a small pair of coils so as to sweep across the 9 proton resonance . This a-c signal of a few hundred micro- _ volts i s then amplified and passed through a phase sensitive r e c t i f i e r to give the required d-c error voltage (see •' figure 12). This flux error voltage, when added to the magnet current error voltage,„provides the f i n a l control of the magnetic f i e l d . Figure h i s a close-up view of the fluxmeter r-f head. One of the modulating co-ils may be seen at the right, on the outside of the search c o i l box. The r - f c o i l and proton sample stee inside the brass case, behind the mod- ulating c o i l . A block diagram of the complete flux control I 1 All,tubes SAGS; A l l condensers in #*f. 25-44 Mc/s ~ L i z. 8 "turns, L 2 «r 3„/*h. K - Kilohm. 12 . epuipment i s shown in figure 5. The equipment built to control the flux directly consisted of the following units: r- f head and stabilized power supply, proton resonance signal amplifier and phase sensitive r e c t i f i e r , 500 c/s oscillator, compensating network, cathode, ray oscilloscope and power supply. Power for a l l these units was supplied by a Sola constant voltage transformer. (c) Fluxmeter r-f head. The cir c u i t of the fluxmeter r - f head following the design of T. C o l l i n s 1 0 i s shown in figure 7. The head contains a weakly oscillating detector consisting of a pair of 6AG5 tubes in a push-pull arrangement. The oscillations are kept small by the two by-pass condensers from plate to ground and feedback from the additional 6AG5 tube used as a low gain amplifier. Only one control, the two-gang variable air condenser, i s needed to tune the oscillator over about a 2 to 1 frequency range. This condenser together with the search coilj. inside of which * i s placed about 1 c.c. of a 0 . 1 molar solution HnSO^, forms the tank cir c u i t which i s loosely coupled to the oscillator tubes. The complete r-f head i s r i g i d l y mounted in a heavy brass box with the search c o i l protruding (figure h). Two kO turn double-pancake1- wound coils are cemented to the outside shield plates of the search c o i l for modulating the magnetic field.. Two r-f heads with additional coils were f i n a l l y used i'igure 8 Proton Resonance Amplifier 8 Phase Sensitive Rect i f ie r 300 V B • © below output 6S07 Figure 9 Compensating Network 6SL7 10 oil 500 c / s «N«0 5 0 - 0 - 5 0 uamp B $ P R O T O N R E S O N A N C E E R R O R ON - O F F IM 220 100 5 T -5 T - M A A — w IM to current >̂ regulator input resistors in kilohms, condensers in u f •, M = megohm 6SF5 d-c on h e a t e r s 1 3 . to cover the frequency range from 11 Mc/s to 55 Mc/s in four overlapping steps as shown in Table 1 . Table 1. Fluxmeter Coil Ranges. Head # Coil # Frequency Range Mc/s Flux Range kilogauss 1 1 55 - 33 12.9 - 7.75 1 2 Mf - 25 10 .3 - 5.9 2 3 27 - 18 6 .3 - h:25 k 19 —11 h.5 - 2 .6 I (d) r - f Head Power Supply. An electronically stabilized power supply 1 1 (Elmore and Sands, p. 373) provided the r-f head with 250 volts and 150 volts (gaseous diode regulated). A 0-50 milliameter inserted i n the 250 volt lead indicated the strength of oscillation i n the r-f head (8 to 10 ma. i n - dicated strong oscillation, 10 to 15 ma. or greater showed weak oscillations, while greater than 20 ma. meant no oscillations at a l l ) . This, together with a voltmeter, was completely enclosed in a steel cabinet and mounted near the magnet. A 6 volt lead-and-acid storage battery supplied the heaters for the r- f head as well as those of the proton resonance signal amplifier. (e) Fluxmeter Signal Amplifier and Phase Sensitive Rectifier. This unit, figure 8 , consisted of a con- ventional two stage r-c coupled amplifier with some negative feedback and a cathode follower output. The output was l l f . coupled to a phase sensitive r e c t i f i e r and output meter. The "bandwidth of the amplifier was limited by a twin-T feedback network, antiresonant at the modulation frequency of 500 c/s. The overall voltage gain at 500 c/s was 1 0 , 0 0 0 . The gain was down 15 4b. at 120 c/s and 2 ,000 c/s; down 21 db. at 60 c/s and 5,000 c/s. This limited bandwidth kept the signal to noise ratio, to about 50 to 1 for the proton signals at the output of this amplifier. The a-c flux-error signal, "was fed via 35 feet of coaxial cable to the regulator chassis, where i t was displayed on a cathode ray tube. A Sylvania lN^O (which consists of 2 matched pairs of 1N3*+ germanium diodes) was used as a phase sensitive r e c t i - f i e r or switch demodulator1^. The values of resistance and capacitance used as "bias.!'10 (220 k and 0 . 1 uf) gave maximum d-c output for the 500 cycle input signals. The 500 c/s local signal for the phase sensitive r e c t i f i e r , and the plate supply voltage were both fed via a shielded cable from the fluxmeter regulator chassis. A centre-reading microammeter with multiplier, connect- ed across the output of the phase sensitive r e c t i f i e r , show- ed when the proton magnetic resonance was being detected. The meter needle, reading 20-0-20 volts f u l l scale, indicated proton magnetic resonance f i e l d regulation by i t s small random motion about centre.. This unit was also completely enclosed i n a shielded cabinet and mounted beside the magnet•< (f) Fluxmeter ReguiaAOj? Chassis. This chassis contained the 500 c/s modulat- Figure 13 SPRAY C U R R E N T S T A B I L I Z E R 0 - 7 0 K V H T - S U P P L Y 12 M A A A A A E IM AC C 16 E T so 01 UF TO SPRAY BARS M» MEGOHM ; K« KILOHM » S G » SPARK GAP R« 30 M, C-O-l pF - 25 KV Z LLI or or O 5 i or o_ c/5 300 200 100 R K « 135 K 190 K 600 K R K • CATHODE RESISTANCE 20 30 40 50 HT- S U P P L Y , K V 60 70 Fig. 10 500 C /S OSCILLATOR : 6SN7 6V6 resistors in kilohms; condensers in of; M megohm, a-c on heaters 15 . ing oscillator, gain control, compensating network, a cathode ray oscilloscope, and a power supply for the above components. The 500 c/s oscillator, figure 10 , differed from the usual Wien Bridge oscillator only in the use of a transform- er load (H333^; in the second half of the 6SN7. The sec- ondary of this transformer supplied about 20 volts to the phase sensitive r e c t i f i e r and the 6V6 power amplifier as well as to the horizontal sweep amplifier tube of the cathode ray oscilloscope.. A phase shifting network was inserted ahead of the phase sensitive r e c t i f i e r and c.r.t. sweep amplifier to compensate for changes in phase that the modulating signal received in i t s path through the 6V6 tube, coupling transformers, fluxmeter head, and amp- l i f i e r . The 6V6 tube supplied up to 100 ma. of current to the 80-turn modulation c o i l s , allowing a few gauss sweep of the magnet's f i e l d . The gain control, f i l t e r network, switch, and Miller integrating circuit are shown in figure 9 as the"compen- sating network'.' The two stage r-c f i l t e r smoothed the output pulses of the phase sensitive r e c t i f i e r . The Miller integrating network provided a long time constant needed for s t a b i l i t y of the flux control loop. The effective grid-to ground capacity i s given by the formula C - Cg ri;late(l+K) where K i s the voltage gain of the stageas^O (g) Attenuator Interconnecting Network.- A simple resistive attenuator network was;: F i g . 11 JLIITJBflJUWMJBUTlOJ of FLUX and CURRENT ERROR SIGNALS proton resonance equipment flux error ——• electromagnet current regulator, amplifier, etc. magnet ourrent error A A A /—-r .05 ohms (manganin) b d-c generator Fig. 1.2 TOTAL ERROR SIGNAL (flux plus current) arbitrary units flux error • 1.0 I - 0.5 I current error I 0.5 I 1.0 gauss off resonance 16., inserted between the output of the proton magnetic resonance equipment and the input to the amplifier of the current regulator apparatus. This interconnecting network gave the desired addition in the direction of flux error signal to current error signal, while keeping the undesirable coupling i n the reverse direction small between the voltage across the manganin resistor and phase sensitive r e c t i f i e r diodes. This may be seen in figure 11 . The attenuator consisted of a 3 megohm and a ^7,000 ohm resistor. This reduced the amplified proton magnetic resonance flux error signal to a few millivolts which was then added to the approximately 25 v of error voltage derived from the magnet current. The relative magnitude and shape of the error signals i s indicated in figure 1 2 . (h) Operation and Performance of the Flux Regulator. The equipment was operated from the accel- erator control console, by setting the oscillator i n the r-f head to the proton magnetic resonance frequency pertain- ing to the f i e l d required for deflecting protons through 90° as read from the graph figure 6 or from the equation (11.11).. The magnet current was set to give a f i e l d just below the required value and increased slowly u n t i l the proton magnetic resonance signal appeared on the cathode ray tube screen mounted at the control panel. The f i e l d was held accurately at this value which defined the energy of the analyzed, accelerated proton beam. In most cases, the flux error signal was strong enough to allow one d i a l "frequency" control of the magnetic f i e l d over about 1 Mc/s 17. in 30 Mc/s, i e . about 0 . 2 kilogauss in 6 kilogauss, without need for altering the magnet current setting control. As a result, the current setting needed only to be changed manually at intervals. (i) Engineering Features of the Magnet Stabilizer. A number of safety devices and interlocks were provided to protect the operator and the magnet from the 12 kilowatts maximum of power i n the c i r c u i t . A r e c t i - f i e r connected in the reverse direction across the magnet coils discharged them quickly and safely i f the c i r c u i t was opened or the power f a i l e d . In addition, power was cut off from the magnet i f the water-cooling failed, i f the current regulator tubes (6AS7) drew grid current or i f the cabinet door was opened to the magnet's generator's shunt f i e l d power unit (^00 volts d-c at 1 ampere). An overload current relay limited the shunt f i e l d current to 1 ampere. Two re-set push-buttons placed the equipment in operation again when a l l faults were cleared. The current regulator alone had six main time constants, five lagging and one leading. The longest one, 3 seconds for the magnet, was large compared to the next one, 1/20 second for the d-c generator's shunt f i e l d s . The four others, from 1/100 to 1/10,000 second were in the input and output circuits of the Brown converter d-c amplifier. Hunting did occur with a large voltage gain in the amplifier but was eliminated by reducing the gain to about 6 0 d b . , leaving a phase margin 1^ of about 1 5 ° . The response time of the 18. regulator to a step voltage input was about 1 second. The flux regulator c i r c u i t i t s e l f had four main time constants. The longest, a h-00 second lead i n the Miller integrating circuit, was inserted to prevent hunting i n the regulator. Two others, about 1/10 and 1/hO second were i n the smoothing network following the phase sensitive r e c t i f i e r . The last one, about 1/100 second was due to the relaxation time of the protons being swept through magnetic resonance by the modulation c o i l s . With the addition of the integrating circuit, a gain of about h$ db. was allowed with good s t a b i l i t y . A good feature of the r - f head oscillator was i t s small d r i f t of about 1 part i n 10,000 over several hours. Silver ceramic condensers were used as trimmers and for coupling of the oscillator c o i l to the air tuning condenser. This minimized the effect of temperature changes on the frequency of oscillation. Changes i n capacity of the large air condenser in series with the small ceramic coupling condenser were reduced in the ratio of their capacities, i e . about 10 to 1. A l l components i n the oscillator c i r c u i t were: r i g i d l y mounted i n a heavy brass case to reduce vibra- tion changes of capacity. The warming up time of this oscillator as well as that of a BC221 heterodyne frequency meter was about % hour. The BC221 i s a calibrated, crystal-referenced, low- power oscillator f i t t e d with an accurate vernier d i a l . It was made for the U.S... Signal Corps and bought as war 19. surplus. The fundamental tuning range, around 1 megacycle has strong harmonics up to about ho megacycles. A chart, calibrated with the instrument allows conversion of the dia l reading into frequency. An internal 1 Hc/s crystal i s provided for periodic checking.:.. After warm-up, when battery operated, the oscillator d r i f t was found to be less than 1 part in 10,000 i n several hours. Since the audio amplifier aupplied with the instrument for "zero-beat" identification was too insensitive, the outputs of this oscillator and the r - f head were coupled by means of co- axial cable to the input of a Hallicrafters SX-62 communi- cations receiver. The zero beat was detected by f i r s t tuning the receiver,;to one of the signals. Then by varying the other, the two signals were brought to the same fre- quency ("zero-beat") which was measured by the B.C.221.- Ear-phones were usually used with the receiver as the noise level in the accelerator room was rather high, (j) Accuracy and St a b i l i t y . The magnetic f i e l d setting was held to within a value set by the homogeneity of the f i e l d over the search c o i l which determined the half width of the Q proton resonance signal . The inhomogeneity of the f i e l d over the search c o i l was about 1 part i n 10,00 which gave rise to a proton magnetic resonance signal width of about 0.3 gauss. The relative accuracy for a f i e l d of 10,000 2 0 . gauss was +T 1.5 parts in 1 0 0 , 0 0 0 . The U.S. Signal Corps B.C.221 heterodyne frequency meter was used to measure the r - f frequency continuously to about 1 part in 10,000 so that f i e l d settings could be repeated from day to day within this accuracy. The Ea l l i c r a f t e r SX-62 communication re- ceiver allowed identification and zero-beating of the proton oscillator and frequency meter. Care had to be taken not to tune to the image of the signals at twice the receiver's <V.' i - f frequency, i e . 0 . 9 Mc/s above the desired signal. 