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The development of a double focusing magnetic spectrometer Smith, Arthur John Stewart 1961

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THE DEVELOPMENT OF A DOUBLE FOCUSING MAGNETIC SPECTROMETER by A. J. STEWART SMITH B. A . , University of British Columbia, 1959. A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in the Department of PHYSICS We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA October, 1961 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis f o r scholarly purposes may be granted by the Head of my Department or by his representatives. It i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department The University of B r i t i s h Columbia, Vancouver 8, Canada. Pat. / n / ABSTRACT A fifteen inch magnetic spectrometer using its fringing field to achieve double focusing has been developed and made ready for experimental work. It spower supply delivers continuously variable currents from 0-100 amperes. The current is stable to one part in ten thousand, being regulated by a transistor amplifier which drives a bank of parallel output power transistors . Interlocks are provided to protect the components against foreseeable hazards. The vacuum and detecting systems are complete, and the spectrometer has been tested with various alpha sources. The best resolution obtained was .57 per cent, but there should be much better resolving power inherent in the spectrometer, unrevealed because the sources used were fairly large. A resolution measurement of scattered protons when the beam from the Van de Graaff is put in to the spectrometer should determine the resolution more accurately. TABLE OF CONTENTS Chapter Page 1 INTRODUCTION 1 11 THE POWER SUPPLY 5 General discussion of the operating principle 5 The Unregulated Direct Current Supply 5 Explanation of Operation 5 Discussion of Various Components 8 a) The Magnetic Circuit Breaker 8 b) The Water Pressure Switch 8 c) The Cabinet Interlock 9 d) The Variac and its Motor 9 e) The Variac Zero Position Interlock 10 f) Zero Reset of Variac 10 g) A. C. Supply to the Rest of the Circuits 11 h) Other Dangers and Their Elimination 11 Thyrector Diode 12 The Fine Regulation Circuit Power Transistor Panel 15 Open loop Gain and Stability 15 A. C. Feedback Loops 18 Null Indicator Modifications 19 - iv -Chapter Page The Voltage Reference Circuit 20 "Direct" - "Remote" Switch 20 Calibration of Supply . 20 The Rough Regulator Circuit 20 Reason for Using this Circuit 20 Hunting of the Supply . . . . . . . . . . 21 III THE CONSTRUCTION OF THE VACUUM SYSTEM AND COUNTING APPARATUS 25 Theory of the Focusing Properties of the Magnetic Sector 25 Vertical or Double Focusing 26 Design of Target and Counting Assembly „ . . . 28 The Vacuum System 29 The Electronics For the Solid State Counter 32 IV THE RESPONSE OF THE SPECTROMETER TO ALPHA PARTICLES FROM VARIOUS SOURCiiS 35 Measurements of Alpha Particle Spectra from Three Small Alpha Sources 35 The Response of the Spectrometer to a Source Made to simulate the Shpe of a Heavy Ice Target 37 - v -Chapter Page Appendix A Operating Instructions for the Power Supply 43 Appendix B Specifications of Certain Components of the Power Supply . -. 45 Appendix C Silicon Controlled Rectifier Transient Voltage Sup-pressor for the Spectrograph Supply 48 Appendix D An Estimate of the Lowest Measurable Crossection for the D(D, / )He4 reaction 49 Bibliography 60 LIST OF FIGURES, Figure Page 1. Block Diagram of the Power Supply 13 2. The Unregulated Direct Current Supply and Safety Interlocks 14 3. The Fine Regulation Circuit 16 4. Modifications to the Null Indicator ...' 19 5. The Voltage Reference Circuit 22 6. The Rough Regulator Circuit 23 7. The Magnetic Sector and its Focusing Properties ... 27 8. The Spectrometer and Counting Assembly 30 9. The Solid State Counter Housing 33 10. The Preamplifier Schematic 38 11. Current Profiles from two Polonium 210 Sources 41 12. Current Profile from Source Simulating a Heavy Ice Target 42 -vii -ACKNOWLEDGEMENTS The author expresses his gratitude to Dr. J. B. Warren, who supervised this work, and to Dr. B. L . White, whose many helpful suggestions and effort in preparing the text are greatly appreciated. The author wishes to thank the National Research Council of Canada for their two awards . CHAPTER 1 INTRODUCTION The Van de Graaf Laboratory has recently acquired a sixty degree double focussing spectrometer and a ninety degree broad range spectrograph for the analyzing of nuclear reaction products. The advantages of using a mag-netic analyzer instead of a counter giving pulses proportional to the energy of the particles are the following: First, magnetic sectors can resolve momentum groups differing by one tenth of a per cent, whereas solid state counters, proportional counters, and so forth would have difficulty in resolving momentum differences of one