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UBC Theses and Dissertations

A high-frequency discharge ion source Chow, Richard Hing 1949

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H I G H - F R E Q U E N C Y D I S C H A R G E I O N S O U R C E by . RICHARD HING CHOW A Thesis Submitted In Partial Fulfilment of The Requirements for The Degree of MASTER OF ARTS THE UNIVERSITY OF BRITISH COLUMBIA September, 194-9 I ABSTRACT A high-frequency discharge ion source was developed yielding 45$ protons i n an SCO microampere, 14 kv energy focused beam of positive hydrogen ions. Higher ion currents could be delivered at higher voltages The discharge was excited i n a pyrex discharge tube, l£ inches in diameter and 9 inohes long, by a 210 Mc/sec. push-pun, oscillator capable of delivering 120 watts power. An electrostatio potential d i f -ference of 1.8 kv applied axlall y with the discharge tube, aocelerated the positive ions formed i n the discharge toward the exit canal. A mag-netic f i e l d of 24O gauss, also applied axlally, shaped the discharge cpn-i c a l l y , and intensified the redness of the discharge, causing the Balmer lines to appear prominently when the discharge was viewed through a spec-troscope. The ions emerging from the exit canal were focused by an elec-trostatic lens using a potential difference of 12 kv. The hydrogen pres-sure i n the discharge tube measured 17 microns, and the rate of hydrogen consumption measured 11 cc. per hr. The proton percentage was found to depend on the oscillator power and c r i t i c a l l y on the gas pressure. The magnetic f i e l d increased the proton percentage, but i n an unpredictable manner. I t was also found that the focusing lens i n front of the probe canal exerted an extracting action on the ions i n the discharge; influencing very strongly the t o t a l ion beam current collected. The general performance of the ion source was found to be satis factory. ACKNOWLEDGMENT The author wishes to express the deepest gratitude to Dr. K. R. More who, as supervisor of this research, made the project enjoyable and profitable through his encouragement and guidance; and to Dr. J. 6. Warren and Mr. T. W. Mouat for contributing many helpful hints towards the e a r l i -er part of the project. The author i s most thankful to the National Research Council of Canada for the financial assistance offered to both the project and the author. The author also wishes to express his pleasure of having worked join t l y with Mr. J . K. Kinnear and Mr. S. B. Woods, together with whom many d i f f i c u l t i e s were overcome. TABLE OF CONTENTS Chapter Page I Abstract ................... 1 II A High-Frequency Discharge Ion Source . 2 III Equipment and Apparatus 4 IV Experimental Procedure ................... 10 V Experimental Results ................... 12 VI Discussion I 4 VII Conclusions 19 Appendices I The Liebmann Procedure for Finding the Potential Distribution for the F i r s t Focusing Lens 20 II Magnetic Analyzer Design 22 III Calculation of Ripple Voltage on the 50 kv Set 22 TV Correction for Discharge Tube Pressure 23 V Ion Trajectories 24 VI Thickness of the Space Charge Sheath 29 Plates To follow page I Ion Source 3 II Layout of Apparatus (View 1) 4 III Layout of Apparatus (View 2) 5 IV Discharge Tube and Magnetic C o i l • 6 V Magnetic Analyzer 7 VI 50 kv Supply and Control Circuit 8 VII Potential Distribution of an Electrostatic Lens ......... 9 VT.II Ion Current vs Magnetic Field Current 13 Graphs To follow page I Proton Percentage vs Pressure 13 II Proton Percentage w Current Through the Magnetic Coil Around the Discharge Tube ...................... 13 III Percentage of Component Ions vs the Oscillator Plate Voltage 13 IV Ion Current vs Probe Voltage 17 Bibliography 30 2 II A HIGH-FREQUENCY DISCHARGE ION SOURCE The usefulness of high voltage generators such as the Van de Graaff depends a great deal upon the characteristics of the beam of charged particles which i s accelerated. This beam of charged particles i s generally produced by an ion gun or ion source mounted at one end of the high voltage generator. A prerequisite for an eff i c i e n t high v o l t -age generator i s , therefore, a satisfactory ion source. For an ion source to be desirable i t must meet the following requirements given approximately i n their order of importances 1. Yield a high current of the desired ions. 2. Produce a mono-energetic beam of the desired ions, well focused. 3 . Be efficient i n the ionization process. 4.. Be simple i n construction, f a i r l y rugged, and have long l i f e . Not a l l the properties mentioned are completely independent of one another. For instance, a high current density ion beam may suffer space charge repulsion which disturbs the focusing effects. On the other hand, unless the beam has a sufficiently high current density, the effect produced upon the target by the beam may be negligible or d i f f i c u l t to detect. The ions produced i n an el e c t r i c a l discharge are extracted through a hole i n the discharge vessel and, unless the process of ioniza-tion i s e f f i c i e n t , the amount of neutral gas escaping into the accelerat-ing column may be so great that e l e c t r i c a l breakdown occurs i n the column. The percentage of desired ions compared to undesired ions must also be high so that no energy i s wasted i n accelerating the undesirable ions. 3 The energy spread of the ions must be low so that focusing i s simpler and the amount of the beam available for a nuclear reaction of given energy i s greater. Up to the present, four main types of ion sources have been de-veloped. These are: 1. Canal-ray (5) (17) 2. Capillary arc (14) (25) 3. Reflection (1) (9) 4 . High-frequency disoharge (3) (10) (18) Examples of each type are given i n the references