A ABSTRACT CYCLOTRON ION STARTING TIMES IN THE SECOND HARMONIC ACCELERATING MODE BY Herman Brenner White, Jr. The analysis of orbit histories of the Michigan State University Isochronous Cyclotron by computer calculations is complicated in the central region because of the strong electric forces. A study was begun to improve the second harmonic operation utilizing the orbit code CYCLONE and measured electric fields in the central region. Pre- sented here is the experimental analysis of the orbit calculations in terms of the correlation between predicted beam positions by CYCLONE and experimentally determined positions by foil burns. The data is presented graphically to exhibit the close fit or deviation of the data with various runs of the computer code, both for previously used fields and for the new fields. Finally the work is extended to help predict the optimum starting time and also therefore, the starting phase of the particle beam. CYCLOTRON ION STARTING TIMES IN THE SECOND HARMONIC ACCELERATING MODE BY Herman Brenner White, Jr. A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Physics 1974 U ACKNOWLEDGEMENTS I should like to thank Dr. H. G. Blosser for his patient guidance during this work. I am also grateful to Dr. M. M. Gordon for his many helpful discussions on this machine and Mr. Dave A. Johnson for his assistance with the computer codes. A.very special word of thanks goes to Dr. Peter S. Miller for his aid in the experiments and cyclotron opera— tion, and Mr. Mike mmumer for assistance in operation of the electrolytic tank. I am indebted to the National Science Foundation for financial support and the MSU Department of Human Relations for support throughout my graduate career at Michigan State University. Finally, I would like to acknowledge the support and love.df my family which made all this possible. ii TABLE OF CONTENTS ACKNOWLEDGEMENTS . . . . . . . . . . . . . LIST OF TABLES O O O O O O 0 O O O O I O 0 LIST OF FIGURES . . . . . . . . . . . . . 1 O FORWARD O O I O O O O O O O O O O O O 2. INTRODUCTION . . . . . . . . . . . . . 3 O meDURE O O O O I O O O I O O O O O 3.1 Electrolytic Tank Measurement . . . . . . 3.2 Source to Puller Field Measurements . . . . 3.3 General Outline of Foil Burning Technique . . 3.4 Burned Hole Measurements . . . . . . . . 4. DATA ANALYSIS . . . . . . . . . . . . . 4.1 CYCLONE Computer Orbit Code . . 4. 2 CYCLONE Calculations and Verification Analysis. 5 0 CONCLUSIONS 0 O O O O O O O O O O O O 0 REFERENCES 0 O O O O O O O O O O O O O 0 APPENDIX. . . . . . . . . . . . . . . . iii Page ii iv vi 12 13 23 36 36 40 53 54 56 Table II III IV VI VII LIST OF TABLES Page Current on probe at different radii by observing glow dissapation at 90° foils. Current and radii given as digital readout on the consol . . . . . . . . . . . . 24 Foil hole radii at 90° and 270° for the first run determined by the transit compass measure- ments and calculations. Angle accuracy to 1 minute. The tri tric radius vector used was 114.937 inc esi.001 inch. South dee (90° data) corrected for radial displacement due to vacuum. Measurements relate to distance from machine center . . . . . . . 28 Hole measurements data for run 1 (24 MeV deuterons) obtained using the foil holders and mechanical drawing as references. Positions corresponds to geometry in Figure 8. Raw data from foil holders alone and final radii to an accuracy of .001 inch. No data shown at 180° . . . . . . . . . . 31 Radii for run-2 using the foil holders and mechanical drawings as reference. Data at 0°, 90°, 180°, and 270° indicated. Raw data from foil holders alone and final radii all in inches (1.001 inch) . . . . . . . . . . 32 AR-vs-turn number data at various starting times for the 0° data. Radii are presented in inches accurate to .001 inch . . . . . . . 49 AR-vs-turn number data at various starting times for 90° data. AR are in inches 1.001 inCh O O O I O O O O O O O O O O 0 5 O AR-vs-turn number data at various starting times for the 180° data. Radii are presented in inches accurate to .001 inch . . . . . . 51 iv Table VIII IX Page AR-vs-turn number data at various starting times for the 180° data. Radii are in inches 1.001 inch . . . . . . . . . . 52 Cyclone calculations output for 24 MeV deuterons utilizing the new electric fields in the second run. Starting time is -35° (rf-degrees) . . . . . . . . . . . . 55 Cyclone calculations output for 24 MeV deuterons utilizing the new electric fields in the second run. Starting time is -40° (rf-degrees) . . . . . . . . . . . . 61 Figure 1. LIST OF FIGURES Page Electrolytic tank model of the central region with the source and puller in the N81 configuration. This structure shows one side of the median plane with the electrodes at the center defining the water level. Scale is 1:1 . . . . . . . 