4 1 The magnetic f i e l d regulator was checked and was able to maintain i t s accuracy for line voltage changes ofHf 1 0 $ . For sharp droPs in line voltage such as switching on the two 15 h.p. motors of the electrostatic accelerator, there was a drop i n f i e l d accuracy for about one second. A variac inserted in the a-c line to the regulator equipment was used for the check against fluctuating line voltage. The regulator s t i l l functioned at voltages down to about 90 volts. On the other hand, the effect of sharp drops in line voltage was to change the magnet current more rapid- l y than the regulator could follow. The regulator was able to recover f i e l d control usually within a few seconds, by i t s e l f , with no manual re-adjustment needed. The good feature was perhaps due to the long time constant (about 7 minues) i n the compensating network, and the shorter but inductive one in the Sola constant voltage li n e .regulator. 1+. Vacuum Deflection Box. A large copper vacuum box, which was f i t t e d i n the one inch gap between the magnet's pole faces, joined the 21. lower end of the accelerating tube to the target tube. Eight ports on this box provided for entrance of the ion beam at the centre or edge of the pole face, i t s exit straight down, simultaneous exit of resolved mass.'land mass 2 beams on one side or the other, and for exit of a single mass com - ponent on one side only. A ninth port allowed auxilliary pumping by a small separate o i l diffusion pump and rotary backing pump. The box was provided as well with shut off valves and a l i q u i d air trap for condensing o i l and water vapors. The whole target box,,which could be isolated from the accelerating tube by a large vacuum valve for quick change of targets or target assemblies,was also provided with two vacuum gauges; a Pirani gauge registering from atmospheric pressure to lO^mm. of mercury and an ionization gauge which extended the range down to 10"̂ mm. Two hollow lengths of thick soft iron shielded the accelerated proton beam from the fringing magnetic f i e l d at the entrance and exit ports of the magnetic box so that consistent results were obtained when the beam entrance; hole was suitably defined. III. The Spray Current Stabilizer. After the magnetic f i e l d had been stabilized to a high order i t was required that variations i n the energy, E, of the beam be reduced so that a,reasonable analyzed beam intensity could be maintained on a target. As the next step in the precision energy control of the accelerator Figure 14 CATHODE F O L L O W E R AS C U R R E N T S T A B I L I Z E R e g = v ~ ' p R k (b) E Q U I V A L E N T (c) WITH T R I O D E , ( l ) , C I R C U I T AS C A T H O D E L O A D O F (2) Figure 15 STABILIZING S Y S T E M O F A C C E L E R A T O R I + S T VAN DE G R A F F G E N E R A T O R A I t ST, AMPLIFI E R , E L E C T R O N GUN i(+) A N A L Y Z I N G M A G N E T , S L I T S (a) B L O C K D I A G R A M (b) E Q U I V A L E N T B L O C K 2 2 . the spray current was stabilized since the accelerating voltage, V, followed the spray current as can be seen in figure 18.. For this purpose a simple adjustable current limiter was inserted i n series with the high voltage spray supply. The two tube circuit,figure 13.,was inserted i n the high voltage lead. Large capacitive 60 cycle currents prevented i t from functioning properly in the earthy lead of the spray supply., An isolation transformer insulated for 75,000 volts supplied the filaments of the two tubes while a selsyn coupled by means of a textolite rod allowedi safe remote adjustment of the current setting control. The current limiting action of the circuit i s that of a cathode follower, an Eimac 15 E, having a large cathode resistance supplied by the pentode tube, the 6 S J 7 . With reference to figure 1*+ (a) and the equivalent c i r c u i t figure Ih (b), i t can be seen that the total current, i p , flowing into a cathode follower tube i s given by:; *k+ r P rp. - E + X V , \ (l-tA ) H - r p ' . (III . 1 ) where V i s the grid voltage, fixed, E i s the plate voltage, yi/ls amplification factor of the tube, r^ i s the internal resistance of the tube, Sr..' R k i s the cathode load resistance, e i s the total rise i n voltage from cathode to grid. o Therefore, i f yU» 1, the cathode follower appears to 2 3 . have a resistance to d-c current of the order o f R ^ . ohms. With reference to figure 1*+ (c) when Sjj. i s replaced by an additional tube (here considered as a triode for simplicity) then the total resistance of the circuit to d-c becomes of the order o f o r exactly:: i a - V a 4- \M$z . * p 2 + C >M 2*1) j p ^ + 1^4 1) R J ( I I I # 2 i where the subscripts refer to the two tubes. When Ri is made variable, the current i a follows i t directly., In addition to being able to vary the equilibrium current, this c i r c u i t tends to prevent any dynamic changes of current from the set value because of the feedback from plate to grid of tube #2 (Miller effect). Consider the response of the current i a to a sudden fluctuation A v a , assuming M.l} r p i a n d rP2 c o n s t a n t : — A i„ - A Va -+ Mz A Vo 2 L (III.3) But A V 2 ^ " 4 J a ( I I I ^ ) 2 so that A i ^ 0 In actual operation A i a is not zero but A i a / d V a , the dynamic impedance of the c i r c u i t , i s very high, of the order of 10',000 megohms, which compared to the value of about 200 megohms for the rest of the spray c i r c u i t gives a stabilization factor of about 50 to 1. The curves, figure 18 (a) and (b), taken with a Brown chart recorder,,show the spray current before and after the installation of 21+. this stabilizer. The spark gap i n figure 13 was set at about 15,000 volts as a protection against over voltage on the 15 E tube. Thus the spray could be varied + 7*5 kilovolts without altering the spray current appreciably, or with the spray voltage control fixed, the spray current could be adjusted remotely over a large range. This is shown by the curves in figure 13 .=> The range of the current stabilizer was from about 100 yd amps to 300 yU amps which was sufficient to .stabilize ttie accelerator's voltage (with a positive beam) from about 0 . 3 to 2 . 0 MeV. IV. Stabilizer for 2 Million Volts. 1. Need for the Stabilizer. With the installation of the spray current sta- b i l i z e r , the voltage fluctuations of the accelerator with a positive beam were reduced from h to 6% to about 1 to 2% as shown by the curves in figure 1 8 . These curves were taken with a Brown Electronik strip chart recorder whose input of 0 - 10 m i l l i v o l t range was fed by a small resistor inserted i n the generating voltmeter c i r c u i t . A vernier pontrol consisting of a 10,000 ohm rheostat i n series with the 500 kilohm cathode rheostat (figure 13) was operated by a reversing two-phase motor and remote switch ,at the control panel to increase the s t a b i l i t y to about 1%. This arrangement required someone to operate the vernier control almost continuously to maintain an adequate beam current of resolved protons or deuterons on the target as the Figure 16 STABILIZING S Y S T E M OF A C C E L E R A T O R B A S E OF D I F F E R E N T I A L PUMP ING T U B E GUN F ILAMENT RELAY 2 7 0 K — 150 0 V O L T S i 2 7 K A C C E L E R A T I N G T U B E I | l 'ON , B E A M Hi /// /// M A G N E T D I F F E R E N T I A L A M P L I F I E R accelerator's voltage varied. The variations in voltage were probably caused by the following: (1) Non uniform charging of belt at bottom and consequent fluctuation i n charge take-off at top. (2) Changes i n motor and belt speed due to line voltage fluctuation. (3) Unequalized resistor stack current due to belt flap or beam striking the inside of the vacuum tube. (*+) Changes in ion source condition due to warm- up or voltage fluctuations. (5) Change i n lens voltages due to same causes as in (h) (6) Ion beam defocussing by striking the f i r s t few accelerator tube sections and contributing to (3) above.. In the above (k) and (5) the voltage fluctuation i n the carbon-pile regulated kOO cycle supply in the top terminal could be of the order of 2%, However rapid variations in (1) and (2) were smoothed by the top electrode which has a comparitively long time constant of about 3 seconds.. 2 . Mpdulated Reverse Electron Beam Voltage Stabilizer. The ."final precise voltage stabilizer used a modulated reverse electron beam controlled by anerror signal obtained from the analyzed proton beam i t s e l f . A pair of insulated s l i t jaws ("sniffers") defining the analyzed proton beam was the source of the error signal which, after amplification, controlled the intensity of the beam emitted by the electron gun mounted at the base of the differential Figure 17 REVERSE ELECTRON GUN FINAL A NODE F O C U S ANODE 2 6 . pumping tube. With reference to figure 16, i f the voltage of the accelerator rises increasing the energy of the analyzed proton beam, then the bottom "sniffer" jaw receives more current since the proton beam appears to be " s t i f f e r " . (It i s bent through a larger radius ^ , equation (II.3 ) ) • The amplifier converts this current difference into a voltage which reduces the bias on the electron gun's control grid so as to increase the electron emission. This increased electron emission continuing up the differential pumping tube acts as an increased load to reduce the voltage of the accelerator u n t i l the proton beam is centred between the sniffer jaws. Conversely, i f the accelerator's volt- age decreases, the upper sniffer jaw receives more current, the amplifier passes an error signal of opposite polarity to the electron gun to decrease i t s emission, decreasing the load and increasing the voltage of the accelerator u n t i l the beam is again centred between the sniffers. (3) Theory of Operation. The accuracy and s t a b i l i t y of the above closed loop degenerative stabilizer depends on the gain of the system (amplification of error signal etc.) and the number I'D and size of the time constants involved in the system J . Since the f i e l d of the analyzing magnet i s highly stabilized, i t s effect on the system time constants may be neglected to a f i r s t order. A block diagram of the system ,figure 15 (a),shows i t to contain only two main time constants, one i n the accelerator's terminal, Tj_, and the other i n the amplifier, T 3 . T i ' i s about 1 .5 seconds when the accel- 27. erator i s loaded with an ion beam, and T is about 0 . 0 0 1 sec. .3 ( 1 0 meg. X 1 0 0 ^Xjxf). was obtained by noting the time for the top terminal voltage to f a l l to 37$ of i t s value when the spray was cut-off when there was no beam, and assuming that the loading was doubled when there was a beam. The "gain" Kj of the top terminal was estimated from a plot of the top ter- minal voltage versus the effective spray current with a pos- it i v e beam. K 2-Ai (sniffer beam current), ju amp/4 ̂ (accelerator volts), depended on the radius of the beam trajectory, the equilibrium value of the beam' current intercepted by the sniffer jaws, and the separation between them. i(-)/i(-f-) was obtained from the performance data of the amplifier and electron gun in operation. Representative values for these are:: K-̂ ss: 8 , 0 0 0 volts/; ̂ Uamps, K2- 1 /(.amps /1,000 volts and ^ 2 0 M amps/>( amps. The block diagram may be condensed into figure 15 (b) and analyzed (see appendix 1 ). It can be seen that since there are only two main time constants, having a ratio of about 1 5 1 , 0 0 0 to 1 , that the system should not oscillate or hunt . Then to evaluate the steady-state error, the equations of the servo loop are ̂ rcitten out as follows: £ - Bi - E c, (IV.1) E D - K G ( S ) £ (IV.2) - KGCSKEj. - E Q ) . E ± 1 K G ( S ) (IV .3) E Q - K G ( S ) t (IV.h) Thus But 2 8 . Dividing (IV.3) by (IVA) gives: j L 1 E. 1+ K G(S) , (IV.5) where the above symbols represent the Laplace Transforms of the quantities and S r . c T ~ + ^ u > ) a complex numbers £• represents the error signal in the system, Ej, represents the constant input quantity ( the energy of the analyzed positive ion beam determined primari- l y by the magnetic f i e l d setting), E Q represents the regulated output quantity (the Van de Graaff accelerating voltage), K G(S) represents the open-loop transfer, function. Now i f a step function input Ej_(S) - e^)/S is applied, the steady state error w i l l be given by applying the " f i n a l - ~ 16 value theorem": steady state error (t ) ^ lim S e i (t) S (1+K G(S)) - ej (t) . K (IV-6) Since the value of K£ = l 6 0 , this steady state error could prove troublesome. However, because of the large time constant of T 1 ? S T x<s/^ T i , i s large compared to 1 for frequencies f >> i , that i s for f » 1/10 or 2 T T Tj f ) 1 cycle/sec.:, In this case, K G(S) z= K / S T I SO that for any variations having a period less than about one second, the system behaves as i f i t has zero steady-state error due to this integration around the loop (appendix 1 ) . The theoretical upper limit of accuracyoof the-system" 2 9 . (about lOOeV). i s less than the practical limit set by the conditions l i s t e d i n chapterXVI* The above linear servo analysis holds (and i s borne out by the performance of the system) so long as the total fluctuations in the accel- erator's voltage are not too large. The spray current stabilizer serves to keep the fluctuations small and the range of the present reverse electron gun current i s also adequate u n t i l the generator voltage approaches 2 MV,where the fluctuations at times are too large for the system to handle well. (M-) The Insulated S l i t s ("Sniffers"). The s l i t assembly, figure.'.-..19,. consisted of a pair of semicircular 0 . 