percent. Second, if one wished to take measurements at small angles with respect to the beam direction, the Rutherford cross-section for the scattered beam particles is usually much greater than that of the reaction of interest, and these beam particles are likely to swamp a counter which accepts all particles incident at these small angles. With a magnetic analyzer, however, unless the momentum of the scattered beam particles coincides with that of the sought after reaction particles, the beam particles are bent far away from the image position at which the reaction particles are focussed, and one can use a solid state counter, for example, with no fear of extraneous pulses caused by coincidence of two or more pulses as occur when the much higher flux of beam particles are striking it. Many types of magnetic analyzers have been developed, using as their focussing principle the property of rays diverging from a point source at small angles, and following circular trajectories, that they will converge again at - 2 -some point after they have been bent by the field. ' For the momentum analysis of charged particles formed as reaction products by an ion beam, a magnetic sector, that is a wedge shaped constant magnetic field, of angle less than 180° is most convenient, since the target can be outside the magnetic field. The common deflection angles chosen are ninety degrees and sixty degrees. The smaller the angle of the wedge, the higher momenta that can be bent for •3 a given area over which the field extends . The spectrograph is used for obtaining a record on a photographic plate or counting with a matrix of small counters an energy spectrum extending over an energy range where the maximum energy resolved is about two and one half times the minimum energy. It has a very low acceptance solid angle, of about 5x10-4 steradians. The spectrometer, on the other hand, is intended for the detailed examination of single momentum groups. The particles enter at angles other than ninety degrees to the edge of the field and, if the entrance and exit angles are chosen correctly, not only can focussing be achieved in the plane perpendicular to the magnetic field, but also the fringing field can be used to effect focussing in the direction parallel to the field. Such focussing in two directions is called 1. W. G. Cross, Rev. Sci. Instr. 22, 717 (1951). 2. W. E . Stephens, Phys. Rev. 45_, 513 (1934). 3. W. G. Cross, loc. cit. - 3 -double focussing, and is described in detail in the references listed. * The acceptance solid angle of the spectrometer is much higher than that of the spectrograph, namely .006 steradians. This solid angle, although much lower than that of other types of counters which can have solid angles approaching 2 IT steradians, is large enough to permit lower crossections to be measured because of the low background count obtainable with the magnetic bending. The purpose of this study was to design the power supply, counting assembly and electronics, the vacuum system and the target chamber for the spectrometer to ready it for use in the detection of any alpha particles result-ing from the nuclear transmutation d(d, f )He^. This spectrometer is capable of resolving momentum groups differing by .033 per cent, and therefore the power supply must keep the current stable to one part in ten thousand in order that maximum resolution may be obtained. Although construction of the power supply for the spectrograph, a 7 supply identical with spectrometer supply with one exception , was carried on at the same time as that of the spectrometer, it is not complete at present. The discussion of the spectrometer supply applies to that of the spectrograph as well. The vacuum system and the target chamber have been developed, as well as the apparatus for adjusting the position of a solid state counter, 4. Ibid., 719. 5. Otto Meier, Jr., e£._aL_, Rev. Sci. Instr. 29, 1004 (1958). 7 . See Appendix C . - 4 -which will be used to count the particles bent by the spectrometer. The image position of the spectrometer has been determined and the response of the spectrometer to alpha particles from various sources has been measured. - 5 -CHAPTER 11 THE POWER SUPPLY In Figure 1, a block diagram of the power supply is shown. The magnet current is obtained from an unregulated direct current supply which converts sixty cycle mains power into direct current with a ripple voltage of about one volt peak to peak. This current is regulated by a bank of series power transistors which are driven by both voltage and current feedback networks which compare the voltage across a standard resistance in series with the mag-net with a calibrated reference voltage . The A. C . input to the power supply is coarsely regulated by a motor driven variac. The purpose of this regulation is to prevent the power transistors from having to dissipate more power than necessary to keep them in their active region. The high current, low voltage requirements for the supply are ideally suited for the use of solid state components for rectifying and series regulating the current. A prohibitive number of vacuum tubes would be necessary to pass the maximum current of one hundred amperes. Unregulated Direct Current Supply: O Q Most supplies of this type described in the literature ' , have em-ployed a motor-generator set as the source of direct current. Other methods 8. 