5 Equipotential contour map for 134° dees from electrolytic tank data, in the N=2, push- push mode. The field coded 2.138.2A is the new field rotated by 45°. The old field, coded 204.5-L, contour map indicates the N=2 source to puller position with the puller recessed into the dee. In both cases these represent 2% contours of the total potential . 9 Equipotential contour map for the source to puller electric field. Both 2% contours and the electric field configuration clearly shows the geometric change in the position of the source relative to the puller gap. Field 1.06.9-S was gathered on a 20:1 potential grid; the old field on a 10:1 grid. Both plotted 10:1 as shown, for N=2 . . . . . . l4 Foil holes near the 0° symmetry line of the machines. The glow comes from the beam burning the foils at 90° on the right and 270° on the left, for the 2nd run, of 24 MeV deuterons . . . . . . . . . . . . . 17 Holes glowing along deflector angle. Position indicated by arrow in Figure 10. Photo shows first 5 turns at 0° and 4 turns at 270°, (lst turns at 270° blocked from view by foil holder at 0°). . . . . . . . . . . . 19 vi Figure Page 6. Foil hole along detector angle as in Figure 5, showing the first turn on 0° just as the beam is about to burn through. Photo of 2nd run. Position of view indicated by arrow in Figure 10 . . . . . . . . . 21 7. Differential probe trace patterns. The probe is positioned at 180° and (a) shows the data at this angle giving the inner and outer turn radii. A full turn pattern with no centering coils in (b) . . . . . . . . . . . . 25 8. The foil holders and their dimensions rela- tive to the center of the Cyclotron at 0°, 90°, and 270°. The measurements are accurate to .001 inch. Note 90° and 270° are presented laying flat on the side viewed from the top. . 29 9. Hole patterns burned on stainless steel screens, exposed at 0°, 90°, and 270°simultaneously. On the 270° foil the screen was too short so the outside radius of the initial (0th) turn is slightly heated and burned, but not enough definition for data. (2nd run) 24 MeV deuterons . . . . . . . . . . . . . 34 10. Plot of calculated orbit leaving the source at a starting time of —35° (rf-degrees), super- imposed on a drawing of the N=2 central region geometry for 134° dees, in the MSU Cyclotron. Data experimentally gathered is indicated by the rectangles at all four positions, from foil burns and differential probe . . . . . 38 ll. Plot of inside and outside radii of foil data for the first data run, against turn number. Plot (a) gives theoretical curve from the CYCLONE code of radius-vs-turn number for various starting times using the new electric fields. The curves for the old fields are shown for comparison in (b). No data shown for 180° . . . . . . . . . . . . . 41 vii Figure 12. 13. Page Plot of inside and outside radii of foil data for the second data run, against turn number. Theoretical curves for various starting times are plotted for the new fields (a) and the old fields (b) . . . . . 45 AR-vs-starting time for the four burn positions, showing comparison of foil position to cyclone calculated radius. Each turn of the data is indicated. Note the greatly expanded radial scale contrasted to figures 11 and 12 . . . . . . . . . . . . . 47 viii l. FORWARD It has been often said lately, that most scientific work reflects very little of the human element behind it. While the explanation of the work might very well be directed to the specialist in the field, the reasons for doing it and the research development behind it surely can be for the general reader. Luis Alvorez has pointed out that, "We should welcome. . .publications in which physicists tell us not only what they did, but why they did it, as well."1 Therefore with this spirit and in this brief forward I should like to relate how this topic came about. After having been involved with experimental modern (nuclear) physics as an undergraduate, I began work in trace elements here at Michigan State University using nuclear scattering techniques. This experience amply whetted my appetite for experimental work, and as a result I ventured off to other laboratories during the summer to increase my effectiveness in nuclear physics. While studying the 208Pb(a,p) reaction at Argonne National Laboratory, I made frequent trips to the National Accelerator Laboratory at Batavia and it became apparent to me that a large part of our study of nuclear and particle physics could be found in the study of the accelerators themselves. One could say understanding what the experiment does depends on under- standing how the equipment works. In the following years I concentrated on accelerators and in particular the MSU Cyclotron. Prof. Blosser presented many questions about the machine (and answers I might add). The question of what happens to acceleration in the "Central Region" of the machine was one question some effort had been put into before. The central region being the area of the beginning history of the particle's acceleration. In this machine often times first harmonic Operation has tended to be the best. Therefore, by studying this central region we felt that second harmonic acceleration could be improved. After spending some time working on the CERN Synchro-Cyclotron, in magnetic measurements and particle detection, I began :making electrical field measurements on the central region of the MSU Cyclotron. One important, and it turns out, very fundamental question arose: "How well can we predict, using these measurements, orbit properties of the accelerated beams in the Cyclotron?" Moreso, how accurate are our orbit calculations for second harmonic operation? Preliminary to the final computations of the orbit properties, a study was necessary after the measurements to verify that the orbit calculations did indeed correspond to what actually happens inside the cyclotron machine. Therefore, it was necessary to correlate the calculated particle properties with observed results which is the intent of this study. 2. INTRODUCTION The Michigan State University Sector Focused Cyclotron is a multi-particle, variable energy machine with a maximum proton energy of 56 MeV. The RF-system consist of two 138° dees and a 42° dummy dee which can be operated in either push-pull or push-push modes, over a frequency range of approximately 13.5 to 22 mega-cycles.2 The difficult analysis of orbit histories has in recent years been made easier by the use of the computer. The MSU Cyclotron Laboratory utilizes the Xerox Sigma-7 computer with which all the calculations for this study were made. The initial orbits calculated are crucial in determining the properties of the final extracted beam, such that the central region of the machine becomes of key importance. The complexity of the central region problem can be in part due to the interaction of particles with the magnetic forces, electrical forces, and space charge forces. Typically to study these forces one generally concentrates on accurately measuring the fields involved. Much attention is placed on the magnetic field outside of the central region,3'4'5 since the particles are affected by magnetic forces here a longer period of time. That is, they are outside of the accelerating gaps longer being bent by the magnetic field than inside the gaps being dominated by the electrical accelerating forces. The electric field of the dees and the particular electric field configuration of the source-puller system becomes very important in understanding the initial orbit 6’7 have been done properties of the beam. Previous studies which discuss the central region geometry and orbit properties for previous electrical field measurements. Even though the theoretical calculations for particle trajectories and properties are based on physical laws, we still use these measurements as observed input data, to predict future behavior. Since the last detail measurements of the electric field in the central region, some physical structure changes have occurred which could change the orbit properties of the cyclotron beam. To study these orbits it was necessary tonake detailed measurements of the central region electric fields for the new geometry. Other measurements were made for the N=l mode.8 Thus this study presents calculations for the N=2 mode to experimentally verify second harmonic orbit calculations. 3. PROCEDURE 3.1 Electrolytic Tank Measurement The central region electric field measurements were 9 The done using an automatic electrolytic tank facility. electric fields obtained were measurements of a rectangular grid of potential values in a two-dimensional array of points, ten square inches in size. The tank is characterized by a motor driven probe and the voltage of each point of the rectangular grid is automatically balanced to ground by a self-balancing bridge and punched on an IBM card. The scale is 1:1 for the actual machine. The tank geometry is a scale model of the central region of the Cyclotron machine as shown in Figure 1. This geometry corresponds to the N=1 mode (push-pull) of accelera- tion with 134°-dees. The electrolyte used was doubly- deionized water, with the water-level in the tank at just above the top of the center electrode at the source position, to correspond to the median plane in the actual machine. A braking system was used on the tank's longitudinal move- ment to increase the amount of time for the bridge circuit to balance. This provides for a more accurate position of the probe at the time the voltage at that position is measured. Also oxidation and erosion of the c0pper surfaces FIGURE l.