cited. The canal-ray type of ion source u t i l i z e s the rays of positive ions emitted through a hole i n the cathode of a discharge tube. A very high voltage i s generally required to excite and maintain the discharge. Consequently, an energy spread i n the beam of several thousand volts i s usually inherent i n this type of source. The current output and over-all efficiency i n ionization are generally low. This type on the whole does not satisfy the requirements desired. In the second type of ion source a discharge i s maintained i n a capillary and the positive ions are extracted either along the capillary or through a hole i n the side of the capillary. In many respects the better ones of this type met the desired requirements. The only object-ionable feature i s that electrodes are required; the life-time of the source being then determined by the life-time of the electrodes which disintegrate under bombardment from the ions. Furthermore, investigators (14) have found that metal inside a discharge decreases the percentage of protons due to the catalytic action of metal for recombination of ions. A design of ion source radically different from the canal-ray ) PLATE I and capillary-arc types i s the reflection type. Electrons from a heated filament are caused to oscillate between electrodes i n a region through which the hydrogen gas flows. A magnetic f i e l d i s also used to constrain the motion of the electrons to prevent any loss on the walls of the source. Although high ion current i s obtainable, the life-time of the source de-pends on the filament which rapidly evaporates at high current. To avoid the undesirable features mentioned above, the high-frequency discharge ion source was developed. In this type the discharge tube i s placed either i n a solenoid or between concentric ring electrodes through which the high-frequency power i s fed. In this manner the amount of metal exposed to the discharge i s reduced to a minimum. Concerning the other requirements, the high-frequency discharge ion source proved satisfactory. I t was therefore decided that a high-frequency discharge ion source should be developed and studied. H I EQUIPMENT AND APPARATUS The main components of the equipment for the ion source devel-oped consist of vacuum plumbing and gauges, an electrode system for focus-ing the ions, high-voltage power packs, a discharge tube, a regulated hy-drogen flow system, a high-frequency oscillator, a magnetic analyzer, and f i n a l l y , a Faraday cup c i r c u i t for measuring current output. The main accelerating column of the ion source i n which a high vacuum i s maintained consists of a fabricated steel tee, three porcelain sections, and steel flanges. The stem of the tee leads to the vacuum pumps. The porcelain sections are assembled between the steel flanges bolted together with insulating textolite rods i n the manner shown i n • 5 Plates I, I I , and I I I . The tee, being at high voltage, i s mounted on i n -sulating textolite sheets onto a wooden frame. A 10 inch glass section shown in Plate III insulates the tee from the vacuum pumps which are op-erated at ground potential. Since the axis of the porcelain section and that of the stem of the tee l i e i n a horizontal plane, (Plates I and III) a fabricated 90° steel elbow (Plate III) i s mounted to enable the diffus-ion pump and i t s water-cooled o i l baffle to be mounted ver t i c a l l y . Thus arranged, the entire apparatus was located at a convenient height. The high vacuum i s measured by an ion gauge located at the steel elbow while the fore-vacuum, produced by two mechanical pumps, i s measured by a Pirani gauge located between the diffusion pump and the mechanical pump. With no hydrogen flow, the main vacuum produced by the diffusion pump was less than 2 x 10"-* mm. Hg.'of hydrogen pressure. The pressure i n the discharge tube was measured by a Pirani gauge located i n the 3ide-arm through which hydrogen flows into the discharge tube. A l -though the glass tubing between the Pirani gauge and discharge tube was about 14 inches long and inch i n diameter the true pressure i n the dis-charge tube was calculated (Appendix 17) to be very close to the reading on the gauge when corrected for.hydrogen. The hydrogen flow i s regulated by a needle valve located between the discharge tube and the hydrogen storage bottle. The rate of hydrogen consumption was measured by observing the rate at which o i l rises i n a glass tube of known cross-section located on the side of the storage bottle. The discharge tube i s made of pyrex l£ inches i n diameter and about 8§- inches long. At the end of the tube from which positive ions are extracted, a cone i s blown inward with i t s apex protruding into the Layout of Apparatus (View 2) PLATE III 6 region of the discharge. The apex of the oone i s flattened into a plateau about 5/l6 inch i n diameter with a hole about 3/l6 inch i n diameter into which i s inserted a dural-probe canal £ inch i n diameter and 9/l6 inch long through which ions are extracted. This glass cone i s f i t t e d over a steel cone so that the steel i s shielded from the discharge, since several investigators (10) (13) (18) have found that metal exposed i n a discharge i s detrimental to proton production. For a similar reason the tungsten probe i s enclosed i n a glass bulb at the other end of the discharge tube connected to the main discharge by a narrow constriction. The discharge tube, i s attached to the steel cone with Vinyl-seal for mechanical strength, and the joint i s coated with plicein wax to insure vacuum tightness. An a i r blast was used to keep the joint cool under operation. The extraction voltage i s applied between the tungsten probe and the steel cone. The ions are then extracted through a dural-probe canal housed axially i n