0 0 5 inch thick molybdenum plates spot welded to nickel leads. The leads were soldered to hollow kovar seals which were mounted in a vacuum tight flanged brass tube section. This was attached to the proton exit port of the magnet The s l i t width was usually set at about 1/16 inch but was used at inch 15 spacing for some of the f i r s t resonances in K (A more easily adjustable set of s l i t s had been made up in a glass section but were not used in most of the experimental , work because of a fracture i n the glass). A set of insulated s l i t s mounted at the mass 2 exit port of the vacuum box was tried at f i r s t and did provide an error signal for stabilizing the proton beam when a reasonable focus of the mass 2 beam was obtained. However since i t was d i f f i c u l t to maintain a good focus of the mass 1 and mass 2 beams together, and also because of the 3 0 . small mass 2 current, this method was abandoned in favor of the proton sniffers. (5) Differential Amplifier. The differential amplifier consisted of two 6SJ7 pentode tubes operated with a common cathode resistor, figure 16. The input current fluctuations from the sniffer jaws were connected to two 10 megohm resistors in the control grids of the tube while the output of the amplifier was taken from the two plates and fed to the reverse electron gun control grid and cathode. A 0-1 milliampere meter in the plate circuit of the #1 tube showed the total emission current of the electron gun filament as well as indicating by i t s random movement that the amplifier was receiving an error signal. A conventional unregulated power supply, supplied 1 ,500 volts to the voltage divider for the ampli- fi e r and electron gun operation. The 6SJ? tubes were selected for low residual grid current,and high mutual conductance and then matched in the circuit for equal plate.currents. d-c coupling was needed throughout the circuit to handle slow d r i f t s as well as rapid variations of accelerator voltage. (6) Reverse Electron Gun. A four-electrode electron gun was built to de- live r up to 50 /A amps of electrons with about 1 ,500 volts for acceleration i n i t i a l l y . The gun, taken from a 5AP1 cathode ray tube, was modified by enlarging the lens apertures and inserting a hairpin tungsten filament as cathode. When tested on a small vacuum system i t produced an electron 31 . beam of about 1G ^aamps focussed to a f inch spot at a distance of 37 inches. The f i n a l anode current was found to be proportional to the electon beam current so that a meter installed i n the f i n a l anode lead (and therefore: at earth potential), indicated the reverse electron beam current that was sent up the accelerator tube.,. This meter was the only part of this and the amplifier c i r c u i t that was mounted at the accelerator control panel. The electron gun was spot welded to nickel leads which were soldered to kovar seals on a brass base plate. The filament of 0.010 inch diameter tungsten, spot-welded to nickel leads,.was mounted with i t s two kSvar seals on a separate small brass plate for ease in centering and re- placement. .This is shown in figure 17 . The curves shown were taken on a test bench with the differential amplifier and the electron gun. The whole assembly was mounted at the base, of the differential pumping tube of the accelerator. A variac in the primary of a .2,500 volt i n - sulated filament transformer allowed adjustment of the filament current to about 7 or 8 amperes at about 2 volts. The total electron emission current amounted to about -|: of a milliampere of which up to 50 ̂ amperes reached the top- of the accelerator. This latter-figure was calculated from the drop in accelerator voltage as a result of this emission loading the accelerator,and a curve of accelerator voltage versus spray current. When the gun was switched 3 2 . on, the accelerator voltage dropped about 300 kilovolts in 1.5 MY. A one megohm potentiometer across a 90 volt battery- provided a bias voltage for the electron gun grid for deter- mining the equilibrium value of electron emission. The focus voltage was l e f t constant at about 250 volts with re- spect to cathode for best operation. Representative values for the electron gun's operation on the accelerator are as follows: Accelerator voltage 1.11 X 10 volts. Spray current 150 JU amps. Positive ion current 7 jU amps. Resolved proton beam h //amps. Electron gun Filament current 8^h amps. Bias setting -50 volts. Total emission. 1 ,000 >/amps. Final anode current 8 ju amps. Electron beam current (approx.) 10 ^aamps. This reverse electron beam, accelerated by up to 2 million volts, could produce many high energy x-rays i f the electrons were stopped at the top terminal by a material of high atomic number. Therefore a low atomic number metal, a plate of aluminum, was used as a stop for the electrons. In addition the top of the terminal above the aluminum plate was surrounded by about 6 inches of lead to absorb the x-rays that were gherated there. As a result, the x-rays from the accel- erator at 1 .5 MV, as measured at the control panel, increased by only about 10$ when the electron gun was in use. Figure 18 SPRAY CURRENT AND A C C E L E R A T O R VOLTAGE ( 0 ) NO STABILIZERS 2 7 4 I 7 0 * 66 I 36 SPRAY C U R R E N T A C C E L E R A T O R V O L T A G E ( N O BEAM) ACCELERATOR VOLTAGE ( 6 U A M P S (4-) B E A M ) (b) S P R A Y C U R R E N T STABIL IZED CO o. 174 5 170 ^ 166 SPRAY C U R R E N T I 48 1-40 1-32 > 1-77 Z 1-70 163 A C C E L E R A T O R V O L T A G E (NO B E A M ) A C C E L E R A T O R V O L T A G E ( 2 6 p A M P S (+) B E A M ) (c) A C C E L E R A T O R STABIL IZED 102 0 90 0 78 ACCELERATOR VOLTAGE ( 10 ^JAMPS (+), 3 UAMPS (-) B E A M ) 2 t T I M E , MINUTES 0 3 3 . V. Voltage Stability and Control. The University of Brit i s h Columbia Van de Graaff accel- erator has been in use in nuclear physics research since the summer of 1951, in various stages of st a b i l i t y . For example, for the production of high energy "y^- r ay s only , from nuclear reactions, l i t t l e voltage s t a b i l i t y i s needed provided the thickness or stopping power of the target (sea part 13); producing the -y"rays i s equal to or greater than the inhomogeneity in energy of the beam. For such experiments, the resolving magnet was not used so as to get the largest possible beam current. About one percent s t a b i l i t y was obtained by using the resolving magnet with f a i r l y wide s l i t s and a manually operated vernier spray current control. There ;were periods, after the accelerator had been running continuously some hours, when the voltage- remained within about 1 to 2% without manual readjustments;. 1 7 A long series of runs were made with the accelerator being used as a continuously variable monoenergetic source of neutrons from the reaction D (d,n)H . For a part of these runs an electronic "cutter" device was used to stop, the counting circuits when ever the voltage fluctuated enough to decrease the ion current to the target below a certain value. This prevented neutrons produced where the main beam h i t the target box from interfering with the reaction under investigation. The above experimental work provided a long term test also of the st a b i l i t y of the f i e l d of the 90° analyzing magnet.which was to form an integral part of the precise 3 * . ion energy control system. The magnetic f i e l d s t a b i l i t y was even sufficient when controlled by i t s current regulator only, with the proton magnetic resonance equipment being used for spot measurements of the f i e l d . • On addition of the precise ion energy control system using the modulated reverse electron beam the st a b i l i t y was brought to within about 0.1$ so that more precise ex- perimental nuclear physics research could be done. Almost no adjustments were necessary once the beam had been set and focussed. Even the i n i t i a l adjustments necessary for good focussing of the beam were made very nuch easier since the automatic feature of the beam centering not only kept the voltage of the accelerator constant but also held the beam on the target (or quartz or molybdenum disk) during focussing. Before this time, focussing was made d i f f i c u l t by the interaction of.the lens, probe, hydrogen gas leak and oscillator controls with the accelerator's voltage. The modulated reverse electron beam for stabilizing the accelerator^ voltage was able to compensate for a l l the variations that were mentioned previously. 1 . Placing the Stabilized Beam on the Target. The i n i t i a l adjustments of the accelerator for obtaining a stable analyzed beam were as follows:- F i r s t a vertical beam of about the desired energy was obtained and focussed approximately by letting i t travel straight down through the vacuum box into a small Faraday cup. Then the magnetic f i e l d was set to the precise value for bending the protons of the desired energy, the reverse electron gun was turned on and the accelerator's voltage 3 5 . adjusted u n t i l the beam "loeked.-on" i n the horizontal d i - rection to the target. When taking the error signal from insulated s l i t s defining the atomic beam, care had to b!e taken in order that the stabilizer did not "lock" on to the mass 2 or mass -3 beams. The modulated reverse electron gun was able in most cases to maintain the beam stable for fluctuations in accelerating voltage as great as 300 KV in 1.2 MY. Small fluctuations in accelerating voltage were held automatically to within about 0 .1$ depending on the focussing condition and arrangment of the s l i t s and apertures defining the beam. A spot about •£ inch i n diameter was obtained at the target, about 27 inches from the magnet, when the sniffers were about 1/16 of an inch apart. . 2 . One-dial Adjustment. The oscillator tuning control, alone, now pro- vided the fine accurate adjustment of the accelerator's voltage in steps as small as 250 electron !volts, and as large as about 100 KeV. That is at any voltage setting from 0 . 3 ^ to about 2 MV the accelerating voltage was not only homogeneous to about 1 kilovolt, but was also changed repeatedly at w i l l i n steps of about 1 kilovolt above or below any desired value. The lower limi t was set by the mechanical arrangement of tuning the oscillator; the upper limit by the maximum electron gun emission. In addition, the accelerating voltage and thus the energy of the bombarding particles was obtained precisely at each step by measuring the proton magnetic resonance oscillator's frequency to- 3 6 . gether with the relation obtained by combining equations (II.3) and (II.3) V - e 2mc2 (V.l> V(MV) ^ k f p 2 ( M c / S N (V.2> where k - e \ 2m | Y r c HV - Mc/s^ (V .3) k was determined experimentally as. discussed in part II. The magnetic f i e l d regulator and the over a l l accelerator's stabilizer operated together as follow-up servo systems i n response to changes i n the frequency settings.. The following procedure was used to change the volt- age accurately in kilovolt steps:; (1) The oscillator frequency was measured by zero-beating with the B.C.221 heterodyne frequency meter (using the Hallicrafter's communication receiver to pick up and .identify both signals). (2) The B.C.221 was increased i n frequency by an amount A fp equivalent to the voltage step desired, from equation (V*2) AfMc/s) - 4 v p _ (*-h) or Af„(Mc/s) - A V (MV) p . 2j~k V (MV). (V.5) (3) The Hallicrafter's receiver was tuned to this new frequency, (set at C.W.), then set to receive A.M. (h) The selsyn's remote tuning d i a l of the proton 3 7 . magnetic resonance oscillator was adjusted carefully u n t i l a zero-beat was heard. (5) The oscillator frequency was re-checked by zero-beating with the B.C.221 and recorded. (6) The accelerator's voltage was determined by equation (V.2) once k had been determined. In going over "y^-ray resonances for an excitation curve, a reading of counts at the point was started after (h) since the magnet and accelerator stabilizing systems respond almost immediately. The time required to carry out (1) to (h) was about 30 seconds, while (5) which required about the same time was carried out during the taking of "~y"-ray counts. It was possible for one man to operate the complete accelerator and take readings for an excitation function but help of an assistant made the task somewhat easier and allowed immediate plotting of the function. For excitation functions, having resonance half-widths of the order of 1 to 15 KeV, the oscillator control was quite sufficient to vary the accelerator's voltage over them. Then as the voltage was increased by more than this amount, the current setting dial (of the Rubicon Potentiometer) of the magnet was increased a small amount, and the above procedure repeated. The s t a b i l i t y of the voltage was demonstrated during each experiment by the a b i l i t y to repeat points taken on a resonance curve (within the s t a t i s t i c a l error of the 3 8 . measurement) and to take readings between two points taken previously. This can be seen for example on the 873*5 KeV 19 F resonance curve,figure 21,and on most of the other experimental curves that were taken. In one particular case, the resonance peak of an excitation curve was repeated on different days within a few parts in 10,000 (of the frequency measurement). A l l curves could be repeated on different days within a few parts in a 1,000. VI. Homogeneity of the Beam and Energy Resolution. Homogeneity in beam energy of about 0.1$ was obtained at voltages up to 2 M;V. The best homogeneity could be obtained however only with low beam currents and .consequent long times being required for a given experiment. The factors which contributed to good homogeneity with f a i r l y good beam currents were found to be the following:- (af)! A strong well defined parallel beam entered the magnet vacuum box. (b) The beam was centred and defined by a small aperture at the magnet vacuum box entrance port. . (c) A pair of shims at the entrance port of the vacuum box was adjusted to obtain the best focus of the resolved beam at 90° in the horizontal and vertical direction. (d)) A second pair of defining s l i t s were placed at the 90° focus. This pair had i t s jaws insulated and provided the error signal for the ion energy control system. 