9. Richard L . Garwin, Rev. Sci. Instr. 30, 105 (1959). S. D. Johnson and J. R. Singer, Rev. Sci. Instr. 29, 1026 (1958). - 6 -considered were: first, a phase controlled silicon controlled rectifier variable voltage supply ^ , which was not used because of the excessive price of the silicon controlled rectifiers at the time; and a saturable transformer working on the magnetic amplifier principle. A recent reference reports the successful development of a supply employing a magnetic amplifier ^ A We felt it would be cheapest and just as efficient to use a motor-driven variac fed from a mains voltage of 220 volts, sixty cyles. The circuit which supplies unregulated, filtered direct current to the magnet and the series transistor regulating panel is shown in the block diagram of Figure 1 and in more detail in Figure 2. The raw A. C. from the wall switch is first connected to a magnetic circuit breaker, which will interrupt the current if any one of several hazardous conditions prevail. The protective circuits will be discussed in detail below. Assuming the breaker is closed, the current passes to the variac. A voltage sufficient to keep the power transistors in their optimum operating range is provided to a transformer with a step-down ratio of 3 .3 This step down ratio is necessary since our variac, which is the smallest model available which will handle the power required 12, has a maximum current rating of thirty amperes and one hundred amperes are needed to give maximum magnetic field. 10. General Electric Controlled Rectifier Manual, First Edition, General Electric Company, Liverpool, New York, 1960. 11. Meier et. a l . , opcit. ,p. 1005 12. For specifications of all the major components used in the supply, see Appendix B. - 7 -The transformer has two electrostatic shields, one connected to building ground and the other to the neutral wire of the mains, in order to minimize the inter-winding capacitance and thus impede the transmission through the transformer of transients appearing on the line voltage. The output of the transformer is connected to a silicon bridge rectifier supplied by General Electric. This rectifier dissipated about one hundred watts at full output, and so is cooled with a blower which starts automatically .when the circuit is energized. The rectified current is then filtered with a choke input circuit, which reduces the ripple to 1.5 volts r.m.s . at full current. A capacitive input circuit is unfeasible with silicon rectifiers because the charging surges greatly exceed the current ratings of the rectifier cells. The magnitude of the choke had to be greater than one millihenry to keep current flowing throughout the forward cycle of the rectifier, so we chose a value of five millihenries, which allowed us to use condensers of a reasonable magnitude to keep the ripple within the desired limit. The capacitance in the filter consists of two 4200 microfarad, 150 volt electrolytics in parallel. Various parts of this circuit deserve special mention, especially the interlocks which protect the circuit against dangerous situations which may arise. All the interlocks are shown in Figure 2. 13. Operating instructions for the supply may be found in Appendix A. - 8 -a) The Magnetic Circuit Breaker: The function of this component is to give us a safe method of shutting off the current when necessary, and provides a convenient method of interlocking various switches to the solenoid which controls the heavy current lines, and thereby prevents the possibility of the current being turned on when all conditions of safety are not fulfilled. The supply is turned on by pressing the momentary contact start button, which when pressed will allow current to flow to the solenoid if all the interlocking switches are closed. The solenoid is a self-latching relay, and will remain closed until the stop button is pressed or one of the interlocks opens . A discussion of these interlocks follows: b) Water Pressure Switch: A flow of water is required at all times when current is flowing to cool the transistor output panel, the manganin shunt, and most important, the magnet coils. A very small flow is sufficient to cool the first two components mentioned, but to keep the magnet temperature within twenty degrees centigrade of the ambient temperature, a flow of one gallon per minute is needed. However, even one third of this flow will keep the magnet below temperatures which might be