--Electrolytic tank model of the central region with the source and puller in the N=1 configura- tion. This structure shows one side of the median plane with the electrodes at the center defining the water level. Scale is 1:1. a musmflm Am... were reduced by cleaning and the use of a dust cover. The cover also prevented conductive materials from contacting the water surface, as well as reducing motion of the water by air currents. Another improvement was the larger size of the data grid, making possible more accurate calculations further out from the machine center. Consistant accuracy of i0.5% was common in this measurement. All electric field data for orbit studies are stored in the laboratory computer library and coded for identification with a heading and a parameter list that gives all pertinent information concern- ing the potential grid that follows. The data (100x100 data points; large electric field) was first checked by plotting it with the computer in the form of an equipotential contour-map as shown in Figure 2. The utility of this procedure was to check that the geometry suggested was in fact reproduced in the gathered data. Also accuracy can be considered if all the equipotential contours are continuous and do not overlap, as they should provide analytical solu- tions to Laplace's equations for this complex geometry. The equipotential contours are plotted for potential values representing 2% of the total range of potentials, that is from 2% to 98%. These contours can be compared with the N22 contours from a previous measurement. It should be noted that the electrolytic tank geometry in this field study is for the N=1 harmonic mode, but the FIGURE 2.--Equipotential contour map for 134° dees from electrolytic tank data, in the N=2, push- push mode. The field coded 2.138.2A is the new field rotated by 45°. The old field, coded 204.5-L, contour map indicates the N=2 source to puller position with the puller recessed into the dee. In both cases these represent 2% contours of the total potential. 10 N wusmflm 300 (2.46 >300 25 FIGURE 7.--Differential probe trace patterns. The probe is positioned at 180° and (a) shows the data at this angle giving the inner and outer turn radii. A full turn pattern with no centering coils in (b). CURRENT DENSITY 26 .rr-r-— =1—fim—1 +~ -r jun: posmou ' ‘ .rsaq '1 a 7’ ——a n - 1 Y 1 . l , 3 1 ' .1 . . z . T . ¢ . . . f or . I: ; + 9 x ‘n- .3 Till: ’ i , a , ‘ A . * %:~mw,“+ a ,4-7. 7;”. r ; _. . . . Yd _.._ ,_ _.-‘,,_..' 44se~ ;-i. .iu1,.i: '"F ”71 'E -i- _rm.;q;;r . , . .! .' 1---;i‘f- "7' I 3 ; 117;” m 0.23 4.079 4:» no 1453' "5.993 708' “III RAM". (a) " V 4"- . g , 0 [ l ; . , ¥ a n - - I A .‘ .‘ ;-. ._ . . - 1-. .'.._-_.‘ . '_ ._ ,__'. ' 1 A , , j i ' I . a . f ‘ ' I f ‘y .. . .1 . ._ , .‘ - - a..- . . -7. - —;— .— (b—-;——o'— u— L---- —-o-—-—- -¢ .—. I I . L 5 ' .: . T ; : : .' ; . ' F 2 l . -~ we» - -—+~+——-—w~w~-‘ r % * ' l f i ‘ i '. 7 ' I ' ' —-— fl—JL ;--» a . (H-iTJh—o ~ / us -. c 4 ‘ - - 5 v ' : ' : . t ‘ . . o ' O I : ' ' i 1 . 1 . 2 I . _ . i . : : -._ . _., .4—7 -. —. 4p--.——f—~——-—— :\—-.—¢— ' . . l , ' ' , ; . .; . L ' ..... . _..-.. Wfi";“l_" ~——~—- -v oL .— f ‘ I ' x . 2 ; ‘ x 1 . 9 . ‘f —-- ----------------- v- —-0 >——-~-—;—o—-—o—.—— -— ———-—c——-O—-.-- F—. “4* ¢ ..... . , ..... i """ ' . . : . I i . o L . i . . ; n ; i 1 L L L 1 1 ' ‘ 1 i L 1 r 1 DIFFERENTIA Figure 7 (w L PROBE RADIUS finches] 27 machine center was used as a radius vector. The position of each hole therefore was measured as a change in angle from the reference position (0°), with an assumed constant radius. Table II gives the radius of the holes, in the first run, with relation to the measured angles using the transit compass method. To check the data initially, the separation between each hole was compared to a vernier caliper measurement of the separation using the foil alone. Table II shows that this difference is as much as 0.1 inches. This method was abandoned because‘of these errors as well as other errors from slight motion of the transit. The data is also corrected on the south dee (90° position) for radial shift of the dees by .0625 inches due to the vacuum. However, it was observed that each foil holder had been constructed with certain dimensions and alignment pins so they could be placed precisely, from the current cyclotron mechanical drawings. This method was pursued such that the position of the holders were known well with relation to the machine and therefore the 270°, 0°, and 90° data were measured with relation to the foil holders themselves. This arrangement is shown in Figure 8. The front edge of the copper holders was used as the reference point. Table III and Table IV give the turn number, radius data, and angles for similar runs of 24 MeV deuterons, where the measurements were all done with respect to the foil holders. In Table IV, the 180° data is taken from the 28 TABLE II.