the steel cone. A magnetic f i e l d , applied longitudinal-l y to the extracting electrostatic f i e l d , i s produced by a c o i l designed to produce about 300 gauss. The combined electrostatic and magnetic f i e l d s are then shaped by the steel cone to help focuse the positive ions towards the probe-eanal. The discharge tube may be seen i n Plate IV together with the magnetic c o i l . The high-frequency power for exciting the discharge i s produced by a push-pull type of oscillator using a pair of Eimac 4-65 A power tet -rodes. These tubes have a plate dissipation of 65 watts and power output of 30 watts each at 210 Mc/sec. The power i s fed to the discharge through transmission lines matched by a T section (U) to two ring electrodes mounted externally about the discharge tube. When matched to two 60 watt light bulbs, the oscillator delivered easily 120 watts of power. Discharge Tube and Magnetic Coil PLATE IV 7 The focusing system consists of a semi-aperture to cylinder lens and a coaxial cylinder lens. I n i t i a l l y both lens were designedto be used for focusing the beam, but experience showed that better focusing can be attained by using only the f i r s t lens for focusing and the last lens for accelerating. The arrangements of the electrodes are shown i n Plate I. Since the lenses are electrostatic, the potential V i n the re-gion within the lenses when charge-free must satisfy Laplace's equation 7 ;V » 0 for a given set of boundary conditions. A solution of the Laplace equation therefore, which f u l f i l l s the given set of boundary conditions w i l l give the potential distribution. (The distribution can be shown to be unique.) Unfortunately, analytical solutions are not possible i n most practical cases of electrode geometry. In such cases use i s made of an electrolytic plotting tank (7) (26) or some numerical-approximation met-hods. One of the latter methods, known as the Liebmann Procedure, i s * used to find the potential distribution for the f i r s t lens. The method i s described i n Appendix I. The resulting potential distribution obtained for the f i r s t lens i s shown i n Plate VII with the equipotential surfaces plotted-in percent. For the second lens, the diameter of the l a s t cylindrical elec-trode i s double that of the previous cylindrical electrode forming the lens. The potential distribution and focusing properties of this lens are well known and can be found i n several books on electron optics, (7) (22) ( 2 6 ) . The beam after focusing i s separated into i t s component ion currents by passing through a magnetic analyzer. This analyzer was de-signed so that mass 3 ions of 50 kv energy can be included i n the analysis. The motion of an ion of charge e e.s.u. and Mass M i n a trans-I t 1 * * XMX 1KHCS MAGNETIC ANALYZER PLATE V verse uniform magnetic f i e l d of H gauss satisfies the equation Hr = c (JOL)i 150e where r i s the radius of curvature of the ion path and c i s a constant equal to the velocity of lig h t , 3 x 1 0 ^ cm./sec. Therefore, for an ion of mass 3 and 50 kv energy: Hr • 5.6 x lCr4 gauss-cm. A radius of curvature of 6,35 cm. was chosen for the geometrical arrangement shown i n Plate V. The f i e l d required was therefore of the or-der of 104 gauss. The shape chosen for the pole pieces was a 60° wedge, (21) a shape commonly used when focusing of slightly divergent ions i s desired i n the analyzer. The pole pieces, each about 1.6 square inches i n area, are separated by a -J- inch a i r gap i n whioh the brass path-chamber of the analyzer i s located. Details of the magnet design and performance i s given i n Appen-dix I I . The magnetic f i e l d i n the a i r gap attained a measured value of 9000 gauss. The component ions after separation by the analyzer are f i n a l l y collected i n a Faraday cup. The cup as shown i n Plate V i s mounted with a Kovar bead onto a flange separated from the main body of the analyzer by a short section of glass. Incoming ions strking this flange cause second-ary electrons to be emitted and collected by the cup decreasing the read-ing of the true positive ion current. Secondaries which tends to decrease the true current reading are also emitted from the analyzer path-chamber when struck by a beamj but their effect i s believed to be negligible because of the geometrical loca-tion of the Faraday cup. 50-KV. SUPPLYCONTROL CIRCUIT PLATE VI 9 Secondaries emitted from the Faraday oup on reaching the analyzer body causes the ion current to read too high. These erratic readings due to' secondaries were obviated by ap-plying bias voltages of about 200 v. between the flange and the cup, and between the cup and the anlyzer chamber. Secondaries emitted from posi-tive ion bombardment have at most 20 e.v. energy (2) (12) so that this or-der of bias voltage was more than sufficient to retard the secondaries. Increasing the bias voltage from zero value up to 200 v. showed ihat the current reading was taken on the well-saturated portion of the ion-current tbias-voltage curve. The reading of the ion current may s t i l l include the secondaries emitted from the analyzer chamber wall to the cup lowering the true ion current reading. The decrease i s believed negligible. The high voltages for the project were produced by four main power packs. The plate voltage for the oscillator was produced by a f u l l -wave center-tap r e c t i f i e r capable of delivering 300 m.a. at 2000 v. The probe voltage was produced by a voltage doubler c i r c u i t f i l t e r e d through a TT section consisting of two condensers and a choke. The power pack was capable of delivering 20 m.a. at 3000 v. The voltage across the f i r s t focusing gap was produced by a voltage t r i p l e r capable of delivering 100 m.a. at 18 kv. The voltage ripple measured at 18 kv was 0.8$ The