3 9 . (e) The beam was shielded magnetically with hollow soft iron cylinders from the changes in fringing f i e l d as the magnetic f i e l d was varied. Conditions (a) and (b) were obtained with care for the calibration and fluorine excitation function experiments. However since only one set of adjustable shims was avail- able on the magnet pole pieces some compromise had to be made in the focussing condition (c). In addition, the cylinder of soft iron at the exit port made i t d i f f i c u l t to place the insulated s l i t s close to the magnet box. But by careful'ad justment, a focus was obtained near the i n - sulated s l i t s and.once obtained, was held by the control ' system for periods as long as h or 5 hours at a time. 1-. Beam Homogeneity. On the assumption that the spread i n energy of the beam can be represented by a Gaussian curve , then the experimental "half-width" of a resonance curve for a thick or semi-thick target, where ^ ^ f"^is made up of g [~exp - J"* 2 + A e 2 - (VI.l) Or for a thin^target^ that i s one where ^ <(. , where:: j"~exp -*-s "^e experimental f u l l width at half max- imum observed on the resonance curve yield of "y -rays uo. plotted versus energy of bombarding particle, A E i s the energy inhomogeneity of the beam, P is the width of the resonance due to the physical nature of the nuclear process (see part III), <^ i s the loss of energy of the incident particle i n traversing the target, l e . the "thickness" in energy units. This w i l l be referred to as the "stopping power" of a target, although in normal usage this would be the dE/dx of the material. Since published "values of P obtained experimentally 2 0 are available in the literature, /\ E may be inferred from equation (Vl.l).pr with less certainty from equation (VI.2). However i t i s never certain that the published value of P represents the "natural" width because of d i f f i c u l t i e s in the calcula- tion of A E. For example, the value for P for the 873 .5 KeV resonance in F 1^ had been given as 5.2 KeV but a recent paper by Bonner and Butler 1^ claimed an experimental half width of if.3 KeV. They used a very thin LiF target (100 eV) and stated their beam energy spread was 0 . 0 8 $ . Since the exper- imental values obtained on thick and semi-thick fluorine targets i n this laboratory for were always less than 5.2 KeV i t was assumed that the P was of the order of *+.3 KeV. Therefore assuming Bonner and Butler's value for target thickness and beam homogeneity would give a value of h.2h KeV for P1 ; then substituting this in equation (VI.l) with the ["exp o f J +* 7 obtained from a thick CaF 2 target, gives for the beam inhomogeneity:: hi. A E - h.72 - h.2h2 - 2 .0 KeV. This amounted to an inhomogeneity of about ± 1 . 0 KeV i n $ 7 3 . 5 KeV or ± 0.12%. This also was checked at 3^0.k KeV with thin targets and was further borne out by the energy resolution obtained on the 873.5 KeV satellites and the 1355 - 1381 KeV doublet resonances. A further check of the homogeneity was obtained by a run over the 873.5 KeV fluorine resonance at 200 - 300 eV intervals on a thin target,figure 21 . The scatter of the: points at these intervals, smaller than the homogeneity of the beam, was of the order of +• 1 KeV. 2 . Energy Resolution. A l l the published "Y*-ray resonances from O^MD1* to 2 .0 MeV in the proton bombardment of fluorine were ob- served and compared well with the good curves of Bonner 21 et al at the Rice Institute,: Texas, and of Bernet et 21a a l at the University of Wisconsin. The two weak sat- e l l i t e s of the very strong 873*5 KeV resonance were resolved as well as the 1.355 and I . 3 8 1 MeV doublet. Table 3a l i s t s published resonance energies,.cross sections and half widths for the y v r a y resonances of fluorine together with the experimental half widths obtained with the Uni- versity of Br i t i s h Columbia Van de Graaff accelerator for comparison. The two new resonances defined during the author's work are also l i s t e d there and discussed later. Table 3a. Fluorine (p, ck Y ) Resonances. 20 Resonance Energy. ER(MeV) Cross section, X 10 2 l +cm 2 Half Width, P(KeV) U.B.C., Sept.-Nov.,1952, HxpCKeV) (KeV) 0 . 3 ^ ,kS6 .598 .669 .831 .8735 .900 .9353 1.092 1.137 1.176 I . 2 9 0 1.355 1.381 1.62* 1.69. 1 . 8 ^ 1.9^ 0.16 > O.032 0.0071 0.057 0.019 0.5*+ 0.023 0.18 > 0.013 0.015 0.019 O.029 O.089 0.30 1.7 < 2 . 0 37. 7 .5 8 . 3 5.2 • 1+.8 8 . 0 < 1.2 h.i ~ 1 3 0 . 19.2 8.6 15 . 3 0 . IF". 3.3 2.1 2 A 1.6 35 . 1.1 7. 1 .0 8.2 0 . 8 ^ . 3 OA k.Q 1.0 8 . 0 , 1 .0 3 . 5 0 . 9 0 . 9 broad 078 2 8 . 5.6 0 . 3 1 3 . 5 • 0 . 3 — • + New resonances. * Approximate target thickness for protons of energy E R. 1+2. VII. Future Operation of the Accelerator. The present arrangement of the accelerator with the above ion energy- control and stabilizing system operates well i n the low voltage region around 300 KV as well as up to 2 MV. However careful i n i t i a l adjustment was re- quired for good operation at 2 MV since the x-rays produced by the reverse electron gun and secondary emission i n the vacuum tubes had a tendency to cause voltage breakdown and i n s t a b i l i t y of a much larger order than could be handled by the automatic stabilizer. Because of the increased, production of x-rays above 1 .5 MV, the intensity of the reverse electron beam had been reduced, which reduced the range of voltage fluctuations over which the stabilizer "could control. As a result, around 1.9 MV, occasional manual adjustment of the spray current was necessary. By reducing the electron loading i n the vacuum tubes and by installing the intermediate shield electrode, the accelerator should be capable of operation up to 3 or ^ MV. Two or three aluminum baffles with about 2 inch diameter apertures inserted in the vacuum tubes could reduce the electron loading without seriously affecting the pumping speed of the columns. If, at the same time, an overhaul of the columns allowed a better vacuum by sealing off any minute leaks i t would reduce the tendency to spark from ionization of residual gas and would allow higher voltages to be maintained. The intermediate shield electrode (shown ^3. in figure 1), has^nottbeehiinstailed to date because of the inconvenience in l i f t i n g i t each time during the i n i t i a l periods of adjustment to the units in the top terminal. If the loading from the reverse electron beam proves to be excessive above 2 MV, there are alternative devices which could be substituted as the control element in the stabilizing system. The simplest would be to use corona 2 2 control by means of athigh voltage triode (25-50 KV). The triode's plate would be connected to a corona point facing the high voltage electrode of the accelerator while i t s grid would be controlled by the sniffer jaws plus amplifier. The great disadvantages of this system are the increase in corona and ionization in the insulating gas surrounding the machine and the slower response due to the lower mobility of the ions compared to that of an electron beam. A more elegant device 2^ uses an insulated "tank-liner" surrounding the machine but inside the pressure tank. A high voltage supply connected to the liner would be con- trolled by the error signal from the sniffers so as to vary the liner to ground potential to correct for accelerator voltage variations. This device would operate as fast, -as the reverse electron gun. Since a large body of nuclear physics research was made possible by the homogeneity of the beam and energy resolution achieved with this accelerator in the energy range up to 2 MV, i t was not f e l t that further development should be pursued for the time being to extend the voltage limi t by reducing the electron loading of the accelerator tubes. h5. Part II. Voltage and- Energy Calibration. VIII. Measurement of High d-c Voltage. 1. Measuring One Million Volts. Greatest precision i s obtained by measuring the ; electrostatic f i e l d produced by the high voltage. For example, in a method due to Lord Kelvin, the force on an electrode ; in'the f i e l d is balanced by a measured weight. However, the force i s proportional to the square of the f i e l d strength, , since from Coulomb's law, F - constant X qj_q2 where q-j_ and q 2, both proportional to ̂  , are the charge on the high potential and measuring electrodes. A linear electro- 28 static voltmeter, the generating voltmeter , described on page *f6, produces a small pulsating current proportional to the f i e l d . The range of this instrument can be extrapolated within 1$ from a calibration at low f i e l d strengths. • A calibrated resistor stack in o i l , to reduce corona, is used on most r e c t i f i e r sets. However, the voltage and temperature coefficients of the metallized or carbon^resistors usually used, precludes aecuraclesoof better than a few per 2 5 a cent . More costly and larger wire-wound resistors can improve this. A; less accurate but s t i l l useful method makes use of U6- polished spheres which are attached to the potential terminals. This sphere-gap method, relies upon measuring the distance between the spheres of known size (and at best under known conditions of humidity and temperature of the surrounding air); when spark breakdown f i r s t occurs 2' 7. Measurements £0 about 5% are possible by referring to published calibra- tion curves although the o f f i c i a l curves changed by 10$ from 193^ to 1936. 2. The Generating Voltmeter. A more accurate and reliable method makes use 28 of a "generating voltmeter" . This may consist of two segmented disks, one fixed and insulated, the other attached to the rotor of ah electric motor. When this arrangement faces a high potential electrode so that the insulated segments are alternately exposed and shielded from the high potential, the current which flows through an external circuit connected to the insulated segments i s directly proportional to the voltage of the high potential electrode. More specifically, i f C i s the capacity between the insu- lated segment and the high potential electrode and V the potential (to be measured), then i f the motor rotates n times per second, the current I. induced in an external circuit w i l l be proportional to 2CVn or: V - KI . (VIII.1) Therefore i f n i s kept constant, the voltmeter may be calibrated at a low voltage and then used to measure much higher ones. The f i r s t calibration of the U.B.C. accelerator ±7* was done by applying 50 kilovolts to the terminal and reading the small current in the external c i r c u i t . It was found that although absolute accuracy of this arrangement was within a few per cent, the relative accuracy over short and long periods was good to about 1%. A generating volt- meter as above with a pair of 6H6 diodes and d-c galvano- meter provides a continuous measurement (within the above limitations) of the voltage of the U.B.C. accelerator. However for more precise measurements, i t i s more convenient to measure the energies of charged heavy particles that have been accelerated by the high voltage. IX. Absolute Measurement of Energy of Heavy Charged Particles. 1. Magnetic Deflection. This method of bending charged particles in a magnetic f i e l d in vacuum involves the accurate-: measurement of H >̂ (equation H.3)» This measurement is subject to errors because of fringing f i e l d effects for which accurate corrections 'are d i f f i c u l t to obtain. The equations of motion of charged particles i n a magnetic f i e l d are relativ- i s t i c a l l y correct. That i s , equation I I 2 may be written as: 2 2 H 0 - mvc - (E 4- 2m 0cE> (IX.l) ' . e — — — • where E, m are the r e l a t i v i s t i c kinetic energy and mass respectively of the particle and 1% i s the rest mass. For protons of energy up to 2 MV, the r e l a t i v i s t i c correction to the momentum is less than 1 part in 1 , 0 0 0 . 2. Electrostatic Deflection (Method, of Herb.1 Snowdon and Sala). This method of using an electrostatic f i e l d for bending charged particles allows for accurate correc- tions to be applied for the effects of fringing fields on the particles entering and leaving the deflector. The new scale for proton "Y^-ray resonances and proton-neutron thresholds was established with the aid of accurately made electrostatic deflectors, f i r s t by A.Q. Hanson and 2*3 D.L. Benedict to 0 .3$ and more recently by R.G. Herb, 26 ' S.C. Snowdon and 0. Sala to 0.1$. . An exact analysis of the operation of the 90° curved 29 deflector by Warren et al was applied by Herb to achieve this accuracy. The two plates were maintained at potentials up to 15,000 volts symmetrically above and below ground to minimize acceleration and deceleration effects. The potentials were obtained from stacks of 500 volt batteries, whose potentials were measured carefully and accurately with a standaed c e l l and potentiometer.-. Corrections were applied for battery d r i f t , and leakage as well as for geometrical, electrostatic and magnetic effects in the arrangement. Then, for an ideal analyzer, considered to have an electric f i e l d determined inside by the simple equations for concentric cylinders and to have zero f i e l d outside, the relation that holds for the ideal path (where **9- the radius equals the geometric mean of inner and outer radius of the analyzer plates).' i s : ; £V» - V 0 • (1 - Y i d , (IX.2) where;; •g-V is the positive battery stack voltage (negative stack i s of the same magnitude). V 0 i s the voltage through which the protons have been accelerated. d i s the plate separation. b i s the arithmetic mean of inner and outer r a d i i . ~)C - e V 0/ (2m0c2) - V 0 (MV)/ 1880. The entrance and exit planes of the deflector were defined by s l i t s which also limited the extent of the electrostatic f i e l d . Corrections were also made for the effects of the f i n i t e s l i t widths. In the hands of R.J. Herb, this method of measuring high voltages from particle energies has proven to be one of the most accurate and reliable to date. 3. Other Methods. Several other methods for measuring the energy of charged particles have been used, but none have exceeded the accuracy of that of Herb et al.. One method however, involving the measurement of the velocity of the particles by timing^ (where actually a frequency i s measured) hass given an independent confirmation of one of Herb's deter- 7 7 minations, the L i (p,n) Be' threshold at 1.882 ^eV. A secondary and less accurate method used in the early days 50. of particle accelerators involved the measurement of the visible range in air of the particles. Besides this, secondary determinations of energy may be made from ion- ization measurements i n gases, heat and count of particles in a calorimeter, scintillations and even s t a t i s t i c a l scattering measurements.. X. The Importance of Accurate Energy Calibration for Nuclear Physics. In the experimental investigation of a reaction of transmutation such as::: X H - a - ^ Y + b + Q , (X.l) this symbolizes a particle, a, bombarding a target nucleus, X, (assumed at rest) to produce a resultant nucleus, Y, with ,the emission of another particle, b. Q., "the reaction energy balance," represents the energy involved i n the reaction. Two generalizations can be applied to this re- action:: (a) . Conservation of momentum (linear and angular), (b) Conservation of mass-energy. If the reaction i s endothermic (endoergic), then there exists, a "threshold" value for the energy of the bombarding particle, a, such that the reaction just takes place. In this case Q is negative:, Q; - kinetic energies of (Y-f- b) - kinetic energy of a, CX.2) which from (a) and (b) represents the net increase in 51. kinetic energy in the centre of mass system of Y plus b or the net decrease of rest mass i n the reaction, from Einstein 1 s energy and mass equivalence relation:; A E - A mc2 (X.3) That i s f - C M + M - M - ),c2, <x-^0 ~ x a y b vrhere the M's represent the rest masses of the respective reactants and; c i s the velocity of light i n vacuum. Thus from an exact knowledge of the threshold of an endothermic reaction the precise-Q;; value can be determined from only approximate mass values. Again i f the kinetic energy of b is also determined, for emission in some particular d i - rection, then both in exothermic(exoergic^ positive Q values)) and endo thermic reactions the Q value may be fixed. In addition, from accurate Q values, accurate mass differences may be calculated from the mass-energy balance, and since one MeV; corresponds to 1/931 mass unit a Q. value accurate to one KeV corresponds to a mass difference accuracy of 6 nearly one part in 10 which even to-day i s at least as, good i f not better than the best precision achievable with mass spectrographs. By choosing a series of inter-related nuclear reactions i t has been possible to build up an excellent set of mass values for the light elements based 31 solely on nuclear reaction data J • As an example consider the following data of Taschek et a l ^ 2 for the reaction T:^(p,n)He^, which i s a shorthand 5 2 - notation for the proton (p) bombardment of tritium (T3) which results in the formation of helium-3 (He3) plus a neutron (n). This may also be written as: T 3 -r- H 1 —> He 3 -f- n +- Q;- (X. 5) In addition, tritium is radioactive decaying to helium-3 plus an electron (/3) plus a neutrino (/O; T 3 ~+ He3 •+-/?