--Foil hole radii at 90° and 270° for the first run detenmined by the transit compass measurements and calculations. Angle accuracy to 1 minute. The trigonometric radius vector used was 114.937 inchesi.001 inch. South dee (90° data) corrected for radial displacement due to vacuum. Measure- ments relate to distance from machine center. -—— -. Position Radius Calculated Measured Separation Separation (degrees) (inches) (inches) (inches) 1°12'=l.2° 2.346 > .769 .623 1°35'=l.583° 3.115 > .569 0524 l°52'=l.867° 3.684 90° > .536 .415 2°08'=2.l33° 4.220 > .468 .371 2°22'=2.367° 4.088 > .436 .355 2°35'=2.583° 5.124 1°18'=1.3° 2.608 > .636 .734 l°37'=l.6l7° 3.244 > .502 .612 l°52'=l.867° 3.746 270° > .435 .514 2° ' =2.083° 4.181 > .368 .469 2°16'=2.267° 4.549 > .469 .408 2°30'=2.50° 5.018 29 FIGURE 8.—-The foil holders and their dimensions relative to the center of the Cyclotron at 0°, 90°, and 270°. The measurements are accurate to .001 inch. Note 90° and 270° are presented laying flat on the side viewed from the top. 30 m wufimflm EESEE + 13. 1 t E muezmo mzioaz SSSw gm ._ “ 31 TABLE III.--Hole measurements data for run 1 (24 MeV deuterons) obtained using the foil holders and mechanical drawing as references. Positions corresponds to geometry in Figure 8. Raw data from foil holders alone and final radii to an accuracy of .001 inch. No data.shown at 180°. 0° 900 270° Turn Raw Raw Raw 4 data Radius data Radius data Radius 0 - .. _ - _ .. - - - - .263 2.076 1 .212 1.992 .432 1.942 .954 2.767 .312 '2.092 .552 2.062 1.137 2.950 2 1.029 2.809 1.183 2.693 1.576 3.389 1.127 2.907 1.316 2.826 1.766 3.579 3 1.636 3.416 1.857 3.367 2.092 3.905 1.775 3.555 1.943 3.453 2.251 4.064 4 2.163 3.943 2.362 3.872 2.530 4.343 2.291 4.071 2.462 3.972 2.693 4.506 5 2.590 4.370 2.844 4.354' 2.949 4.762 2.722 4.502 2.918 4.428 3.097 4.910 6 3.016 4.796 3.265 4.775 3.354 5.167 3.112 4.892 3.337 4.847 3.461 5.274 7 3.441 5.221 3.492 5.272 32 TABLE IV.--Radii for run-2 using the foil holders and mech- anical drawings as reference. Data at 0°, 90°, 180°, and 270° indicated. Raw data from foil holders alone and final radii all in inches (1.001 inch). 0° 90° 180o 270° Turn Raw Raw Raw 4 data Radius data Radius Radius data Radius 1 - - .572 2.012 2.517 .893 2.706 - - .650 2.090 2.710 1.087 2.900 2 1.057 2.837 1.303 2.743 2.994 1.497 3.310 1.234 3.014 1.521 2.961 3.114 1.710 3.523 3 1.668 3.448 1.906 3.346 3.455 2.031 3.844 1.847 3.627 2.106 3.546 3.613 2.235 4.048 4 2.181 3.961 2.425 3.865 3.910 2.515 4.328 2.338 4.118 2.596 4.036 4.045 2.676 4.489 5 2.660 4.44 2.896 4.336 4.195 2.951 4.764 2.780 4.56 3.030 4.470 4.433 3.076 4.889 6 3.081 4.861 3.306 4.746 4.679 3.340 5.153 3.173 4.953 3.438 4.878 4.784 3.452 5.265 7 3.465 5.245 3.558 5.338 33 differential probe trace pattern shown in Figure 7. The differential probe gives the beam current at positions that are digitally displayed at the control consol. By knowing the beginning and end positions of the probe in the machine system one can measure the probe trace pattern, (measured as 8.29 inches) and taking the ratio of these numbers define a conversion factor that gives the position of all points on tl'e probe trace pattern in units of the machine dimensions. The width of the peak was con- sidered the radial length of the beam and the sharp edge of the peak is the outer radius of the beam. This procedure was verified visually by noting when the glow of the foil hole dissappeared when moving the differential probe from its outer most radius to inside the second turn. As was seen in Figures 4 and 9, some holes were flat on one edge and rounded on the other. Since the holes were not shaped the same, it was necessary to consider the width of the beam as the acceptable data. Magnetic field data for input into the computer cal- culations was taken from the measured fields previously mentioned. A lagranian point-interpolation was done using the cyclotron settings to generate the raw field data, depending on the particle and its energy as well as the rf-frequency, main magnet and trim coils settings.S 34 FIGURE 9.--Hole patterns burned on stainless steel screens, exposed at 0°, 90°, and 270° simultaneously. On the 270° foil the screen was too short so the outside radius of the initial (0th) turn is slightly heated and burned, but not enough definition for data. (2nd run) 24 MeV deuterons. 