dangerous, although the magnetic field would change somewhat from its value at ambient temperature. Sufficient protection for the components and the magnet is provided with the installation of a water pressure switch, which is closed for water pressures above twenty-five pounds per square inch, and is open for ' - 9 -pressures below this. The switch is in series with the magnetic breaker, and the breaker can remain closed only when the pressure switch is closed. Thus, current flow ceases whenever there is a lack of sufficient water pressure; and also, the supply cannot be started unless water is flowing, since the solenoid will never be able to close when the water switch is open. c) The Cabinet Interlock: This switch does not allow current to the solenoid whenever the door to the supply cabinet is open. Its function is obvious and it operates electrically in the same manner as the water switch, with which it is in series. d) The Variac and its Motor: The variac can supply thirty amperes at 220 volts, which is more power than needed. Therefore, one would like to limit the swing of the variac slider so that the output voltage cannot rise above that need for maximum current. This is accomplished by a microswitch provided which restricts rotation between two limits which may be set by adjusting two rings on the shaft which prodtrude and strike the microswitches when the rotation exceeds the critical value. These microswitches are shown in Figure 2. The motor is a two directional type, the direction of travel depending upon which winding the potential is applied to. The motor is driven by a feedback circuit shown in Figure 5 which keeps the voltage across the output transistor panel at 3 .7 volts. So Iwhen the magnet current is set at zero, the variac will position itself to deliver 3.7 volts at the output of - 10 -the rectifier. The lower microswitch is set so the minimum voltage at the rectifier output is five volts in order to make certain that the lower microswitch is activated every time the current is set to zero. The fuse in the secondary of the variac was in a very inconvenient., position so the variac was modified to have the fuse on its main terminal board. e) Variac Zero Position Interlock: If the magnetic breaker opened when current was flowing, the variac of course would remain at the position it had before the current stopped. If then the start button were pressed, energizing the variac and the step-down transformer would produce large transients which could damage the rectifiers, and also put a strain on the power transistors. ; To ensure that this can not happen, an interlock has been designed which opens a switch in series with the start button when the variac is not at the zero position. This interlock consists of a relay driven by 110 volts supplied from the stop button through the unused pole of the zero position microswitch on the variac shaft. The existing wiring in the variac had to be modified by reversing the two leads coming to the micro-switch, since the common pole of the microswitch was connected to the motor winding rather than to terminal 1 on the front of the motor as needed to make the operation of the interlock possible. f) Zero Reset of Variac: If the magnetic breaker should open leaving the variac in a non-zero -11 -position, it may be returned to zero by pressing the stop button and holding it down as long as necessary to let the motor drive the coil to zero. When the stop button is pressed, it applies voltage to terminal 1 of the motor, causing the variac to return to zero. This supply line is connected across the normally closed posi-tion of the start button, which is not otherwise used, in order to prevent the start and stop buttons from being pressed at the same time when the variac is not at zero. This is necessary because the voltage from the stop button driving the variac to zero also closes the Zero Position Interlock relay, so if one were to press the start button, the magnetic breaker would close even though the variac were not at zero. The traverse limiting microswitch on the variac stops the motor when the zero position is reached, so there is no danger of damaging the motor by holding down the stop button too long when returning the variac to zero. g) A. C. Supply to the Rest of the Circuits: • The null indicator shown in Figure 1, and the blower to cool the rec-tifiers require 110 volts a.c. This is supplied directly from terminal 2 of the variac, thus insuring that when the variac has voltage applied to it, the other circuits also are provided with power. Therefore, the null indicator power switch sould always be left in the "ON" position to make starting procedure simpler. All that is re-quired to start the whole supply, then, is to turn on the water and press the "start" button. h) Other Dangers and their elimination: Other circumstances which may damage the apparatus are as follows: - 