-+- iycl+ Ep , (X.6) where E^ i s the maximum kinetic energy the electron ("beta- ray") carries away. If the rest mass of the neutrino i s assumed to be zero®, then by subtracting equation (X .6) from (X.5) where the symbols are taken to mean the atomic masses of the nucleiy the neutron - hydrogen mass difference may be obtained quite directly: n - H 1 - (T 3 - He3) - Q, (X.6a) - Ep - Q, (X.7) Ep is known with an uncertainty of about one KeV. Taking Herb's value of 0.9933 KeV as the energy of the strong Al 2' ?(p, V ) S i 2 ^ resonance, Taschek determined the thres- hold for reaction (X.5) as 1019 ± 1 KeV. When corrected for the centre of mass motion this threshold yielded a Q, value of - 763.7 ± 1 KeV for the reaction.. Taking the value of E^ - 1 8 . 5 KeV for the end point of the(*-ray 9* S.G.Curran, J. Angus and A.L. Cockcroft, Nature, 162, p. 302 (19*4-8) conclude from a study of the tritium /3-ray spectrum that the neutrino rest mass must be less than 0.002 times the rest mass of an electron. 5 3 - spectrum from the decay of tritium, then from equation (X.7) n --H1 ^ 782 ± 2 KeV. (X .8) This value was 28 KeV higher than the previously accepted^ value and approximately 20 KeV lower than the then recently determined value of Bell and Ellio.t^ 1 +, hut was in agreement 35 with the revised figures of Tollestrup et a l . From this i t is clear that the fundamental mass difference between neutron and proton can be accurately deduced so long as a reliable absolute energy scale can be provided from which accurate threshold measurements may be made. In this connection i t may be noted that up t i l l 19^9 an erroneous energy scale, based upon the Li' ?(p, "Y* )Be^ res- onance at khO KeV, had been accepted. Historically, the above , y )Be^ resonance energy was determined by Hafstad et a l 2 ^ in 1936 with reference to the voltage of their Van de Graaff accelerator. Their accelerator had been calibrated up to 500 KeV with a potentiometer and high voltage stack of resistors. This fixed voltage point, 1+l+0 KV +• 2 $ , after confirmation by several other experimenters^led to the adoption of a standard voltage-energy scale in nuclear physics. However as the experimental data and theoretical knowledge of nuclear physics increased, i t was realized that the choice of the lithium resonance energy value as a calibration point was an unfortunate one for two reasons. The f i r s t was that the voltage scale was too low by about 1 .5$ due to errors in calibration. The second was-that the resonance energy value had to be corrected for the continuous yield above resonance, a factor of about 1 KeV. These errors were pointed out as a result of the different investigations in nuclear physics concerned mainly with the neutron-hydrogen mass difference. This i s the fundamental quantity involved in a l l mass-energy determinations. The erroneous low energy scale however persisted u n t i l January 191+9 when the important results of H.E. Herb, S..G. Snowdon and 0,. Sala established the now accepted voltage and energy scale. While at present no satisfactory nuclear theory exists which can predict the positions of nuclear energy levels, i t i s important to establish the existence and accurate position of such levels from measurements of resonance maxima even i f only to seek regularities in the positions of such levels by inspection. Such a phenomenological approach was useful i n atomic spectra and i s beginning to be of use in nuclear physics, although at present i t is the order of magnitude of level separation which has significance rather than the exact energy of the "excited" states?' 7 XI. Absolute Voltage and Energy Calibration.. Calibration of the voltage and energy scale of the U.B.C. accelerator was carried out with reference to the absolute voltage determinations of Herb et a l . This, rather than an independent absolute determination, was used because of the r e l i a b i l i t y of Herb's values over the past 55. \t years. In addition, i t was f e l t that this calibration would be more accurate than one based on the calculation of H ^ in the analyzing magnet for oC -particles of . known energy for the reasons given in chapter IX. :'.-::-\ 26 Herb, Snowdon and Sala made three absolute voltage determinations based on the constants of a large electro- static ganalyzer. These determinations (in absolute volts-, rather than international volts) stated i n terms of the resonance or threshold energy of three different nuclear reactions aret. the L"i7(p,n)Be'7 threshold 1.882 MeV (XI.1) an A l 2 7 ( p , ̂ )S128 resonance 0.9933 MeV a F ^ C p ' o C 1 , Y)016 resonance 0.8735 MeV The uncertainties in the measurements are given to be about 0 . 1 $ . The determinations were carried out by bombarding in turn carefully prepared thick and thin targets of materials containing the above elements and noting the yield of neutrons or ~Y-rays as the energy of the incident protons was varied. The author of this thesis carried out a similar procedure in the calibration of the U.B.C. accelerator, with the exception that the above fixed point of 0.8735MeV was used to calibrate the magnetic analyzer. XII. Calibration of the University of B r i t i s h Columbia Van de Graaff Accelerator.. A number of determinations of the fluxmeter frequency 56. at which the peak of the ' reaction in fluorine at 0.8735 MeV occurred were carried out to find an experimental value for k from equation (V.2); k r V gmillion volts 2« (XII.1) f (megacycles/sec.) 1. Preparation of Targets. Thin and semi-thick fluorine targe'ts were prepared in vacuum by evaporating CaF2 on to clean polished copper backings. They were always exposed to air before they were used. Very thin targets of a few hundred angstrom units thick, were desirable to keep the experimental width of the resonance curves as small as possible for several reasons. (1) A sharply peaked, narrow resonance curve defines the energy of the bombarding particles more closely than a broad topped, wide curve. (2) The inhomogeneity of the proton beam and " ;the stopping power of the target can be estimated more closely when they are small compared to the widths of the resonance curves. (3) The natural half-widths (width of the resonance curve of half maximum) of the resonance curves can be calcu- lated with greater r e l i a b i l i t y . (h) The fluorine reaction gives a large yield of Y"~ r ay s s 0 that well defined curves may be obtained from very small amounts of fluorine. 2 It has been calculated that 3 to 9 micrograms per cm.. P Y R E X T U B E D ENTRANCE HOLE IN 0 005" THICK MOLYBDENUM 3 M SOFT IRON 1̂  OD 3" l-D- SLITS AND T A R G E T BOX A S S E M B L Y M A G N E T VACUUM BOX ( C 0 P P E R) 27' I 6 INSULATED S L I T S ( M O L Y B D E N U M ) S Y L P H 0 N B E L L O W S TARGET ON R O T A T A B L E HOLDER - f - i i SOFT IRON 2 " 0 D - 1 " 2 , D ' P Y R E X T U B E J L ^KOVAR S E A L S T A R G E T BOX ( C O V E R R E - MOVED) FARADAY CUP OTHER M A T E R I A L S , B R A S S - , O-RING S E A L S B E T W E E N S E C T I O N 57.. of CaF 2 have a stopping power of -§• to 2 KeV for protons of about 1 MeV i n energy.. Taking the density of CaF 2, d - 3.18 gms./cm2», then the thickness of a layer of lO^gms./cm is given by: t - 10~^/3. l8 - 300 X 10~ 8 cm.- A small amount of CaF 2 was weighed on an analytical balance and then evapor- ated from a hot spiral tungsten filament (in vacuum) on to a sheet of 0 .005 inch copper.. From the weight of the CaF 2 used,-about 250 ^giias., and the area of the copper, 2 about 50 cm., i t was assumed that a film of about 1 to 2 KeV in stopping power would be formed. These calculations were found to be of the right order, when the yield of ~y~-rays from these targets was checked. The time taken to evaporate the thin layers was only a few minutes with a filament temperature of about 1300° f and at a pressure; of 1 .5 X 10"*5 m m # 0 f mercury. Thicker targets were also prepared by using larger amounts of CaF 2 and longer times. In this case, the number of interference fringes formed on the target backing gave the order of the thickness of the layer formed. A thin polished crystal of natural fluorite was used for the thick target. A. coarse mesh of nickel gauze spot welded to a nickel backing held the crystal i n place and prevented the accumulation of charge on i t . 2 . S l i t s and Target Box Assembly. The arrangement of s l i t s and the targets box used during the calibration experiments are sho\<m in figure 19 . The positive ion beam was defined by a 1/8 inch hole inches 58. above the magnet box. It then passed through a 3/8 inch hole in a thick soft iron cylinder before entering the magnet box and being deflected through 9 0 ° . The resolved proton beam then emerged through a inch hole in another soft iron cylinder, was defined again by a set of insulated molybdenum s l i t s 0 .085 inch apart and then proceeded to the target. In the target box were three targets plus a disk of quartzjfor focussing, a l l mounted on a paddle wheel that could be rotated through an 0-ring vacuum seal. A% thick glass window allowed observation of the targets during bombardment. During the f i r s t calibration runs the target box con- tained the CaF 2 crystal (thick^ one thin target, one semi- thick target and the quartz: focussing disk. During sub- sequent runs, several thin targets were used so that a fresh one could be rotated into the path of the beam as soon as: any o i l or carbon film became v i s i b l e . Runs were also made on the copper backing to evaluate the contribution of the background to the recorded counts. These runs on fluorine targets were made i n September, 1952, with the targets at room temperature. During the September runs, one spot on a fluorine target was bombarded for several hours before, the build-up of an o i l or carbon film on Its surface amounted to about one KeV in stopping power for 873.-5 KeV protons. This amount of surface contamination was easily seen although 59. about i of this amount could be detected f i r s t by observing an upward shift in the fluxmeter frequency for the 8 7 3 . 5 or 3 ^ A KeV resonance curves. However on November 12, 1952, after a number of alterations had been made to the ion source and to the vacuum box's pumping system, i t was found that a carbon film was building up very quickly (1 KeV in about 30 minutes), especially when larger proton currents (3 to h ^aamps.) were being used. The target holder had been provided with a hollo\</ core for water cooling or heating. Therefore steam at 100° C was passed through i t to heat the targets before and during bombardment.. The f i r s t re- sult of this heating was to boil off grease and o i l from the G-rings in the target box and condense i t on the inside of the glass window and pyrex tube. The glass window and pyrex tube were washed and cleaned in dilute n i t r i c acid while the disassembled target box and G-rings were baked under an infra-red lamp for several hours. It also appeared that the old targets had acquired transparent o i l films of a few hundred eV in stopping power for 873*5 KeV protons, from being present in the vacuum, system for over a month, with no l i q u i d air in the trap. The 0-rings although orig- inall y used dry, gave off considerable o i l vapors under baking i n the open ai r . They withstood the heating and sealed well again dry.. The o i l was also changed in the small diffusion and mechanical pumps attached to the vacuum box and some small leaks in the fore-vacuum connections Figure 20 "V-RAY 'COUNTING EQUIPMENT BLOCK "DIAGRAM NAI CRYSTAL TARGET PROTON BEAM - PBJOTOMJLTIPLIER PRE - AMPLIFIER LINEAR AMPLIFIER DISCRUCCNATOR SCALER GALVANOMETER CURRENT INTEGRATOR TIMING CLOCK 6 0 . eliminated. This did not prevent the carbon or o i l film from building up on the target when bombarded at room temperature, perhaps because the main vacuum column's pumping system was dirty. However, when the targets were heated to 100° G before and during bombardment, no carbon or o i l film was found. For example, on Nov. 18 and 19,1952 after 9 total hours of bombarding one spot during a 12-g- hour continuous run, the spolj about 5/16 inch in diameter, appeared to be brighter after bombardment than the rest of the target. 