voltage across the f i n a l lens was produced by a special 50 kv X-ray transformer half-wave r e c t i f i e r set capable of delivering 25 m.a. at ± 50 kv. The ci r c u i t including f i l t e r s i s shown i n Plate VI. The vol-tage ripple as calculated i n Appendix III was found to be approximately 0.2$ 0-r. THE POTENTIAL DISTRIBUTION of an E I * CTROSTATIC I£NS «nd TRAJECTORIES of • SING U-CRARGFD POSITTVJ'. ION. SCALEtlNCHES -0 1 PLATE VII 10 IV EXPERIMENTAL PROCEDURE The entire vacuum system was f i r s t l y pumped down to the lowest pressure attainable with the diffusion pump. The needle valve was then closed and the storage bottle f i l l e d with tank hydrogen. The oscillator was turned on and tuned with the plate voltage at 1000 v. Even at the lowest attainable pressure with no hydrogen flow a blue discharge was ex-cited i n the discharge tube. This blue discharge, due presumably to evolu-tion of various adsorbed and absorbed gases, died out slowly i n about 5 or 10 minutes. When hydrogen was allowed to leak i n at a rate such that the Pirani gauge read about 4O microns, the discharge excited was at f i r s t pale pink. The Balmer series appeared prominently when the discharge was viewed with a spectroscope; but the background bands and lines, due pre-sumably to molecular hydrogen and perhaps other impurities, were also strongly excited. After about one half hour of continuous operation the discharge attained a b r i l l i a n t red. The Balmer series appeared with about the same intensity as before, but the bands were very faint i n the back-ground. A few lines not belonging to the Balmer series s t i l l appeared, but fa i n t l y . The b r i l l i a n t red color of the discharge (18) denotes a high percentage of atomic hydrogen ions i n the discharge. On subsequent start-ing of the discharge after having been extinguished even after some ten or twenty hours, the b r i l l i a n t red can be attained within five or ten minutes. The heat-light power given off by the discharge was equivalent to about 4O watt electric light of the same color. When the discharge has attained the desired color, the longi-tudinal magnetic f i e l d was applied. The discharge then assumed a conical shape tapered towards the steel cone i n the discharge tube. The position 11 of the magnetic c o i l was then adjusted u n t i l the taper pointed directly i n -to the probe canal. Above the glass cone shielding the metal one, the dis-charge was purplish red. Close examination of the discharge showed that i t s shape occurred i n conical layers of various shades of red; from a d u l l purplish red at the outer layer to a b r i l l i a n t f i e r y red at the core. The next step was to apply the probe voltage to extract the ions from the discharge through the probe canal. When this voltage was f i r s t applied, the discharge became pale probably because of gases released by the tungsten and dural probes when bombarded by electrons and ions. For the same reason probably the probe current at this stage was observed to be unsteady. Eventually, after about 15 minutes the discharge resumed i t s former colors and the probe current became steady. The positive ion cur-rent extracted was then measured with a micro-ammeter properly biased; the entire focusing system serving as a deep Faraday cup. The maximum ion current collected was of the order of 50^u a. with about 1000 v. probe voltage. The f i r s t focusing voltage was then applied together with the probe voltage. I t was found that only certain combinations of voltage values could produce a large positive ion current beam of the order of 700JOL a. Further increase i n probe voltage usually caused the ion cur-rent to drop unless the focusing voltage was also increased. The focusing voltage required was of the order of 12 kv. I t was decided that a focused beam of 12 kv energy should be suitable for analysis, especially since lower magnetic currents would be required for the analyzer c o i l s . The analyzer was therefore mounted and the total ion current reaching the analyzer was indicated by a micro-am-meter (not biased) while the current reaching the Faraday cup of the analy-zer was measured with a properly biased galvanometer. With the analyzer coils i n p a r a l l e l , the magnetic current was varied i n steps from zero to five amperes, and the corresponding current collected i n the cup was re-corded. After each set of readings the analyzer magnet current was de-creased to zero very slowly while the direction of the current was reversed rapidly one way and then another. In this manner the poles of the magnet was de-magnetized f a i r l y completely. Often when i t was desired to find the maximum proton current i n the Faraday cup as a function of one of the parameters, say the pressure, the analyzer current was adjusted u n t i l the proton peak current appeared on the galvanometer. The parameter was then varied u n t i l the maximum i s reached. The peaks of other ions were then found and compared. V EXPERIMENTAL RESULTS Using the procedure described a plot of the ion current was ob-tained, as shown i n Plate VTII, against the analyzer f i e l d current. Op-eration of the discharge over long periods of time showed that the para-meters used i n obtaining the above plot were most favourable to high per-centage proton production. These parameters are: Pressure i n discharge as measured by the Pirani gauge (actual scale read-ing) » 4-0 microns, corresponding to 17 microns pressure for hydrogen. Measured rate of hydrogen consumption • 1 1 cc. p.hr. at atmospheric pressure. Current applied to magnetic c o i l around discharge tube * 5.6 amp. This current produced 24-0 gauss at .the center of c o i l . Oscillator plate voltage s 1500 v. Total oscillator current = 300 ma. 13 Probe voltage » 1790 