12 -The blower for the rectifiers not being on, a break in the power line to the magnet, a short circuit in either the A . C . or D . C . power lines, and finally voltage transients across the rectifiers . The blower is connected so as to come on when the magnetic breaker closes, and therefore except for burning out of the motor of the blower, the rectifiers will always be cooled. One should always listen the noise of the blower when turning on the circuit. A break in the power line to the magnet when current is flowing will cause a large reverse voltage to be generated across the magnet, which might damage the insulation of the magnet coils. The magnet is protected against such occurance by a rectifier connected in the non-conducting direction across the magnet coil. If the power line should break, the energy will be dissipated slowly since the rectifier will then be in the forward direction. Short circuits are handled by fuses in the magnetic breaker and in the secondary of the variac. The transistors, having resistors in the emitter leads, are not in danger of blowout. The rectifiers can stand large surge currents of up to nine hundred amperes for the short time taken for the fuse to blow. Voltage transients across the rectifiers are likely to be the most frequent and the most dangerous of the abnormal conditions mentioned above, and therefore will be discussed in more detail. In the spectrometer supply, a General Electric Thyrector diode was placed across the input to the bridge rectifier. This diode is similar to a Zener diode in that it conducts only above a certain voltage, in this case 70 volts. Therefore any transients coming down the lines will be dissipated by this device. 0> I O-2 2 0 v. A C -<}>Zo neut . »-Magne t Ic c i r c u i t b r e a k e r i n t e r l o c k s •and s t a r t and e top b u t t one R e f e r e n c e v o l t a g * 0-c i r c u i t 9--O 9-V a r i a c M o t o r Bough r e g u l a t o r c i r c u i t 9 ~° S t e p - d o w n °" t r a n s f o r m e r . r e c t i f i e r , ond f i l t e r T r a n s i s t o r a m p l i f i e r N u l l indicator M a g n e t M a n g a n i n s h u n t - © - T I I' -e-i ! T r a n s i s t o r power pane l A C -f e e d b a c k n e t w o r k 9 D C f e • a b a c k —o »-n e t x o r k FIGURE 1 BLOCK DIAGRAM OF THE POWER SUPPLY Magnetic c i r cu i t breaker Cab ine t I n t e r l o c k and b l o w e r FIGURE 2 THE UNREGULATED D.C. SUPPLY - 15 -The main cause of these transients would be the turning off or on of large equipment nearby, or the shutting off of the supply for some reason while current is flowing. In Figure 3 is shown the circuit which controls the magnet current. The desired current is set by adjusting the setting of a helipot, as discussed in the section on the Voltage reference circuit, and shown in Figure 4. The Helipot voltage is compared with the voltage developed across a .01 ohm manganin resistor in series with the magnet, and the difference voltage is amplified by a Brown Null Indicator, which feeds into the transistor amplifier 14 driving a bank of 2N278 power transistors in series with the magnet. The current these transistors will pass is determined by the current fed to their bases. The transistors are in the emitter follower configuration, a characteristic of which is that the emitter current is nearly independent of emitter-collector voltage, provided the collector is always negative with respect to the emitter. Therefore, provided that the collector voltage is high enough.to keep the collector voltage negative throughout the swing of the ripple, very little ripple current will pass through the transistors . The .2 ohm resistors in the emitter leads of the output transistors are to ensure that the transistors share the current equally. A calculation of the open loop gain of the system will now be made, from which one can estimate the theoretical stability of the magnet current. 14. The transistor amplifier, with a few modifications, is the same as that described in Garwin, op. cit. , pp. 105-107. U n r e g u l a t e d D C Coble t o n u l l i n d i c a t o r o u t p u t 3 0-l O I50v 3 9 0 K - V \ / V — i M a g n e t AMA/— j a n l n s h u n t M a n g •01 o h m s 12 2 N 2 7 8 ' 8 i n p a r a l l e l 4 \ 12 e m i t t e r res is to rs 9 0 - 2 a 2 5 W-I 5 0 © 10 K , 5 v 2 2 © n 3 — 2 f 3 3 Q f t 2 N 4 3 3 3 0 f t 5 v 2 N 4 3 1 2 2 0 f t 3 3 0 * 1-5 - i p -v S v. zener d f o d * _ I 5 0 © 2 N 4 3 In?" 12 v 4 P S T 115 vo l t A C • re kiy FIGURE 3 2 N 2 7 8 4 I O O >47| K ° To n u l l i n d i c a t o r n p u t R e f e r e n c e V o I t a g e C a b l e t o , r o u g h r e g u l a t o r 4 c h a s s i s -© 2 THE FINE REGULATOR CIRCUIT - 17 -Consider a current L applied to the input terminals of the null indicator. The sensitivity of the null indicator is .001 microamperes per millimetre scale deflection on the meter of the instrument, and the meter sensitivity is 100 microamperes