3» Counting Equipment.. Ai block diagram of the y^-vay counting equipment i s illustrated i n figure 2 0 . ~Y~-rays which were intercepted at 0 G with respect to the beam by a Nal crystal optically coupled to a photomultiplier tube, pro- duced scintillations (irimctheo crystal) which gave rise to electrical pulses in the tube. The pulses were amplified and passed on by the discriminator, i f their height exceeded a certain value, to a scaler ci r c u i t where they were counted. A galvanometer and current integrator 3^ connected to the target holder (which was insulated from ground) recorded •jbhe amount of charge and hence the number of protons incident on the target. An electrical timing clock, the scaler, and current integrator were controlled by one switch so that a simultaneous reading of the time, the number of counts,and the charge was taken at each bombarding energy point. Figure 21. 6 1 . , h. Checking the Counting Equipment. A,close check of the efficiency of the counting equipment was kept during a l l the experimental work. A l l the electronic equipment was operated from regulated power supplies^supplied from a stabilized 115 volt a-e line source. The photomultiplier tube, an RCA. 5819» was operated at a constant d-c voltage within about 0.1%. Differential and integral bias curves were taken to determine the optimum settings of the discriminator and photomultiplier. In addition, the overall counting efficiency of the equipments was checked at the beginning and at the end of each day's run. A radioactive source i n a standard position was used for this test. The efficiency was found to vary by not more than a few per cent from one day to another, most of which could be attributed to voltage fluctuations in the photomultipier and discriminator c i r c u i t s . 5. The Calibration Curves and Determination of k. Seven separate runs were taken over the 8 7 3 . 5 KeV/ ~Y*-ray resonance in fluorine during two weeks in September, 1952. Readings of the yield of Y *-rays for a fixed charge of bombarding particles were recorded at intervals spaced from about 300 eV to 2 KeV. Six of the resonance curves are plotted in figure 2 1 . The thin targets ranged from about -£- to 1.5 KeV in stopping power while the semi- thick one was about 20 KeV. The details of the calculation of and corrections for target thickness are given below for this preliminary calibration. A discussion of the theory and reasons for these corrections is given later in part III. •6§. Three further sets of runs were taken i n November, the, last using heated targets,and additional average determina- tions of k were made from them. . , 6. Calculations and Preliminary Results. Cl) ^he stopping power of thin target #1 was calculated f i r s t . The thin targets #1 to #f were numbered according to the position from which they were taken in the evaporator, #1 being closest to the hot filament and #*f being furthest away. The peak of a thin target resonance curve occurs at an energy value, E, given by^: E - % + €/2 (XII J.a) where E R i s resonance energy assuming an i n f i n i t e l y thin target, and £^ is the stopping power of the target (or thickness)} for protons of energy E R. It may be shown that is given by dividing the area under the thin target resonance curve by the height of the step in the thick target resonance curve. The area under the thin #1 target resonance curve, from a large scale plot was 2 2 5 .^ Mc/s counts.. The height of the step of the thick target curve was 10,800 counts. Also from equation (V . 5 ) , 0.15^5 Mc/s £i 10 KeV (assuming the correct value for k). Therefore the thickness of thin #1 target was: 225A X 10 - 1 .35 KeV lOVSp""" 0.154-5"" (XII..2) (2) The stopping power of the other thin targets was calculated by comparing their peak yields to that of thin #1 target for the same resonance after correcting 6 3 . for the amount of charge of protons and for the solid angle subtended by the counter. (Cosmic ray and copper back- ground was negligible at the 873.5 KeV resonance, but was subtracted at the other resonances where i t was apprec- iable). The peak yield for a target that is thin compared to the half-width of the resonance i s proportional to the target thickness. For example, thin #11 target had a peak yield of 1918 counts in 165 seconds for a charge of protons of 30.8 JJ> c (microcoulombs) at a counter-target spacing of 8-̂ r inches. Gh the other hand, from the resonance curve of thin #2 target, the peak yield was l6,3*+5 counts in 27 seconds for a charge of 26.6 jm. e at a counter-target spacing of 2% inches.. The solid angle for #2 was up by a* factor of ( 8 . 5 / 2 . 2 5 ) 2 - 1*+.27;while the charge was down by a factor of 30.8/26*6 - 1.158.,- Therefore i f #2 were as thick as #1, the expected peak yield would be: lV.27 X 1918 - 23,635 counts 1.158 or the thickness of #2 16.3^5 - 0.692 . the thickness of #1 23,635 1 The peak yields.* for the different targets were also compared at other resonances and an average was taken. The results in Table 2 give the order of the thicknesses of the targets for protons of 873.5 KeV energy. Exact values of thick- ness are not usually known because of non-uniformities in the layer of target material. 0 Table 2 . . Thickness of Thin Targets* Target # Ratio , thickness at 873 .5 KeV 1 1.0 1 .35 2 0.765 1 .0 3 0.567 0.75 h O.298 O.k (3) Values for k in equation (XII. 1): were obtained from the fluxmeter frequency readings corresponding to the peak number of counts recorded. For example, for target #1, the peak yield occurred at an energy of 873.5 -H 1.35/2 —-87 1f . l8 KeV corresponding to a frequency of 27.02 Mc/s. Therefore: k - 0.87^18 - 1.197^ X ID" 3 MeV/Mc/s2 ~ ( 2 7 . 0 1 5 ) 2 ^his was repeated for the other thin targets. However, for the semi-thick and thick targets, whose resonance yield curve consists of the integral of the thin target curve, the yield corresponding to the resonance energy occurs half way up the step (see chapter XV ). For example for the semi-thick target,- the step height was 9 , 0 0 0 - 300 - 8,700 counts so that half way up was 8,700/2 4- 300 - ^,650 which corresponded to a frequency of 27.003 Mc/s. Therefore: k - .8735 - 1.1979 X 10~3 MeV/Mc/s2. ( 2 7 . 0 0 3 ) 2 " " This was repeated for the thick target curve corrected for the extra yield above this resonances due to onset of the 900 and 935.3 KeV ones. The results are given i n Table 3 for the Sept.-, 1952 runs.- 6 5 . Table 3. Evaluation of k. Target # k X 1 0 3 (k - k) X 10 7 (k .- k ) 2 X l G l l f Thin 1 1.197^ 7 h9 2 1.1976 9 81 h 1.1967 0 0 h 1.1985. 18 32^ Semi thick 1 1.1979 12 l ^ f 2 1.1973 6 36 Thick 1.1917 50 2,500 Total 8.3771 3,13^ k'- 8.3771 X 10" 3 - 1.1967 X 107 3 7 standard deviation - 313^ X 1 0 J + - 21.2 X 10"" Probable error (p.e.) - .67^ X 21.2 - 1̂ - X 10" ; % probable error - Ih X 1 0 ~ 7 X 100 „ - 0 .12$, 1.1967 X 10-3 k - 1.197 X 10~ 3 MeV/Mc/s2 0.12$(p.e.,7 measurements), ^11.3) 1 check was made at the 31+0«^ KeV fluorine resonance which is also used as a standard by many experimenters. A resonance curve taken with target #2 was used. However, the stopping power of this target for.3 ^ 0 . ^ KeV protons i s increased by a factor of about 2 .06 (as taken from the sl;ope of Bethe's most recent curve 3^ for the range 6 6 . of protons in a i r ) . Therefore the peak yield occurred at 3^+0.̂  -j- 2 .06/2 ^ 3^1 »33 KeV corresponding to a frequency of 16.892 Mc/s. Therefore k - t , ^ 1 3 V . - . - 1.1966 X 1 0 " 3 ~ (16.892) 2 difference - (1 .196? - 1.1966) X 10~ 3 - 0 .0001 X 10~ 3 $ difference - 1/1.1967 X 100-0.008$ This close check was very reassuring. The calibration equation of the accelerator may be stated to an accuracy made up of the sum of the squares- of the two uncertainties (since the uncertainty in the measurement of f„ i s about ± 0 .01$); the 0 .1$ for the 8 7 3 . 5 KeV value from Herb and the ± 0.12$ for the value of k; ie., about ± 0 . 1 6 $ . ^his gives for the Sept., 1952 data, V(MVi> - 1.197 X 10-3 f (Mc/s) 2 0.16$ (XIIA) ~~ Pi ^Provided that singly charged mass 1 beams (protons) are used, the V(MV) may be replaced by E(MeV) without alter- ing equation (XII.J-f). When mass 2 or 3 are used, the appropriate factor of >/~2 or ,/~~3 must be used.' (k): The fluxmeter frequencies at which the other resonances i n fluorine should occur were calculated by means of equation (XIIJ+) and compared to the frequency values observed experimentally. The results are given below i n Table The experimental frequency at which the resonance peaks occurred was corrected for the stop- ping power of the target for protons of that energy. For Table h. Calculated and Observed Fluxmeter Frequencies for Fluorine Resonances. h MeV Experimental f p Mc/s Calculated f Mc/s difference Mc/s % di f - ' ference in f p o.3>+ô  16.866 16 .,863 +0 ..003 + 0.018 .k36 20.111 20.150 - 0 . 0 3 9 ~o'.19 .598 22.316 22.336 - 0 . 0 2 0 - 0 .09 .669 23.62*+ 23.6^-1 - 0 . 0 1 7 - 0 . 0 7 . .831 2 6 A 1 8 -26.3^9 +0.069 + 0.26 .8735 Calibration 27.011+ ± 0 . 0 8 .900 27..^25 2 7 A 2 1 + 0.00^- +,o.,oi5 .900 2 7 A 2 9 2 7 A 2 1 +0.008 + 0 . 0 3 .9353 27.961 27.95^ +0.007' +-0.025 .9353 27.9kQ 27.95^ - 0 . 0 0 6 -O.D25 1.092 3 0 . 1 ^ 3 0 . 2 0 V - 0 . 0 6 0 - 0 . 2 0 1.137 30.8»+0 30.821 + 0.019 + 0.06 1.176 Broad 3 1 . 3 ^ . 1 . 2 9 0 32.755 32.828 - 0 . 0 7 3 - 0 . 2 2 1.290 32.709 32.828 -0.119 -O.36 1.355 33.519 33.6^5 - 0 . 1 2 6 - 0 . 3 7 1.381 33.836 33.966 - 0 . 1 3 0 - 0 . 3 8 1.381 33.839 L 33.966 - 0 . 1 3 7 - 0 . 3 7 . 1 . 6 2 * 36.663 r 1.62* 36.6^2 1.69 * 1.8h 37.657 37.576 +•0.091 + 0_.2>+ 39.139 4 New determination 6 7 . example, the fluxmeter frequency corresponding to the ex- perimental peak yield at the resonance energy E R ^ 3*+0A KeV was 16.892 Mc/s when thin #2 target was used. This target had a stopping power of 2 .06 KeV at 3kO,k KeV. Since 1.03 KeV corresponds to a shift i n frequency of 0.0256 Mc/s, this amount was subtracted from the above to give the corrected experimental frequency of 16.866 Me/s. The calculated frequency from equation (XII.h) i s : f p (Mc/s) - 2 8 . 9 0 ^ ( M e V ) ± 0 .08$ (XII.,5) Good agreement with equation (XII.5) i s shown in Table seven of the eleven calculated frequencies for the resonances below about 1.2 MeV have an error less than the p.e. which should be attached to the calculated frequency, namely £fv - %-Ay - A f - A k - j : 0.,08$ (XII .6) f p v ' e k where A fp> A V, A ^ ? A k , are the p.e..'s or uncertainties respectively in each quantity. In these measurements the calculated frequency for the resonances above about 1.2 MeV begins to show a larger difference which was considered attributable to the effect of the fringing magnetic f i e l d on the beam. On this hypothesis at high fields, the effective radius of the path of the bent beam would be increased so that a smaller f i e l d , H, would be needed for the same H ̂ or momentum of the particles in the beam. The effective increase in ̂  would appear to be less than h parts in 1,000 up to 2 MeV in proton beam energy corresponding to a magnetic f i e l d of about 10,000 gauss. Consequently, a small f i r s t order correction could be added to equation ( X I l A ) , 6 8 . of amount A V -2 A f - 0.0072 V so that for voltages above 1.2 MV, the calibration, V(MV) - 1.20^ X 10~3 f (Mc/s) 2 ± 0.5$(p.e). (above 1.2 MV) p (XII.7) After further checks on the 873.5 calibration curve using a mass .2 beam, this hypothesis proved to be incorrect./ 7. Final Calibration and Checks i n November. 1952. The ion source focussing conditions were different from those used i n the September, 1952 calibration. In the energy selector, a 0.022 inch thick molybdenum disk with a 1/8 inch aperture was added just below the original entrance aperture to the magnet, (see figure 19)-, and the exit s l i t s were replaced with thicker pieces of molybdenum,, 0 .022 inch thick. The s l i t spacing was decreased to O.O67 inches. Larger beam currents were available so that extra curves were taken using the less intense resolved mass 2 and mass 3 beams to extend the fluxmeter's, and hence the accelerator's, range of calibration.. From equation (II. .3), H - c / 2mV , (II.3a) isl e and from (II.8 ) , f p - H, (II . 8 a ) 2 7 T so that the fluxmeter frequency needed to deflect through 90°a mass 2 beam at 2V was the same as that required to deflect a mass 1 beam at hV or was twice that required for a mass 1 beam accelerated by only V. For exciting the same resonance as given by a mass 1 beam accelerated through 4. V volts, a mass 2 beam of HH needs to be accelerated 6 9 . through 2V since each particle in i t breaks up on impact with the target into two mass 1 particles, each having half the total kinetic energy, for the energy preventing this breakup is only a few eV. Thus, to obtain the 0.8735 MeV resonance curve with a mass 2 beam, the accelerator voltage was set to 1.7*+7 MV and the fluxmeter frequency to 5 1 +.l l8 Mc/s. This fluxmeter setting was equivalent to that for a mass 1 beam at 3.^9^ MV. In a similar way, the fluxmeter was checked at equivalent mass 1 settings of 1.362 and 3.863 MV by obtaining the 0.3lfOlf MeV resonance curve with mass 2 and mass 3 beams respectively. Table 5 gives the results of the calibration runs taken over the 873•5 KeV resonance with a mass 1 beam during November 5 to 13 , 1952. The average value of k from equation (XII.1). was used, as on page 66, to compute the "calculated fp" in Table 6 for the check runs over some of the other fluorine resonances. This is repeated for tables 7 and 8 for the November lk - 17 runs and for Tables 9 and 10 for the November 18-19 runs. Close agreement, within ± 0 . 1 $ , i s shown between the three k values from the 873 .5 KeV calibration runs taken in November although they are a l l about 0,k% lower than the September, 1952 value for k. The mass 2 checks on the 873.5 KeV resonance show that the fluxmeter frequency reads Q.k% high at 5^.1 Mc/s. This is confirmed by the checks on the 3*+0.!+ KeV resonance with mass 2 and mass 3 beams. The calibration equation of the accelerator, from the November Table 5. Re-determination of k, Nov. 5-13 ? 1952. Thin target J ? -O.h KeV at 873.5 KeV.. Date Time (k X 1 0 3 ) (k - k) X 1 0 7 (k - k) X 101)+ 5 L ^ :00p.m. 1.1882 - 2h 576 5 8:00p.m. 1.190>+ - 2 h . 7 11:00p.m. 1.1886 - 20 hOO 7 11:30p.m. 1.1907 +- 1 1 13 9:i+5p.m. 1.1931 + 25 625 13 10:30p.m. 1.1921 ,+ 2 1 hhl Total 20^7 k - 1.191 X 1 0 " 3 MV/Mc/s2 ± 0 . 1 $ , f p (Mc/s) - 28.980 J V(MV) Hh 0 . 0 7 $ . Table 6. Calculated and Observed Fluxmeter Frequencies for Fluorine Resonances, Nov. 5-13, 1952. Thin target #+. Date Time Bie;am Mass ER(MeV) Exp. fr, Mc/s Calc. f T Mc/s 1 % Diff in f„ 5 5 :00p,.m. 5 8 ; k 5p.m. 7 9 :00p.m. 7 9 :15p.m. 13 10 :30a.m. 13 10 :*+0a.m. 13 . 