35 RA DI U 8 (inches) Figure 9 4. DATA ANALYSIS 4.1 CYCLONE Computer Orbit Code Beam orbit calculations for this study were done using the precise orbit code known as CYCLONE. This code utilizes exact median plane radial equations of motion for particle trajectories in crossed electric and magnetic fields. Details of the electric fields are accounted for in three ways, which corresponds to the part of the program in which these various fields are used: (a) Source-puller region; in which the first part of the program considers the initial turn and uses the source to puller electric field. (b) ”rf focusing" region; the second part of the program considers the first four turns and uses the large electric field; (c) the main acceleration region utilizes a step- function time-dependent potential in much the same way as the idea of assuming step function energy gain at each acceleration gap. CYCLONE also provides provisions for study of equilibrium orbits, electrostatic deflector and magnetic channel. How- ever, none of these studies are included. 36 37 Out put from the CYCLONE program is provided in the appendices. Analysis of the CYCLONE program is presented here in the form of graphs, which compare the radius vs. turn numbers for various starting phases and radius vs turn number for the foil burned data presented earlier. In the use of this code it was necessary to pick the correct start- ing phase which would correspond to the foil burns. The method used initially was to run the program in succession changing the dee voltage until the beam is aligned with the radial slit on the initial turn at 1.713 inches radius for 180° as can be seen from Figure 10. However, the dee voltage can be closely approximated by using the differential probe trace to determine the number of turns and using the equation: Ef/n = 4 V sin[N0 /2] dee dee where Ef is the final particle energy. n = number of turns N = Harmonic number edee = angular length of the~dees. Thus knowing the maximum energy gain per turn, it is possible to determine the approximate dee voltage. 38 FIGURE 10.--Plot of calculated orbit leaving the source at a starting time of -35° (rf-degrees), super- imposed on a drawing of the N=2 central region geometry for 134° dees, in the MSU Cyclotron. Data experimentally gathered is indicated by the rectangles at all four positions, from foil burns and differential probe. 39 I80° dee dee 270°. + . n —9 0° (7 i '2 I dunvny inches | dee 00 Figure 10 40 4.2 CYCLONE Calculations and verification Analysis In Figure 11, the results for one run are plotted against CYCLONE calculations for starting times (in rf-degrees) from -20° to -50° in 5° intervals. Figure 11a shows the results for the new fields and Figure 11b the results for the old fields. By comparing the width of the foil holes and the theoretical curve, one can compare which curves are accurate and therefore (since the only altered parameter are the electric fields), which fields correspond best to what actually exist in the Cyclotron machine. The width of the hole to some extent, is the degree of uncertainty in the beam position. Even though the measurements are accurate to within .001 inch, the center beam spot is still uncertain by the width of the burned hole. On the 0th turn only the outer edge of the hole is well defined. Examining first the old field data (Figure 11b), it is found that at -20° starting time, a close fit is possible for data at 270° and 0° out to the fifth turn. In the sixth and seventh turns only the 0° data is closely fitted by the curve. This phenomenon is observed for the other starting times as well to such an extent that none can give a close correlation for all the holes at once. It becomes necessary to change starting times to fit the data only at a specific angle. 41 FIGURE ll.--Plot of inside and outside radii of foil data for the first data run, against turn number. Plot (a) gives theoretical curve from the CYCLONE code of radius-vs-turn number for various starting times using the new electric fields. The curves for the old fields are shown for comparison in (b). No data shown for 180°. 42 FOIL BURNS RUN 1 l.2~ 1.2~ 1.2- q a 4 4 1 4 d .1 a 4 8 a av 4W av a a a v a av a av a a a v a av afi av av av a I am . av av. av av a a? v a 3 av av ar a. afi a v av av av av av afi a v av av av 4v av av a r 1v #1 av av 1T av as v av v av av av av a v av av av av av av a v av av av av av av a 1 Av. 1! av av av av .a v av av av ar av av a5 v av av av av av av a v av av av av av av a T av av av av av at aul v av v av av av v a v av av av av av uv a v av av av av av av a 7 av av av av av av 13 v av av ar av av av a v av av av av av av a v av av av av av av a 1 av av av iv a... av a2 v av av av a. av av a v av av av av av av a r av av av av av av a r 1' 1W 1' 1' av 1v. 1 1‘ v av av aw av av av a v av av av v av a v av fl av av v av a P E b b D p h a r a u n J j q d J1 4 v < 1 d v 1 a a v a v 4 q a q 4|< d a J. 1 4 11 J} 1 q 4 4 4 1 8 I av a a a a a a v. a a av av a av a v a a av av a av a I 1% L av av 1 av 17 v a a av av a av a v. . 0 Av U a1 0 AW a . afi a v av av 5 av a a a v. 0 11 u av av a 5 av as v 5 av av 3 av a 2 a a v — av a Ur _ av a _ afi M v av a v av a av T __ av .4 av. __ at a __ av as v Too av av To av a n av a v av a av av a av a v av a av av a av a .