v. Voltage across f i r s t lens B 12,300 v. Total ion current e 600jua. The pressure reading of 4-0 microns corresponded to 17 microns pressure for hydrogen. Calculation i n Appendix IV showed that,because of the length of glass tubing between the gauge and discharge tube, the pres-sure i n the discharge i s decreased, but only to l6jjf microns. In the above run the t o t a l ion current of 600^ ua. was not the maximum attainable. By increasing the voltage across the f i r s t focusing gap to 18 kv and adjusting the probe voltage, the output ion current i n -creased steadily to 800 ji a. Since 18 kv was the maximum output of the t r i p l e r c i r c u i t power pack, no further attempt to increase the current was made although saturation was not reached. The plot shown i n Plate VIII shows the peaks of Mass 1 and Mass 2 to be f l a t . These plateaus occur presumably because the beam diameter i s les6 than the width of the Faraday cup. The aperture i n the leading flange of the analyzer was inch i n diameter; the Faraday cup was •§- inch i n diameter. Therefore, when a resolved beam moves within the cup as the magnetic current i s varied, no change i n current w i l l be observed i n the galvanometer. Therefore, the peak current reading can be taken as pro-portional to the t o t a l like-mass ions forming the beam current. Better resolution can be obtained, however, by putting narrow s l i t s i n place of the aperture and i n front of the Faraday cup. The percentage of protons i n the beam responded i n varying de-grees to changes i n the various parameters. Systematic studies of the percentage proton as a funotion of each variable was attempted. Unfortun-ately, a l l the variables were not mutually independent of one another, and IC^DRREHT COLLECTED IN FARADAY CUP VS. 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' 1 1 ' "3 J -—H 1 '/ill ' 1 1 ' --I —H ill' -Hi -Mil -i i i / III! -Hi h 1 a i P7 IN -Hi h 1 E -i 3 ltd i / MM i -Hi 'III < -i 3 / 1 1 -11 1 >s? | hp -/ | 1 — vr --11 1 1 1 1 * > 1 | ; 1 -/[ J 1 — -I 1 I -1 1 1 'ill 1 1 / > 1 -1 ! MM' 1 Q 1 / 1 1 1 » 1 1 1 III » 1 \ 1 UJ r -11 1 1 1 fc~ iT i -f j 1 1 | 1 '1 /III VII ! 1. 1 / i i  1 1 1 NJ 1 II ' , 1 -j--• -/-1 l 1 1 1 ---j--• -/-1 1 i i 1 ..1 ---i 1 1 1 i i -j-1 '1 -i l 1 ! i -j-I l:i 1 1 i 1 i i i 1 1 1 • r 1 1 1 i i i 1 1 1 !' 1 1 i I l i i -1 '1 i > .1 ! -; • 1 1 1 1 1 i -1 i i i i I ---1 T ----1 _ --1 T -1 -1 --~r r 1 -1 l 1 1 ~r r i 1 I 1 i i 1 I-1 1 i I 1 I i | 1 u 1 Mil ( ~> 1 1 i r\ r 1 1 1 u ?i -1 0 MM i cn n 1 IC -1 1 1 1 II i 1 1 1 1. MM 1 1 1 I 1 I 1 1 1 i 6 1 1 ) 1 t i | 1. i i 1 1 i 1 1 | i i l i i 1 1 1 No. 246 GRAPH PAPER, CLARKE a STUART CO. LTD., VANCOUVER, B.C. the task proved extremely d i f f i c u l t . However, the following results i n graphical forms were obtained: Graph I : Percentage of protons as a function of the pressure on the Pirani gauge. Graph I I : Percentage of protons against the current through the mag-netic c o i l around the discharge. Graph I I I : Percentage of protons, mass 2, and mass 3 ions against the oscillator power* VI DISCUSSION Performance of an ion source can be controlled and improved i f the behavior of the ions between the i n i t i a l stage of ionization and f i n a l stage of striking the target i s known. The various processes of ioniza-tion of gases by co l l i s i o n are offered i n the literature (6) (16) (20) (24). The treatments are of course theoretical and s t a t i s t i c a l ; and their applications suffer great limitation because of the geometry and non-ideal conditions of practioal cases. The subject of electron and ion optics i n determining trajectories occupies a similar position. Traject-ories of charged particles i n fi e l d s can be found analytically only for a few mathematically ideal cases, but fortunately numerical and graphi-cal methods exist which are applicable to most practical cases. The potential distribution of the lens system has already been determined num-er i c a l l y : the trajectories of the ions must s t i l l be found. Since the lens used i s electrostatic i n nature, the di f f e r e n t i a l equation of a charged particle i n the f i e l d may be readily derived (26) from the principle of least action: Jy^ m v. d s • 0 using the Euler Equations of the variation principle. I f the path of the charged particle l i e s i n the meridonal plane of an axlal l y symmetric sys-tem, the d i f f e r e n t i a l equation of motion obtained i s r " - 1 * r ' fygV - r' 9J,\ 2V VZ> r 07> where r and Z are the coordinates, V the potential, and r' r " the f i r s t and second derivatives respectively with respect to Z. I f the rays always make small angles with the axis, the equation can be expanded i n a power series and terms of higher order than the f i r s t i n r and r« can be neg-lected. The paraxial ray equation r " s - V L , - Yj. ' r 2V 4V i s then obtained. Analytical solution of the ray equation i s possible only i n a very few special cases. The mathematical potential distribution must f i r s t be known. Because of this last requirement, therefore, a mathemati-cal trajectory for the charged particles i n this ion source focusing sys-tem cannot be found easily. Resorts must therefore be made to a numerical or graphical method. Two numerical integration methods given i n Zworykin, Morton, etc. (26) are commonly used for finding focusing properties of electron lenses used for image formation. For a beam-forming system, such as that used i n this project, a graphical method i s much quicker and just as satisfactory. A method described i n Appendix V based on Snell's Law i s used to obtain the trajectories (shown i n Plate VII) of a singly-charged ion of various energies and orientations. The trajectory i s independent of the ion mass for non-relativistic consideration. Trajectory