12 :30p.m. 13 1 :30p.m. 13 1 :H-0p.m. 13 10 :00p.m. 1 1 1 1 1 1 3 3 3 1 0.900 0.900 1.355 1.381 0 . 3 ^ o.3^oH- 0 . 3 ^ 0.3>+o^ 0 . 3 ^ 0.9353 27.535 27 . hk-7 3 3 . W 33.975 16.937 16.9^1 51.120 50.930 50.996 27.998 27.^93 27h9:3 33.736 3^.056 16.908 16.908 50.723 50.723 50.723 28.027 +0.1*+ - 0 . 1 7 - 0 . 2 6 -0.21+ + 0.17 -+-O.20 + 0.68 + 0 A 1 + 0 . 5 ^ - 0 . 1 0 Table 7. Thin target #6, - 1 . 0 KeV at 873. 5 KeV. - i Date Time k X 1 0 3 (k - k) X 1 0 7 (k - k) X 1 0 l l f Ih .10 :*+ 5p.m. +•15 225 15 9:If5p.m. 1.I9H1 +10 100 17 i+:00p.m. 1 .1925* - 6 36 17 ^:30p.m. 1 . 1 9 3 2 * + 1 1 17 5:00p.m. 1 . 1 9 2 9 * - 2 If 18 1:1+5a.m. 1 . 1 9 2 0 * - 1 1 121 18 2:00a.m. 1 . 1 9 2 5 * - 6 36 Total 8.3518 "̂ 23 * Target heated to 100° C. k - 1.193 X 1 0 " 3 MV/Mc/s2 ± 0 . 0 5 $ , f B - - 2 8 . 9 5 2 n / V(MV) ± 0 . 0 6 $ . Table 8., Calculated and Observed Fluxmeter Frequencies for Fluorine- Resonances. Nov. 1^-17. 1952., Thin target #6. Date Time Beam Mass ER(MeV) Exp. f B Mc/sv Calc. f T Mc/s 1 $ Diff. in f„ l^f l^f 17 17 17 17 17 17 17 18 18 2:30p.m. 6:00p.m. 2:00p.m. 2:10p.m. 6:00p.m. 9:00p.m. 9:20p.m. 10:11p.m. 10:25p.m. 12:10a.m. 12:30a.m. 2 3 1 1 2 1 1 1 1 1 1 O . S ^ 0 . 3 ^ 0 . 3 ^ o.34o*f 0.8735 1.69 1.69 1.69 1.69 1.69 1.69 33.879 50.919 16.900 16.927 5^.387* 3 7 . 7 ^ 6 * 3 7 - 7 5 6 * 3 7 . 6 7 6 * 3 7 . 7 2 9 * 3 7 . 6 9 9 1 37.756 * 33.783 50.67*+ 16.892 16.892 5^.118 37.638 37.638 37.638 37.638 37.638 37.638 +-O.28 + O.69 + 0 . 0 5 + 0 . 2 1 +0.1+8 +-0.29 + 0 . 3 1 +.0.10 -k-0.2*+ +0.16 + 0.31 * Target heated to 100° C. Table 9. Re-determinatlon of k. Nov., 18-19. 1952 > Thin target #7, ^ - 1 .5 KeV at 873-5 KeV., Date. Time k X 1()3 (k - k) X 1 0 7 (k - k) X 1 0 l l f 18 6:30p.m. 1.1925 0 0 18 9:30p.m. 1 . 1 9 3 0 ^ + 5 25 18 9ih5j>:.m. 1.19 i +5* + 20 *+00 19 5:*+5a.m. 1.190^- - 21 M+l 19 5:55a.m... 1.1919 - 6 36 Total 5.9623 902 A l l targets heated to 100° C, only one spot bombarded. * semi-thick target #3, ^ ^ 2 0 KeV.. k - 1.192 X 10"3 MV/Mc/s2 ± 0.1$ , f„ (Mc/s) - 28.958 v/ V(MV) ± O.12%. IT Table 10. Calculated and Observed Fluxmeter Frequencies for Fluorine Resonances. Nov. 18-19. 1952, Thin target #7. Date Time Beam Mass ER(MeV) Exp. f Mc/s p Calc. f n Mc/s p % Diff i n f p 18 18 19 19 19 10:l+-5p.m. 12:00p.m. 1 ^a.m. 3 :lf5a.m. 3 :̂ 5a.m. 1 1 2 1 1 1.381 1.69 0.8735 1.9k 1.9k 33.9^6 37.72^ 5^.3^2 1+0.391 ^ . ^ 1 9 3^*030 3 7 . . 6 M 5^ .129 ^0.336 M-0.336 - 0.26 + 0 .21 + 0 A 2 +•0.12 + 0 .21 A l l targets heated to 100° C, same spot used as for data in Table 9 .  7 0 . data i s therefore, V(MV) - 1 . 1 9 2 X 10~ 3 f 2, ± 0.1%, (XII .8) (up to 1 .0 MV) ' , , and adding a f i r s t order correction, V(MV) 1.181* X 1 0 " 3 ti ± 0.5%. (XII.9) (from 1 .0 to 3 .5 MV) 8 . Calibration of the Generating Voltmeter. Figure 22 shows the linear i t y of the generating voltmeter readings plotted against the square of the flux- meter frequency for the September, 1952 data after calibration at 873.5 KeV. A. similar line was obtained for the November data. The generating voltmeter i s therefore reliable within the reading error of i t s meter, about 5 KeV in 873*5 KeV or 0 . 6 $ , and rather better using a Brown recorder with a 10 inch long scale to observe the current. XIII.. Summary of Results on Calibration. 1. Reproducibility and Absolute Calibration. The short time reproducibility of the accelerator voltage is.very good to within 0 . 2 $ , from the data on the 873 .5 KeV resonance, over a period of hours to severall. days. The absolute voltage calibration from the November data i s good to about the same order of accuracy over several weeks. However, over the two month period from Sept. to Nov. 1952, i t was only good to 0.*+$. The reason for this was partly due to the changes in the focussing conditions in the magnet box, and at the ion source. Either this or perhaps electrostatic charging of parts 71 . of the accelerating tube, may produce small changes in the angle at which the beam enters the magnet box. A change in the entrance angle of only a few minutes of arc would cause the beam to describe a sli g h t l y shorter or longer path in the magnetic f i e l d and therefore require a smaller or larger magnetic f i e l d , than in the case of vertical incidence, to deflect a beam of the same energy through the exit s l i t . The resulting small change i n fluxmeter frequency would give a small error in the voltage calibration. Sparks in the accelerator may give a similar result. Therefore, for most accurate work, the voltage or energy scale of the accelerator should be calibrated with- in a few hours before and after, or i f possible, during an experiment. Alternatively, with more d i f f i c u l t y , better collimation of the beam could be introduced. The energy resolution expected from the exit s l i t spacing of 0.067 inches for a beam radius of 8 .8 inches is:: , . ' 4 E ^ 2 AP. 2 X 0.067 , — 0 . 0 1 6 , or± 0 . 0 0 8 , E 8.8 ~ (XII.1) which is 8 times larger than the reproducibility actually PI achieved. A similar result was also found by Bennet et a l who also used a reverse electron gun stabilising system. One great advantage of the U.B.C. ion energy selector i s the reproducibility and precise measurement of a magnetic f i e l d setting independent of any magnetic hysteresis effects. Points taken in any order over a resonance could be fit t e d to a smooth curve. 72. 2 . Possible Sources of Error in Absolute Energy Measurements. In these calibration the positive ion beam was centred at and defined by the small entrance aperture at the magnet box and focussed carefully on the target. It was believed that the 90° focus of the beam occurred just inside of the magnet box since a spot size of about 5/16 inches was produced by the beam '3*+ inches from this point after passing through the 0 .06? inch s l i t 7 inches from this point. It was found, however, that the stabilizing system could hold a poorly focussed beam on the target, at times, but at slightly different fluxmeter setting than that for the properly focussed one for the same point on a resonance. Again the fluxmeter r-f head measured the magnetic f i e l d over an area of about 1 cm2 at one upper corner of the gap between the pole faces. An average f i e l d along the path of the deflected ion beam was then inferred from this. Errors up to a few parts in a thousand in frequency (or magnetic field) might occur i f the ratio of these two fields changed at high magnetic f i e l d s . From previous work on the magnet3 the author had found that the f i e l d strength over the pole face of the magnet at 10,000 gauss varied by as much as *+0 gauss i n 10 ,000 gauss up to an inch from the pole face edges. A further check on this at different f i e l d strengths would seem advisable i f an increase in the accuracy of the beam energy measurements i s needed. 73 Part III. Determination of Some Nuclear Excitation Functions. XIV. Resonant Reactions^ 7 In many cases when a nucleus is bombarded by a nucleon such as a proton, neutron or alpha particle, a compound nucleus having discrete energy levels, E R, i s formed. We may properly speak of the existence of this intermediate or compound nucleus only i f i t has a lifetime greater than the characteristic nuclear time (time for a nucleon to 21 travel across the nucleus, about 10" seconds). An average lifetime of such a compound nuclear state may be deduced from the energy level width, ^ E, from Heisenberg's. un- certainty relation; e.g. for &E - h KeV, l8 it£ _h_ ̂  6.6 X 1CT 2 7 lCf s e c , \ E ~ >',0QQ X 1.6 X l O " 1 2 (XIV.1) which i s small compared to the above. This compound nucleus may lose i t s surplus energy by decaying to the ground state via the emission of "^"-rays or, i f energetically possible, by particle emission to the ground or an excited state of a residual nucleus. The residue nucleus, i f l e f t in an excited state, w i l l also decay be the emssion of a ~y~ray. When the energy levels of the compound nucleus are widely 7h. separated, the reaction yield of particles or -rays exhibits strong resonances as the energy of the incident particle i s varied corresponding to the formation of the compound nucleus in one of i t s possible excited states. In such resonant reactions we wish to dcetect and measure accurately the maxima in the excitation function since this gives directly the location in energy and number of the excited states of the compound nucleus. The "level width", which is related to the probability of decay of the compound nucleus, may also be ascertained i f the natural shape of the resonance can be measured. Further arguments, based for example on the angular distribution of the emitted particles or quanta, make i t possible in some cases to assign an angular momentum quantum number and a parity to the stationary state. In this way i t is hoped to build up a detailed picture of the energy levels of at least the lighter nuclei, from which in the present poor state of our knowledge regarding nuclear forces, we may at least hope to select nuclear models which yield level schemes i n accord with the experimental data. This in i t s e l f w i l l be a major advance toxrards a proper understanding of inter-nuclear forces. XV. The Breit-Wigner -.One-Level Dispersion Formula. 1. Reaction Cross Section and Y i e l d . ^ Consider a beam of charged particles of N per second and cross sectional area "a" cm striking a target 7 5 . of thickness t cm. containing """•^/'nuclei per cm3. If we assume no overlapping of nuclei then the number of nuclei n, in the path of the beam is given by,, n - ^ / a t.. (XVJ?) We define the cross section.for a reaction, (j , in terms of the above and the yield, Y, in disintegrations of the type under consideration per second, by the equations: Y - N n <T - N V t <T~, (XV.2) "a where has the dimensions of area (cm2). 0 may be interpreted as the effective area that the target nucleus presents to the incident particles. In other words, 6 i s proportional to the probability of occurrence of the reaction. Representative values for (f for (p, ~f ) reactions are of the order of 10""2l+ cm2, a convenient unit termed one "barn". It is found from experiment, that (7""sometimes varies with the energy of the bombarding particles i n a characteristic resonance way. This variation of (f~ over a "If-ray resonance may be simply described by a one-level "dispersion formula" as proposed by Breit and Wigner, provided that the resonance i s \tfell defined and well separated in energy from other resonances. In the case of a simple (p, if) resonant reaction, the dispersion formula gives: <T"(P, if ) - g TT "Xp /V /rad (E - E R ) V i I (XV.3) where: g i s a s t a t i s t i c a l weighting factor determined by the spins of the nuclei involved, Aĵ p - Xp/2-rr where \ is the De Broglie wavelength of the incident particle in centre of mass coordinates, 76. j~"p is the particle width (at resonance energy E-^), i e . f~p/fi is a measure of the probability of decay of the compound nucleus via re-emission of a proton of the same .energy. Included in this term is the effect of Coulomb and Centrifugal barriers as i t may be written as: r* Res - (2 HI). Res P ( X ) o P > where R i s the radius of the nucleus, B is the penetration factor, Res is the reduced width, a constant set by the P particular nucleus, n . r a d  is the "reaction" width, i e . in this case a measure of the probability of decay via -radiation, f" 1 i s the total level width or resonance width, here: just P p + Frad- E is the energy of the bombarding particle, E R is the energy of the bombarding particle at resonance, f1 i s related to the lifetime, ^ , of the particular state of the compound nucleus by the uncertainty relation of Heisenberg; f* 'J"<s h/2TT . Since the probability of decay of this state, P - 1/<J , then P - K P . In;:;general over a sharp resonance these widths w i l l not change significantly from their value at resonance, so that the variation i n 0 over a resonance is settled by the resonance or dispersion form of the denominator. If the total level width exceeds the experimental energy resolution, A E, then E^ and f"1 can be obtained d i - rectly, and the absolute yield of *Y"-radiation at resonance 77., provides a'measure of CT\ (the value of <Z~~ at the resonance energy) provided the number of nuclei/cm 3 in the target is known and the yield i s measured over a sufficient range of angles to estimate the total &\ . Prad i s unlikely to exceed a few eV so that the total width w i l l only exceed the experimental resolution (about 1 KeV) i f F~p is large.; enough (about 1 KeV). (a) Under the afore mentioned circumstances where f~* > A E resolvable, CT-z-nX2 Had r ( x v . 5 ) (E - E R ) * + i f 2 At resonance, <Ti - 8 TT A 2 ^Prad/P , (XV.6) so that <7~- i V2 (XV.7) (E - E R . ) 2 + ± r 2 Hence measurements of the shape of the resonance curve, E R, and (T~^ give a value of g P?ad» (b) When He 4 E, then only the cross section averaged over the level can be measured, and this is usually done by using a thick target and a bombarding energy, E, greater than E^ by an amount at least equal to the resolution of the beam. Assuming no higher resonance is. involved, the yield in this case can be found by integration of the cross section over the resonance. 2. Application of the Dispersion Formula to Show the Peak Yield For a Thin Target Resonance Curve Occurs at E-=_Ep+4/2. For an i n f i n i t e l y thin target, i e . where the 78. loss of energy in the target, ^ e q u a t i o n (XV.2) gives the yield of ~)f -rays directly. However, when the resonance width \ ' , and the loss of energy ^ i n a thin target are comparable, the yield of "^-rays i s obtained by integration of the Breit-Wigner formula over the resonance energy range: /"E y ~JE -g? — — i Uv.8) where y is the yield per incident particle, €. i s the stop- ping cross section per disintegrable nucleus in the target. Wow £^ ^"^ft € , i f ̂  and € do not vary over the resonance, Substituting for (f~ from (XV.7) and integrating gives: T ( ? ) -6~kr (tan" 1 E-E R - tan" 1 E - E R - f ) . 