- av av at 1 av aUl v av av av a av a v av w av av a av a v av a av av av av a vv 1' L LI 1'. lav. Av- 13 v av a av av 4r av a v av a av av av av a v av a .v ar av av a T LV 1 17 11 IV LT #2 v Av a av av v av . av a .v a. . av v av a av 8 av v av a v av a av .ar av av al v a a av av av av 4 v afi av av av av v av u av av av av a h a b x} E h b b a a b r P P F} P b P, b P E 3 0. 8 8 u. nw 8 0 H.8~ 3.6~ 2.t+~ 8.0 H.8- 3.6~ m®r 2H- 6.0 23* 8.0 8.0 6.0 [bi NUNRE [0 TURN [a I Figure 11 43 With the new fields (Figure 11a) the observation tends to be similar with the exception that for one starting time it is possible to fit accurately all the turns at all the data angles simultaneously, namely -35° and -40°. By plotting the different starting times for this run it is possible to observe the position of the Cyclone data shift— ing radially at the turns but still restricted to pass through the initial radial slit at 180°. The accuracy of the source to puller field and large electric field for the old data account for the shift in position according to turn number. In contrast Figure 12a fully illustrates the close correlation of Cyclone theoretical calculations to the measured field data. Data in Figure 12 also includes the 180° beam position making the analysis complete for four different sectors of the machine. Accurate agreement between experimental and theoretical positions was deter- mined to be approximately .01 to .2 inches. Using the data from the second run this is illustrated better by introducing a parameter corresponding to the change in the positioncfifthe beam by Cyclone and the foil burns. There- fore we denote: AR T Rfoil burns - Rcyclone as this change in position. Data for the foil burns, however, is presented as an inside and outside radius. Therefore, the centroid of this hole was considered the 44 FIGURE 12.--Plot of inside and outside radii of foil data for the second data run, against turn number. Theoretical curves for various starting times are plotted for the new fields (a) and the old fields (b). 45 FOIL BURNS RUN 2 ,afi. 1 ‘9‘..qu r .. . lII’:v..I' '.' {YURINISVJH L. . . a . v 8 a a a a a A A A A a v a av av av . v. 1 11 Av v a av Av v a av 0 av ! v a av av v a. A If 0 av v a av 3 av v a av av v a av _ av v .a a av _— av v a av n av v a a av av v a a av av v a a av av v a a av av v a a av av V A A A! A! v A 1 lv 11 v a a av av v av a av av v av a av av I IV a 1' [I v a. a av av v av a av av v I av a av av l 1v 1 1T 1' v v Av v v v v v V I I V a b h b I b r a 1 a A a a a a a a A a av a a v a av a av av av a v av av Av av av A! A? v av av av av av av a v av av av av av D av U a v av av av av av 5 av a v Av A.- Av av av av O 18 v av av Av av av 2 av 2 a v av av av av av _ av _ a v av av av av av av a r av av av av av __ av __ as v av av av av av 0 av O a v av av av av av T av T a v av av av av av av a v av av AT av av .av .a v av av Av Av av av a “HI v av av Av av av av a v av av av av av av a v av av av av av av 13 v av av av av av av a v av av av av av av a v av av av av av av a 1 ar 1: av av 11 av a2 v AV av av av Ar Av a v av av av av av av a v av av av av av I av I a 7 av Av av av av aav al v v v av v v av a v v v v v v v v v v v v v v a a v v a a b b a a a a a 3 0 0 . B 3 H . fl 3 3 E E E E E B 5 H 2 . 6 u. 3 2 l 8 u. 3 8 6 6 6 8 u. 3 2 1 0. 1 Figure 12 46 beam position and this was considered Rf for the AR calcula- tions. These calculations are presented in Table V thru Table VIII. In Figure 13 AR isplotted against starting time for successive turns, at each angular position of the data. By choosing a starting time at those turns where the line crosses 0.00 inches, it is easy to pick the initial starting time which gives close correlation to the foil data for this particular N=2 run. In this way a close determina- tion of the initial phase at which the peak intensity portion of the beam leaves the ion source and consequently its phase dependence in the initial few turns can be studied. This is also a means of determining if the foil holes can be fitted at only one angular position at a time easily. In Figure 13 at 0° this seems true since the slope of the lines indicates a wide spread in starting time yielding a large range in data matching. The other angles indicate that -35° starting time should give accurate results for the second, third and fourth turns with a slightly larger spread at the fifth and sixth turns. 47 FIGURE 13.--AR—vs-starting time for the four burn positions, showing comparison of foil position to cyclone calculated radius. Each turn of the data is indicated. Note the greatly expanded radial scale contrasted to figures 11 and 12. 48 v..?.l A _ T I A D In 0 0 8 1 m .123qu loa'Oo 8 2 J 0. 0 q. T .l A 1 D o vl 0 ll 7 2 I L r I 8 . 