per centimetre. Therefore the current gain of the null indicator is 100=104. .01 In series with the two thousand ohm meter of the null indicator is a 3,300 resistor. Thus the total impedance of the meter circuit is roughly five thousand ohms . The input impedance of the transistor amplifier shown in Figure 3 is also approximately five thousand ohms, so the same current will flow into this amplifier as into the meter. Since the output of the null indicator is a cathode follower, and thus appears as a constant voltage source, the full gain of the null indicator is transferred to the transistor amplifier. In calculating the gain of the transistor amplifier, only an approximate value can be arrived at because of the large variation in the current gain among individual specimens of the same transistor type. Approximating the gain of each transistor stage by twenty-five, a number which is the average short-circuit current gain for the two types of transistors used, we find, since there are four stages in this amplifier, including the power output transistors, that the gain of this amplifier is 4 x 10 .^ Thus, the total open loop gain of the system is ap-Q proximately 4 x 1 0 . Now to arrive at the theoretical stability, consider a variation di of - 18 -the magnet current. An error voltage of .01 di appears across the shunt. Because the total input impedance of the null indicator, the helipot in the voltage reference circuit, and the one hundred ohm resistor in series varies from eleven hundred ohms when the helipot is at one of its extreme positions, to sixteen hundred ohms when the helipot is poisitioned to give out half of the voltage from the Constant Voltage Supply. Thus the worst value for the theoretical stability occurs when fifty amperes are flowing, and is found as follows. The input current to the null indicator is thus •01 di = 6.25 10-6 di. 1600 9 This current is amplified by a factor of 4 X 10 , and so the corrective current applied is 2.5 X 104 dl, and we see that the stability is 2.5 X 104. Fast disturbances of equilibrium appear as large voltages across the magnet. These voltages are fed through a 10 microfarad, ten thousand ohm path to the base to the base of the first 2N43 transistor, and thus eliminated. Slower variations of frequencies in the range from about one cycle per second to ten cycles per second, which are too fast to be passed to the null indicator through the direct current loop because of the magnet time constant, and too slow to appear as large enough voltages across the magnet to be reduced to one part in ten thousand be the transistor amplifier, are fed through a four microfarad condenser to the null indicator input, where, even though the null indicator response is - 19 -falling off in this frequency range, the 10^ gain of the loop will eliminate var-iations in this range. The fast feedback loop and the large inductance of the mag-net, about one henry, ensure that transient currents will be negligible. An output of 70 microamperes from the Null indicator is required to bias the transistor amplifier into its operating range, and therefore the meter of the null indicator does not read close to zero as one might expect, but reads about ten small divisions from zero. The sensitivity of the null indicator should be set at its maximum, but the zero setting is immaterial since it is automatically established by the feedback loops. The zener diode across the base-collector diode of the last 2N43 transistor limits the collector to base voltage to six volts, and thus prevents the transistors from exceeding their power ratings In the event of lag or breakdown of the circuit regulating the variac motor. The null indicator has been modified by disconnecting the ground lead from the input condensers and by soldering output terminals across the meter. The batteries are switched on and off by a 110 volt a.c. relay, which also turns on a battery in the rough regulator chassis shown in figure 5. The null indicator for chassis must be insulated from ground or the circuit will not operate. LPJLQJ ' 3 3 k c h o k e i n p u t 3 -3 k Remove t h i s c o n n e c t i o n t o g r o u n d FIGURE 4 MODIFICATIONS TO THE NULL INDICATOR Meter ( / \ A d d output l e a d s h e r e - 20 -Voltage Reference Circuit This circuit, shown in Figure 5, supplies a variable calibrated voltage to one terminal of the null indicator, which tries to keep the voltage across the manganin shunt at the same value. The voltage may be varied either at the supply cabinet, or remotely from the main control panel for the Van de Graaf machine. A very stable voltage is obtained from a Honeywell Zener Diode Constant Voltage Unit. Depending upon the setting of the "direct-remote" switch, this voltage is applied across one of two helipots, each of which is in parallel with two resistors and a trimmer potentiometer. The voltage given out by the Constant Voltage Supply