A of Plate VII shows an ion created i n the discharge 16 tube emitted paraxially from the probe canal after f a l l i n g through 1790 volts probe voltage. For this particular case, the path of the ion event-ually coincided with the axis of the lens system. Trajectory B shows an ion created i n the discharge tube emitted through the canal with maximum divergence possible. I t was ultimately bent parallel to but off the axis by about I/64 inch. Trajectory C shows a diverging ion assumed to be created after the uncharged parent molecule or atom has drifted through the canal. The ion thus created starts into the focusing f i e l d with practically zero en-ergy. Its path i n the field-free region i s shown to be slightly divergent and off axis by about £ inch. The variation i n energy due to the ripple voltage of the various power packs was found insufficient to alter trajectories A and B appreciab-l y . The indices of refraction at the equipotential surfaces for these cases are compared i n Appendix V with the original indices used to obtain the trajectories. When an ion travels down the column i n a beam, the off axis trajectories are altered considerably by the mutual space-charge repulsion of the ions. Equations have been derived by Thompson and Headrick (23) for finding the longitudinal cross-section of a beam of electrons suffer-ing from space-charge spreading. The method has been extended by R. N. Hall i n an unpublished paper to ion beams i n an accelerating column. Be-fore the methods can be applied, however, the radius of the beam at cert-ain positions along the axis must be known. Since time did notpermit such measurements to be taken the space-charge effect could not be taken into consideration. The peculiarity mentioned i n the Experimental Procedure of the 17 maximum positive ion current extracted using the probe voltage alone being only a small fraction of that obtained when the f i r s t lens voltage was ap-plied i s believed to be due to an ion sheath i n the v i c i n i t y of the exit canal. This theory i s also held be otherj Tuve, Dahl, and Van Atta (24)j and Buechner, Lamar, and Van de Graaff (4), who found similar effects i n their investigation. The effect of the space charge sheath may be outlined as follows: A collector of positive ions (or electrons) i n a discharge has been shown by Langmuir and Mott-Smlth (15) to be surrounded by a space charge sheath whose thickness i s given by: x = k.336 x IO" 6 V3/2(1+.02A7 vT)] * L I vT x 8 thickness of sheath i n cm. V s potential i n volts of the collector with respect to the surrounding space. I = current density i n amperes per cm.2 T = absolute temperature of discharge The thickness of the sheath calculated approximately i n Appen-dix VI using conditions i n this investigation was about .8 cm. above the canal-probe i n the cone with a probe voltage of about 2000 v. A sheath of this order of thickness was actually observed above the probe canal when the magnetic c o i l obstructing the view was removed and the probe voltage applied. When the probe voltage i s low, the sheath i s thin, and ions can d r i f t out through the canal. When the probe voltage i s high, the sheath thickness decreases the opening i n the canal, and only ions at the outer edge of the sheath can d r i f t out into the focusing f i e l d . The focusing f i e l d i n Plate VII was plotted under the assumption that the space within the electrodes i s charge free. I f positive charges GRAPH IV  Ion Current Against Probe Voltage exist i n the canal, the focusing f i e l d w i l l be modified. Some of the lines of force w i l l terminate on the charges instead of the steel cone. In this manner, the focusing f i e l d w i l l extract ions as well as focus them. Further experimental support for the above may be qualitatively given as follows. With no focusing voltage, the t o t a l current extracted as a function of the probe voltage i s given i n Graph IV. At low probe voltage, the thin sheath permits the ions from the discharge to d r i f t through. As the voltage i s increased, the thickness increases decreasing the number of ions dri f t i n g through u n t i l a minimum i s reached. Further increase i n probe voltage causes the thickness of the sheath to become so great that the mutual repulsion between charges causes the ions i n the canal to be repelled into the accelerating column. The constraining mag-netic f i e l d probably helps to focus the ions through the canal so that the maximum increases for higher magnetic f i e l d s . I f the above i s true, then a much higher ion current should be obtainable i f an electrode i s placed as close as possible to the exit canal on the accelerating column side so that a steep voltage gradient can be applied to extract the ions. This electrode w i l l serve the same pur-pose as the grid-electrode of a cathode ray tube where focusing i s chiefly done by another electrode. Of course, for ions much higher voltages w i l l be required. This electrode should also serve as an aperture stop. One possible disadvantage may be that the ions extracted thus may dif f e r i n energy from those d r i f t i n g through the canal. Should this be the case, then d i f f i c u l t y may be encountered i n obtaining good focusing. 19 VII CONCLUSIONS The high-frequency discharge ion source constructed has operat-ed satisfactorily. I t possessed most of the desirable properties sought i n a good ion source. I t i s definitely superior to the canal-ray, ca p i l -lary-arc, and reflection type ion sources constructed i n the past. The reduction to a minimum of the amount of metal exposed to the discharge constitutes an important factor i n obtaining a high percen-tage of protons. The pressure i n the discharge also influences ihe per-centage proton c r i t i c a l l y . The performance of the ion source, although satisfactory, sug-gests improvements which may lead to a much better source. 