2 a o n... Hmmcoc: md -30 r. (degrees) -'+0 -50 To [degrees] p > L 0 _ _ a_/_ A I T l A D \II 06 Tu 0 [39 0 _m r 0o 1 as e d l 0[ 4m. 0 T I la 0 6 8 6 2 1. 2 0 0 n.v 0 _ 2 A _ v T - A D \J 06 .l O 139 0 .e r e d .I IIO[ a“. o T ., 233.567 1 vavooo 1 0 b 5 . o .13 c 3 B. 2 J 0 J 9. o. o o m. o. 39.9.: mG Figure 13 49 TABLE V.--AR-vs-turn number data at various starting times for the 0° data. Radii are presented in inches accurate to .001 inch. =_ 0 g- 0 =_ O .- To 20 o 25 To 30 Turn 7 AR Turn :3 AR Turn # AR 2 -.10917 2 -.05425 2 -.00680 3 -.15193 3 -.08832 3 -.03048 4 -.l7938 4 -.llO47 4 -.04890 S -.16167 5 -.09047 5 -.02808 6 -.12886 6 -.05992 6 .00073 7 -.04187 7 .02213 7 .07880 T =-35° T =—40° T =-50° o o o 2 .03717 2 .07729 2 .14044 3 .02008 3 .06690 3 .14726 4 .00598 4 .05696 4 .14535 5 .02654 5 .07793 5 .16879 6 .05357 6 .10421 6 .19491 7 .12753 7 .17430 7 .25954 ——a flaw.“— Ma LM “ a . f . O O‘ur v 3;! 50 TABLE VI.--AR-vs-turn number data at various starting times AR are in inches 1.001 inch. for 90° data. IDs-20° To=-25° To3-300 'T'En f AR Turn i AR Turn i 15R 1 -.21456 1 -.20647 1 -.19713 2 -.06761 2 -.05594 2 -.04354 3 -.02155 3 -.00672 3 .01021 4 .01094 4 .02952 4 .04973 5 .06107 5 .07913 5 .09795 6 .11762 6 .13233 6 .14858 Td=-35° T°=-40o To=-50o 1 -.18418 1 -.17095 1 -.15976 2 -.02854 2 -.01317 2 .00300 3 .02899 3 .04830 3 .07280 4 .07222 4 .09483 4 .12131 5 .11978 5 .14101 5 .16504 6 .16822 6 .8740 6 .20568 51 TABLE VII.--Avas-turn number data at various starting times for the 180° data. Radii are presented in inches accurate to .001 inch. 108-20° To=-25° 108-300 Turn 4 AR Turn # AR Turn 4 AR 1 .09764 1 .10317 1 .11120 2 -.04084 2 -.03301 2 -.02233 3 -.O7833 3 -.06744 3 -.05468 4 -.10045 4 -.08683 4 -.07072 5 -.18726 5 -.17445 ' 5 -.15749 6 -.16931 6 -.15635 6 -.13934 T°=-35° -‘ 108-400 108-500 1 .11449 1 .11699 1 .13138 2 -.01574 2 -.00821 2 .01655 3 -.04401 3 -.03303 3 -.00321 4 -.05878 4 -.04592 4 -.01125 5 -.14496 5 -.13258 5 -.09423 6 -.12820 6 -.11696 6 -.07866 52 TABLE VIII.--AR-vs-turn number data at various starting times for the 180° data. Radii are in inches t.001 inch. ”a. '-—— To=-20° r°=-25° To=-30° Turn 4 AR Turn 4 AR Turn # AR 1 -.07183 1 -.02733 1 .01148 2 -.12476 2 -.07124 2 -.02321 3 -.16068 3 -.09939 3 -.04513 4 -.19118 4 -.12493 4 -.06577 5 -.21657 5 —.l4746 5 -.08504 6 -.20827 6 -.13803 6 -.07487 o=~35° toe-40° toe-50° 1 .04004 1 .06503 1 .12410 2 .01288 2 .04565 2 .12294 3 -.00354 3 .03447 3 .12303 4 -.02175 4 .01894 4 .11937 S -.03968 S .00385_ 5 .11381 6 -.03093 6 .01143 6 .12394 5 . CONCLUSIONS It has been shown that this experimental procedure is useful in the prediction of a good starting time and thereby a good starting phase. The orbit radii and their correlat- tion to theoretical predictions seem to give a clue that a starting time of -35° to -40° gives a precise initial phase that best fits all the data. It is therefore concluded that this range for the starting time can be translated back to the actual machine thru the starting phase of the particles and thereby give better operation in the second harmonic mode. This study of the central region electric fields has made it possible to substantiate our theoretical predictions. This investigation confirms that the new electric fields are accurate and reliable for future central region studies. 53 _. -2: n “ALMAM fi’i‘aaastam Emr a . , , ‘ In .‘. REFE RENCES REFERENCES Adventures in Experimental Physics, Issue 2(1972), p. i. W. P. Johnson, Radio-Frequency System of the MSU Cyclotron, Proceedings of the International Conference on Sector-Focused Cyclotrons and Meson Factories, CERN, April 1963. B. T. Smith, Michigan State University Cyclotron Project Internal Report, MSUCP-B, November, 1960. R. Berg, Michigan State University Cyclotron Project Internal Report, MSUCP-l4, January 1963. R. Berg, H. G. Blosser and W. P. Johnson, Michigan State University Cyclotron Project Internal Report, MSUCP-ZZ, August 1966. M. Reiser, Michigan State University Cyclotron Project Internal Report, MSUCP-20, June 1964. H. C. Blosser, ”Problems and Performances in the Cyclotron Central Region, IEEE Trans. Nucl. Sci. §§f13 (14), 1966, (1-14). Larry L. Learn, Private communication. M. Reiser and J. Kopf, Automatic Electrolytic Tank and Digital Computer Program for Calculations of Ion Trajectories in Crossed Electric and Magnetic Fields, The Review of Scientific Instruments Vol. 36, No. 7, July 1965. 54 10. 11. 55 D. A. Johnson, Private communication. H. G. Blosser, "Physics 961--Winter Term, 1971" Internal Report, MSU Cyclotron Laboratory (1972), p. 76. adage)? .4 a. ‘WM‘F p. ‘2‘- ‘tiu-au- . T “Tali-h Alia. APPENDI X flint»... . ii. KIRIMMFPP L1. kayak UH Ltnviv... w. 56 TABLE IX.--Cyclone calculations output for 24 MeV deuterons utilizing the new electric fields in the second run. 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