depends upon the amount of current it is supplying, and the magnet current is calibrated by varying the trimmer potentio-meter. To calibrate the magnet current, measure the voltage across the manganin shunt with the helipot dial set at 50.0. The voltage across the shunt should be .4635 ohms, because the resistance of the manganin shunt is .9270 ohms. The remote and direct circuits must be set to give out the same voltages for the same settings since the switch can be turned from direct to remote only when the two are reading the same . Otherwise the system will hunt and oscillate. Rough Regulator Circuit As was previously mentioned, the collector-emitter voltage must be kept negative at all times in order that the transistors be in their amplifying range. Also, this voltage must not exceed six volts, for then the zener diode conducts, and the ripple voltage from the unregulated direct current supply will be am-- 21 -plified by the transistors and thus appear across the magnet. Therefore the circuit shown in Figure 6 was designed; this circuit keeps the Variac output voltage at a level which gives a collector-emitter voltage across the output transistors of 3.7 volts. When the transistors have 3.7 volts across them, there is no point in the ripple cycle at which either the transistors saturate or the zener diode breaks down. The circuit operates as follows: A portion of the collector voltage is subtracted from the 1.5 volts of a dry cell and the difference is amplified to drive one of two relays, depending upon the polarity of the difference voltage. The NPN transistor (2N167) amplifies when the collector is not negative enough with respect to the emitter, and the PNP transistor (2N68) amplifies when the collector is too negative . The large inductance of the magnet leads to an oscillatory condition when the reference voltage of the helipot is changed quickly. For example , consider raising the helipot setting. The feedback circuit of Figure 3 tries to increase the current and increase the voltage across the manganin resistor till it reaches the new reference setting. The transistors become saturated when the base current increases, and therefore the relay closes and begins increasing the input to the rectifiers, and the unregulated D. C . voltage rises . The magnet opposes any change in current, so the voltage across it increases in step with the increasing D. C. voltage, and the transistor voltage remains low, thus keeping the variac voltage rising. When the manganin shunt voltage finally To n u l l Honeywe l l Zener V o l t a g e Reference 9 D i r e c t -remote s w i t c h i n d i c a t o r i n p u t - V * To m a n g a n i n shun t -4 -o 3 -c-Cable f r o m c a b i n e t t o m a i n c o n t r o l p a n e l R e m o t e c o n t r o l p a n e l FIGURE 5; THE VOLTAGE REFERENCE CIRCUIT N e u t r a l w i r e d t o t e r m i n a l 2 o f V a r i a c m o t o r C d b l s t o T r a n s i s t o r A m p l i f i e r 1 4 3 2 Q p Q J \ T o c o l l e c t o r s o f p o w e r p q n * l -° '330n I l . 5 u • 2 7 0 J 2 ' / 2 N P o t t e r a n d B r u m f i e l d B S 4 4 0 9 J 6 6 T o e m i t t e r s o f p o w e r p a n e l _ / 2 N 1 6 7 \ 3 3 0 H — 250 i 5 v . 250 pi 15 v. 2 N 6 8 1.5v. \ H a m m o n d 1 6 7 B 6 0 FIGURE 6 THE ROUGH REGULATOR CIRCUIT B S 4 4 0 9 J T o t e r m i n a l —c r of V a r i a c m o t o r To t e r m i n a l o f V a r i a c m o t o r To V a r i a c o t e r m i n a l 2 - 24 -reaches that of the reference, the base current to the transistors decreases, they come out of saturation, and a large voltage develops across them which causes the other relay to close, forcing the unregulated D . C . voltage to decrease. As before the magnet opposes the change and a large overshoot occurs again. This oscil-lation will continue, and to stop it, the reference must be turned to zero, and increased slowly to the desired value. This oscillation is not dangerous, and it was the only one encountered in the testing of the supply. The supply will not oscillate for any other reason, except if the direct remote switch is changed when the two helipots are at difference settings, a condition which also causes a quick change of reference voltage. The mains voltage for this circuit is supplied from the transistor amplifier chassis, as is the relay which disconnects the bias battery when the circuit is not in use . The PNP (2N68) transistor is cascaded with the NPN (2N167) transistor for two reasons: first, the 2N167 cannot handle the power needed to drive the relay, and second, if an NPN transistor were used to drive the relay, two opposite polarity power supplies would be required instead of just one. - 25 -CHAPTER 111 THE CONSTRUCTION OF THE VACUUM CHAMBER AND COUNTING APPARATUS Before discussing the technological details of the spectrometer assembly, a short description of the focusing principles of a magnetic sector will be given. For a mathematical