2 € pj2~ ~p72~ (XIV.9) To find the maximum yield as a function of the energy, of the bombarding particle for a fixed target thickness, ^ , (XIV.9); may be differentiated with respect to E and equated to zero. This shows that the peak yield occurs when: E - E R +- *T, (XV.JLO) 2 and by substituting this in (XV.9), this peak yield i s given by:: ? ) - t ^ " 1 (XV.11) m a x e p 3. Relative Yield of Thick and Thin Targets. Equation (XV.11) may now be compared to the peak yield from a thick target, i e . one where ̂ ')V/~1. This is given by considering equation (XV.9) in the limit as tends to i n f i n i t y : ym (o°) - ^kJZ^L* (XV.12) J max 2H& 7 9 . Dividing (XV.ll) by (XV.12) gives, • W « * * > - 7 r ^ (XV.13) which shows the relative peak thin target yield compared to that from a thick target. Now the area A(i^ ), under a thin target resonance curve is given by the integral of the yield over the resonance:: A ( f ) Jj )dE - 7T f (7RH - § ymax(-), TResonance 2 £ (XV^lH-) from equations (XV.() and (XV.ll), which shows that i t i s only proportional to the energy loss in the target and the thick target yield step. It may also be shown that , this area is independent of -the homogeneity of the.beam and the nature of the thin target yield c u r v e . 2 1 a The yield for a thick target curve as a function of E is given by equation (XV.9) with rthick =• 2 ^ r |JT + tan"X ±*g?J ( x v . 15) h, (p. o*»V) Resonant Reactions. A few light nuclei show discrete resonance levels for (p, oC ) reactions. Thus in p ! 9(p ? ocV)Q16, sharp levels are found corresponding to maxima in the yield of low energy oC-particles, as 0^ is produced in a state with excitation energy of 6 to 7 MeV. Thus these alpha resonances may be investigated by measuring the V"-ray yield. The emission of more energetic oC-particles corres- ponding to formation of 0̂ -6 i n the ground state i s not possible for these states of the compound nucleus Ne 2 0/ 80. owing to symmetry properties. The Breit-Wigner formula can also be applied to these resonant reactions; in this case, f r a d must be replaced by XVI. Limits of Energy Resolution. *fl 1. Doppler Limit to Energy Resolution. The parameters E R, [~* and CTR may be evaluated to a precision determined by the experimental definition of the bombarding energy, E. However, the amount of energy that i s available for excitation of the compound nucleus must be calculated i n the centre-of-mass system of the compound nucleus. Due to the thermal motion of the target nuclei, the effective energy of the incident protons, w i l l be spread out (Doppler broadening of level) over a range of energies having the gaussian distribution: " ( £ Q " E ) dE, (XVI.l) N(E)dE. - _1 f> ?r>2 2 TT D v where D - I 2m_ E 0 kT, • V M m is the ratio of the mass of the proton to the mass M of the target nucleus, T i s the absolute temperature, k i s Boltzmann's constant. For the energies and the targets considered here, this amounts to an uncertain!ty in E of the order of 100 eV. 2. Practical Limits to Energy Resolution. Evaluation of the parameters of (p, c*. "Jr") resonant 81. reactions requires a source of bombarding particles easily variable and homogeneous in energy and of sufficient i n - tensity for 'accurate measurements to be taken in a reasonable time. In addition, thin targets are needed for identification and resolution of the resonances, especially when the curves are narrow,and closely spaced. The main factors which de- crease the definition in the energy, E, of the proton beam are: (1.) Variations i n the energy of the ions em- erging from the ion source and focussing lenses, (2.) Loss of energy of the ions by collisions with gas molecules i n the accelerator colums, (3.) Voltage fluctuations in the accelerator due to corona, sparks and belt rubbing, (*+.), Deterioration of target with time due to bombardment and formation of o i l and carbon films, (5.) Uncertain variations in target thickness. On the other hand, the homogeneity of. the beam may. be improved by using narrow:siits on the analyzer to define the energy and by using very thin targets (so that the energy loss in a l l parts of the target i s small). In the U.B.C. accelerator, the r-f ion source keeps the variations in (1.) of the order of 100 eV or less. With a vacuum of 2 X 10"̂ mm. (good for the size of the accelerator tubes, about 20 feet long by about 8 inches in diameter), the mean free path of the protons is of the order of 20 feet so that factor (2.) i s small. Voltage fluctuations are Figure 26   8 2 . kept small by the ion energy control system which has a theoretical upper limi t of about 100 eV. Target deterior- ation i s minimized by keeping the intensity of the beam as high as possible so that the time required for a run over a resonance is as small as possible. The other consider- ations of using narrow s l i t s and thin targets reduce the yield of "y"-rays per second so that longer times are required to obtain sufficient counts for good s t a t i s t i c a l accuracy. A compromise between maximum homogeneity and low intensities of beam must be made. However due to the method of ion energy control adopted at U.B.G., good homogeneity is ob- tained with up to k% ^amperes of resolved protons. XVII. The Proton Bombardment of Fluorine. 1. ~y"-rav Excitation Function. The "y^ray excitation function from the proton bombardment of fluorine i s shown in figure 2 3 . The y'-rays of 6 and 7 MeV energy are produced in the reaction: F 1 9 + H l _ ^ N e 2 0 ^ 0 l 6 ^ H e * f o 1 6 V . (XVII.1) Proton capture radiation has been observed at the 669 KeV kp resonance , but was ignored in this work because of i t s extremely low intensity. The experimental counting arrange- ment was the same as in part II, section XII. A l l the published resonances between 0.3i+0>and 2 . 0 MeV were observed as well as two new resonances at 1.62 and 1.8*+ MeV. Figure 2 3 . Figure 27 J ' 1 9 ( P , < * " ^ ) 1.84 M E V RESOiMMTCE / i l l background subtracted 3 9 . 0 3 9 . 4 . 39 .8 Figure 28 F 1 9(p,O^V) RESONANCE WITH MASS 2 BEAM SEPT. 1952, - 1.5 KEV ACCELERATOR VOLTS, V(MV) 1.722 1.747 1.772 i : _ J I . • i. l 54.2 54.4 54.6 fp(Mc/s) Figure 29 F (£,c*T) RESONANCE, 873.5 KW CALIBRATION; NOV., 1952 • THIN TARGET, £f - 1.5 KEV", TARGETS HEATED TO 100° C Ep(MeV) 874 879. 27.06 27.10 27il4 f (Mc/s) \ 8 3 . These are l i s t e d i n Tables 3 a , 5 } 7 and 9 . The curves that make up figur e 23 were normalized at the 0.8735 MeV resonance by correcting the y i e l d for target thickness, charge collected and counter-target spacing.. The cosmic ray background, about 1/5 count/sec. was n e g l i g i b l e and was not subtracted. A charge dependent background from the copper target backing above 1 MeV was also not subtracted but i s plotted beneath the f l u o r i n e excitation function. Some of the resonance curves are plotted on a larger s c a l e . i n figures 2k to 2 9 . The widths of the resonances shown, and l i s t e d i n Table 3 a , are equal to or l e s s than the widths of the best previous work"."2^-* A further check of the ov e r a l l resolution of the present experimental work i s the peak to trough r a t i o of the 1 .355-1.381 MeV doublet. After subtracting the copper background, t h i s r a t i o i s about 1 0 : 1 , to be compared with about 8:1 obtained 21 21a by Bennet et a l and 5 s l obtained by Bernet et a l . 2 . New Resonances at 1.62 and 1.8*+ MeV. During the course of this i n v e s t i g a t i o n two new resonances were observed at approximately 1.62 and 1.8*+ MeV. Two separate runs were made over the 1.62 MeV resonance with d i f f e r e n t targets as shown i n figur e 26 , and the 1.8*+ MeV resonance shown there as well, i s pl o t t e d Fi.c^re 30 . N 1 5 (p. CX T") U 9 8 K E Y RSSOIIAMCE  8i+. again i n figure 27 with the copper and cosmic, ray background subtracted. These energy values were assigned with reference to the preliminary c a l i b r a t i o n of the accelerator. However, with reference to the f i n a l c a l i b r a t i o n , these energy values should be altered to 1.60 MeV . 1% and 1.82 MeV 1%. XVIII. The Proton Bombardment of N 1^. The -ray resonances r e s u l t i n g from the proton bombardment of N y are shown i n figures 30 and 31• The 'y-rays. of ^ MeV energy come from a r e a c t i o n * 3 that i s analogous to the f l u o r i n e one: ^ "K 1 ^ 1 6 * ^ 12 . k N ^ + H —> 0 — C -V- He c 1 2 -+- V\ (xviri.l) Proton capture r a d i a t i o n also occurs at 1 .05 MeV but i t s i n t e n s i t y i s weak compared to the hfe MeV T~-rays. Semi thick, targets of KNO.̂ , enriched to 60% with N 1^ were evaporated onto s i l v e r backings i n vacuum. During the experiments, the targets were cooled to about -70° C with a mixture of s o l i d C0,2 and ether to prevent loss of the nitrogen. Y,iel*d. from this reaction i s small compared to that from f l u o r i n e which had to be eliminated as a contaminant from, the beam stop on the target box. Since large beam currents were needed, no attempt was, made to define the beam at the magnet box i n order to check the resonance energy values. No resonances were observed above 1.2 MeV because of the. r a p i d l y r i s i n g background observed from a l l target backing materials tested. These included copper, s i l v e r , platinum, tantalum and tungsten. 8 5 . Of these possible target materials, tungsten offers more promise i n extending the N-^Cp, c* " y ) reaction to 2 MeV since i t s background y i e l d was the l e a s t . However, i n sheet form i t i s very d i f f i c u l t to cut or machine. The angular d i s t r i b u t i o n of these N 1^ gamma rays has been investigated i n this laboratory using the s t a b i l i z e d beam to achieve constant operating conditions over long periods of time. 86.. Appendix 1. The Laplace Transformation Method of Analysis. The d i f f e r e n t i a l equations of the components of the system are written out, the Laplace transforms are taken and then solved usually f o r the output quantity i n terms of the input. The inverse Laplace transform then gives the output quantity as a function of time for the p a r t i c u l a r input conditions. However, information about s t a b i l i t y , and transient response of the systems may be obtained by analyzing the Laplace transform without the need of f i n d i n g i t s inverse. To further s i m p l i f y the analysis, i t i s con- ventional to introduce a c e r t a i n concept, a "transfer function", defined so that the Laplace transforms of the separate units of the system may be written down by inspection. F;or example, consider a simple r-c network, where the con- denser i s i n t i a l l y uncharged. Let the Laplace transforms of the current i ( t ) , the input voltage, e ^ ( t ) , and the output voltage e Q ( t ) , be denoted by I(S), L — I(S), L [ ^ ( t ^ j - EjiCS) and L £e 0(t ) j - E 0(S) respectively: i ( t ) R WW' | e ± ( t ) zjr C e Q ( t ) The d i f f e r e n t i a l equation of t h i s c i r c u i t i s : Ri(t(> -t- i j i ( t ) d t - e ^ t ) , (1.1) ©o(t) - I j i;(t)dt. (1.2) 8 7 - Taking the Laplace transformation of these two equations: |I(S) - E i ( S ) , (1 .3) E 0(S) - __1 ICS) . (l.>+) sc . . From ( 1 . 3 ) , K S ) - Ej(S) iT+77 (1.5) and from ( l . k ) and ( 1 . 3 ) , _11~ E 1(S)SC1 ' L 1 SRC J E 0(S) - _ J , [ | > ( 1 # 6 ) SC or Bo(S) - 1 Ei(S).. 1+SRC . . The "transfer function", KG(S) of the network i s defined by the equation: E D(S) - KG(S)Ei(S).. (1 .7) In this case, K - 1 and G(S) - 1/(1 + SRC). The "time constant" of the network i s T - RC. Further, t h i s network may be replaced by an equivalent box containing t h i s transfer function: E ±(S) — 1 +- SRG E n(S) Recognitions-, of the behaviour of this transfer function from experience, or tables, under general input conditions allows prediction of the behaviour of the network without carrying the solution any further. Since t h i s transfer function could be obtained using the usual impedance concept from a-c c i r c u i t theory i t can be seen that p r a c t i c a l l y , 8 8 . . i f S i s spe c i a l i z e d to S - j , the steady-state response of the network i s obtained. I t must be remembered however, that while the impedance concept of a-c theory applies d i - r e c t l y only where sinusoidal voltages and currents are concerned that the Laplace transformation method i s v a l i d for any type of voltage or current waveforms. Two transfer function "boxes" i n cascade may be re- presented by multiplying their transfer functions together, provided that the input of the second does not load the output of the f i r s t . I f i t does, then the c i r c u i t must be analyzed as a whole. The open-loop transfer function for the accelerator's s t a b i l i z e r , i e . the Laplace transform of the r a t i o of the output to the input error signal i s given by: KG(S) - K i K 2 K l (1 . 8 ) ( l + S T i K l - i - S T 3 ) where S £r j ^ - j 2 T T f . For a l l frequencies, j u» >^ j T^, so that when u> T-j_ > 1, ^ T3 i s n e g l i g i b l e compared to 1. In addition K - K 2 i s V> 1. Thus for any variations having a period less than about 1 second, 1 ^ S T i . (1.9) " 1 +~ KG(S) ~ Under these condition with a step input function, Sj_(S) £ e ^ ( t ) , the steady-state error becomes: steady-state error (t -^cP ) - l i m SfST-j / e i ( t ) f > 1 S-^0 [Ell f i i L K J s K » 1 . , S T X » T3 ., 0. - 0 89 REFERENCES. 1. The Physical Society; "Reports on Progress i n Physics", v o l . XI ( 1 9 k 6 - k 7 ) page 1, London, 1 9 k 8 . 2 . S.B. Woods; "A Search for the Photodisintegration of Neon with the U.B.C. Van de Graaff Generator", Ph.D. Thesis, unpublished, U.B.C, 1952. 3 . D.A. Aaronson; "Design, Construction and S t a b i l i z a t i o n of a Large Electromagnet", M.A.. Thesis, unpublished, U.B.C, 1950. k . J.B. Warren; "High Voltage E l e c t r o s t a t i c Generators and Their Application to "the Production of Energetic Electron, Ion and Neutron Beams", Document L P - 17, . page 2 8 , National Research Council of Canada, Chalk River, 1 9 k 6 . 5 . D.H. Halliday; "Introductory Nuclear Physics", pages k 9 6 , k 9 7 , and 512, J. Wiley and Sons, N.Y., 1950. 6 . H.A. Thomas, R.L. D r i s c o l and J.A. Hippie; P.R., 28, 787 (1950). 7. G.E. Pake; Am. Jour, of Phys., 18, k 3 8 and k 7 3 (1950) . 8 . N. Bloembergen, E.M. P u r c e l l , and R.V. Pound, P.R., 22, 679 (19^8). 9 . M.E. Packard, R. S. 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Thesis, unpublished, U.B.C., 1951. 39. H.A. Bethe, Rev. Mod. Phys.,21, 213 (1950). ho. H.A. Bethe, Rev. Mod, Phys., % 69 (1937). hi. S. Devons, Op c i t , p . 6 0 . h2. S. Devons and M. Hine, Proc. Roy. S o c , 199!A. 56(19^9). !+3. A. Schardt, W.A. Fowler, and.C.C. Lauritsen, P.R., 8 6 , 527 (1952). hh. C.A. Barnes, D.B. James and G.C. Neilson, Canad. J. Phys. 3 0 , 717 (1952) .


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