20 APPENDIX I The Liebmann Procedure for Finding the  Potential Distribution for the F i r s t Focusing Lens (26) Since the electrodes have rotational symmetry, an i n f i n i t e l y thin s l i c e through the axis of symmetry i s sufficient to give a two dimen-sional description of the potential distribution. Before plotting the f i e l d for the f i r s t focusing lens consider f i r s t a two dimensional charge-free space enclosed by the curve C and d i -vided into a rectangular coordinate net work of mesh width d as shown in Fig. 1. In this region any electro-static potential distribution which exists must satisfy Laplace's Equa-tion subjected to the proper bound-ary conditions. Laplace's Equation in two dimension i s : ?2y + ^ 2 V - 0 ^x 2 ^ y 2 Fig. 1 Now i f i n Fig. 1 V 0, V^, V2, V3, and are the potentials at points o, 1, 2, 3T and 4 respectively, then at point 0 Approximately and fd2j \ + /32y \ = 0 Wx 2/ (dj2j o o (Jh-) i 1//HL) - (EL) } U x 2 / 0 d | U x ; l 0 \)xJo3 J (JUL) = l / f i l ) - ( & ) ) 21 Since fd V ) = V, -Vo ; r Vo-VJ [tx Jl0 d ^ x A3 d / H \ = Va-Vo j / J L O = Vo-V»  \d7J20 d vXyVo^ d i t follows that Vo = i (Vi + v 2 + v 3 + v 4 ) I f at an irregular boundary the mesh width d i s not equal i n a l l directions, e.g. d]_, d 2, fyt and d^ in Fig. 1, the approximation equation takes the form: Vo = d,d> dsd* J 1 /VJL + l l ^ + _ i / l i Y i i ) d,d3+did^ 1d,+d3U, dW drfd4^da d * / j This last equation i s cumbersome and i t s usage can usually be avoided by changing slightly certain geometry of the electrodes without altering appreciably the potential distribution i n the region of chief concern. For instance i n the f i r s t lens a tapered cut i n the flange shown in Plate I i s replaced by a square cut as shown i n Plate VII. The effect of the change on the potential distribution at the axis i s believed negli-gible. Before computing, a scale drawing twice actual size was made of the electrodes. The region between electrodes was then divided into a rectangular network of mesh width inch. The cone was made a r b i t r a r i l y 0 volts while the cylindrical electrode was made 100 volts. Potential values were then assigned a r b i t r a r i l y but reasonably to each l a t t i c e point. The equation derived previously was then applied starting at a point near an electrode and progressing from point to point at f i r s t along a surface of an electrode and then eventually covering the whole network. At each point the value Vo was calculated and substituted i n place of the old value. The whole procedure was repeated throughout the network several times u n t i l the change in the value of Vo was less than 1. In this manner 22 the potential distribution shown in Plate VII, was obtained with the equi-potential surfaces shown i n percent. Further details and refinements of the method can be found i n references (7) (19) (26). APPENDIX II  Magnetic Analyzer Design The f i e l d required to bend the ions through a radius 6.35 cm. i s about 104 gauss. Allowing for fringing f i e l d i n a i r , flux density i n iron pole pieces » 16000 gauss. Assume the f i e l d intensity creating this flux i s 80 oersted; i.e.^x " 200. The length of iron path ss 66 cm. The length of a i r path s 1.2 cm. M. M. F. = 10 ATT Hdl [SO x 66 f 1.2 x 104j = 17,280 ampere-turns Y. \ I I " I f two coils are used, each must have about 8600 ampere-turns. Dimension of yoke permits 1800 turns of #18 Formal enamelled wire on each c o i l . Currents up to 5 amperes are then required and water-cooling must be pro-vided. APPENDIX III Calculation of Ripple Voltage on 50 kv Set For the 50 kv set, the equivalent f i l t e r system i s shown Fig. 1, « b o x io«* J\-V ~ ± So KV =r C = o.5 jruA 23 The charge Q on C i s given by Q = V C I f period of discharge i s ^ t , then discharge current I i s : I = Ag_ At C AV A t AV = I At c Percent ripple 8 AV x 100 8 l A t x 100 V V C Positive ion current • 1 m.a. Bleeder current • 1 m.a. Corona and Leakage = m.a. Total = 2.5 m.a. V 8 50 x 10 3 V A t = 1/60 sec. :•Percent ripple 8 l/6$ APPENDIX IV Correction for Discharge Tube Pressure The geometrical arrangement of the discharge tube and Pirani - t f r — gauge may be represented by Fig. 1. Since no gas flow exists between the gauge and the junction, the pressure difference must be zero. The mean free path corresponding to this pressure i s about .5 cm., being of the order of the radius of the tubing .3 cm., Knudsen's equation may be used i n this range. The equation as given by Dushman (8) i s : P, P3 Pirani Gauge F i g . l To. Ho. IN Discharge Tube Q a ( P i - P 2 ) F where Q a quanti ty of gas flowing through the tube i n Micron cm.3 s e c . " 1 P| > Pa B pressure difference between the ends i n Microns and F - 3O48O a3 pf cm.3 s e c . " 1 1 y I a B radius of tubing i n cm. B .3 cm. 1 ° length of tubing i n cm. B 35 cm. T • absolute temperature B 293 K M • Molecular weight of the gas B 2 Subs t i tu t ing above value, one f inds F = .33 x 104 cm.3 s e c . " 1 Since the flow of hydrogen at atmospheric pressure i s known to be 11 cc . per hr or 11 u.cm.3 p . s . , one may put 3600 Q - P,V, = P a t . V a t . s 760 x lp3 x 11 ii .cm.3sec." 1 , 3S00 J . ' .Pa B P, - 2 F Subs t i tu t ing the numerical values Pa = 17 - i ; - P 2 = 16§JI. APPENDIX V  Ion Trajector ies (26) Consider i n F i g . 1 an ion i n a po ten t i a l region V| moving wi th v e l o c i t y v, in to region V 2 d iv ided by an i n f i n i t i s m a l boundary making an angle 6 t wi th the normal. When the i on passes through the boundary i t suffers accelera t ion i n the -y d i r e c t i o n but not i n the x d i r e c t i o n , so that i t s path now makes an angle 9*with the normal. 25 Now v, sin 6, = v» sin 8* From mv3 = Ve Consider the equipotential surfaoes i n Fig. 2. V j , Vg, and V ^ . where these potentials are measured with respect to a point where the ion has zero velocity. The ion i n region between V i and V"2 i s assumed to have approxi-mately an average energy of Vi ¥fz 2 volts, and between V2 and V3, Va.tV3 volts. The equipotential sur-2 faces are considered to be i n f i n i t i s -mal boundaries between region of d i f -ferent but constant potentials. There-fore i f the ion direction at point 0 on surface V2 i s (AO,) the new direction i n region (2) can be found from the method previously shown by applying as follows$ Produce (AO) to (OE) of any length. Draw a perpendicular (OF) to equipotential surface a$ 0, and draw EF normal to OF. Measure from F along (FE) a length (FH) such that 26 (FH) = / V3 »V* (FE) V Va. 1-V, With centre 0 and radius (OE), describe arc (EDS). Through H draw a line (HD) parallel to (OF) to cut the arc at D. (OD) i s the new direction for the ion i n region (2). The procedure i s repeated at each surface and the trajectory i s obtained. The method i s f a i r l y accurate i f the angle of incident i s not too great. Higher degrees of accuracy can be obtained by using more equi-potential surfaces. For the trajectories i n Plate VII a probe voltage of 1790 v. and focusing voltage of 12.3 kv were used. Indices were obtained for an ion starting from the discharge tube f a l l i n g through the entire voltage. (Column A). In Column B, the ion f a l l s through the only lens voltage. In Column C, the voltage fluctuation due to the ripple of the power packs were taken into account i n calculating the indices. These indices are tabulated i n Table 1. For Column C, the total fluctuation i s found as follows: (a) For r . f . oscillator assume a l l of the 120 w. i s delivered through electrodes say 10 cm,2 area into discharge. The Poynting vector i s therefore _ P = 120 x 10' ergs./sec,/cm.2 . 10 and P = C (E X H) Gaussian units Assume E axial with discharge tube, H concentric, and P perpendicular to walls. In H 2 gas <H) B {E| .-E2 = AJL x 120 x 10 7 • 16 e.s.u. C 10 1000 Maximum energy acquired by a singly charged particle i n A.C. f i e l d i s derived as follows: F = m a a m dv dt F = e E = e Eo sin wt ;-m d v = e Eo sin art m dv 8 e EoJ 0 'sin w t dt mv max 8 e Eo Maximum energy gained by ion i s ? 8 1 (m v )' 'max -~- K max' 2m " 1 E o ^ x lpi£ e.v. 2m\ w / 1.6 For protons: Wm s l x lO'^e.v. Energy spread due to r . f . i s negligible. (b) Maximum ripple possible for probe power pack s 2% Voltage fluctuation * .02 (2000) = AO volts (c) Voltage ripple on 1st lens - ,8% - .008 x 12,000 = 90 volts Theoretically, maximum spread = 130 volts Corresponding value of energy of beam - 13,950 v TABLE 1 Equip: Surface I n d e x o f R e f r a c t l o n i n percent A B C U . l kv 12.3 kv 13.9 kv (Maximum energy of beam) 1* .97 .58 .97 .97 .71 .97 3% .97 .84 .97 IS .97 .88 .97 5% .93 .77 .93 10% .86 .71 .86 20% .86 .77 .86 30% .89 .95 .89 A0% .91 .88 .91 50% .93 .90 .92 60% .94 .92 .93 70% .96 .95 .95 75% .97 .97 .97 80% .97 .97 .97 85% .98 .98 .97 90% .98 .97 .98 95% .98 .97 .98 99% .99 .98 .99 29 APPENDIX VI Thickness of the Space Charge Sheath (15) The formula given by Langmuir and Mott-Smith holds only for plane electrodes. The canal probe may be considered plane and the effect due to the hole i n the probe neglected. Inside the canal the formula does not hold because of the cylindrical surface. ' Area of top of the probe = TT ( 2 ^ 4 a .4 cm2. Probe current - 5 x 10"^a. Positive ion current to Probe 2.5 x 10"^a. •:• I s 2.5 x 10" 3 = 2j> x 10~3 amp./cm2. •4 4 T i n the discharge i s about 5P00° Kj i t s influence on x i s very small. V = 2000 v. Whence substituting the numerical values into the formula i = \ 2.336 x 10~ 6 xjV3/2(1-.0247VT ) one obtains for the tickness of the sheath x = .8 cm. 30 BIBLIOGRAPHY 1. Ardenne, M. Von. Phy. Z. 4 2 , 5-6: 91 - 101, 1942 2. Baerwald, Ann. der Phys. 41* 643, 1913 3. Bayly, A. J.j and Ward, A. G. Can. J. of Research A, 26: 69 - 78 March, 1948 4. Buechner, Lamar, & Van de Graaff J. App. Phys. 12: 133 and I4I, 1941 5. Craggs, J. D. Proc. Phys. Soc. London, 54J 439, 1942 6. Rev. Modern Physics, 2: 124 - 232, 1930 7. Cosslett, V. E. "Introduction to Electron Optics" Oxford Press, 1946 8. Dushman, Saul "Scientific Foundations of Vacuum Technique" P. 91-92 John Wiley & Sons, Inc., 1949 9. Finklestein R. S. I. 11: 99 - 97 March, 1940 10. R. W. Hall, R. S. I. 19: 905, 1948 11. J. H. Van Hofweegen and J. S. Knol Philips Research Reports Vol. I l l No. 2, A p r i l , 1948 12. Jacob, L. "High Voltage Physics" Methuen & Co. Ltd., 1934 13. Lamar, Buechner j & Compton Phy. Rev. 51 (936) June 1, 1937 14. Lamar, Buechner, & Van de Graaff J . App. Phys. 12: 132, 1941 15. Langmuir and Mott-Smith G. E. Rev. 37: 449, 538, 1924 16. Loeb L. "Fundamental Processes of E l e c t r i c a l Discharge i n Gases" John Wiley & Sons, Inc., 1939 17. Oliphant & Rutherford Proc. Roy. Soc. A I4I: 259, 1933 18. Rutherglen, & Cole Nature Vol. 160, No. 4068 P. 545, Oct. 18, 1947 19. Shortley, G. H. and Wilier, R. J. App. Physics 9: 334, 1938 20. Smith, L. P. & Scott, G. W. Phys. Rev. 55s 946 - 953, May 15, 1939 21. Stephens, W. E. Phys. Rev. 45: 515, 1934 22. Terman, F. E. "Radio Engineer's Handbook" P. 322, McGraw-Hill Book 31 Company Inc., 1943 23. Thompson & Headrlck I. R. E. 28: 318, 1940 24. Townsend, J. S. E. "Electrons,in Gases" Hutchison's Scienti f i c and Technical Publication, 1947 25. Tuve, Dahl, & Van Atta Phys. Rev. 46: 1027, 1934 26. Zinn, W. H. Phys. Rev. 52: 665 - 657, Sept., 1937 27. Zworykin, Morton, Ramberg, H i l l i e r and Vance "Electron Optics and the Electron Microscope" John Wiley & Son, 1946 

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