treatment of this topic, various papers are available, most of them basing their discussion on the work by Cross 15,16,17 _ j n p ^ ^ g 71 there is a schematic of a sixty degree magnetic sector. The primary focusing depends on the fact that the particle with the trajectory S A D S' spends more time in the uniform magnetic field which is present throughout the area of the sector than does the particle travelling the path S B E S ' and thus is bent more, and thus the trajectories of the two particles intersect at some point S' on the exit side of the sector. Similarly, the particle with the path S C F S' is bent less than the other two particles, and the trajectories will intersect with one another at some point ; ' on the exit side of the sector. For small angles a, the tra-jectories of all particles whose direction when leaving the position S differ from the direction of the central ray S B E S' by less than a will intersect the tra-15. 16. 17. W. G. Cross, op. cit., pp. 717-722. W. E . Stephens, op. cit., pp. 513-518. M . Camac, Rev. Sci. Instr. 22, 197 (1951). - 26 -jectory of the central ray at positions very close to S* , and thus a focus appears . So far, the angles b and c can be chosen almost arbitrarily, the only restrictions being that b cannot be too large because then particles might strike the walls of the spectrometer. In the focusing arrangment above, particles divergingvertically will not be focused. Vertically is defined to mean in a direction perpendicular to the plane A C D F , which is defined to be the hori-zontal direction. However, the fringin fields at the entrance and exit edges of the field can be utilized to focus vertically diverging particles at the same focus S' if the angles b and c are chosen correctly. Cross shows that when b is positive; i.e. when the direction of rotation from the central ray to the perpend-icular to the edge of the field is counter clockwise, then the fringing field focuses the vertically diverging particles . Similarly, when c is positive, vertically diverging particles are also focused. For negative values of b or c , the fringing field defocuses the vertically diverging particles . Cross' treatment of the double focusing equations in his paper shows that a practical design to achieve double focusing should include the following consideration. First, for horizontal deflection angles of sixty degrees or less, b should be chosen to give more vertical deflection than necessary to achieve double focusing, and c chosen to defocus the particles enough to result in a vertical focus at S'. This limitation on b and c is necessary to have the focus within a reasonable distance from the exit edge of the field. Another limitation is that the object distance should be greater than or equal to the radius of curvature T a r g e t FIGURE 7 THE MAGNETIC SECTOR AND ITS FOCUSING PROPERTIES - 28 -of the trajectories which is given by r = my , where mv is the momentum of the qB particle, q is the charge of the particle, and B is the magnetic field of the sector. The reason for this is that otherwise i b becomes too large and the particles are in danger of striking the walls of the spectrometer. The parameters of our spectre-meter have been chosen with the above criteria in mind, and are listed in Appendix B. Another method of two directional focusing is to shape the edges of the field to give double focusing properties. This method involved more expense and design, but according to Cross will probably give just as good results as the fringing field method used here . In order that particles entering the spectrometer could be focused and counted, a target chamber at the object point and a vacuum box and counter housing at the image point of the spectrometer had to be designed. A schematic drawing of the system appears in Figure 8. The target box, designed to hold a 4 liquid air trap on which can be frozen a heavy ice target for the d(d, Y )He reaction, or to hold an alpha particle emitting source for calibration of the instrument, is composed of a bellows section on either side of a brass box. The box is provided with a whdow through which the position of the source or target may be viewed, and a thin copper tube through which the heavy water vapour may be squirted. The box is mounted on the central shaft of the spectrometer so that the target may be placed on the axis of rotation o f the spectrometer. The target box is placed at the height of the beam from the Van de Graaf; i .e . , - 29 -forty-four inches above floor level. The flexibility of the bellows sections allows rotation of the spectrometer of about thirty degrees to either side of the beam direction, which is more than ample for the d(d yY ) He^ experiment, where the alpha particles can be confined to a cone with half-angle less than twenty degrees. From the target chamber, the particles proceed into the spectrometer, and after having been bent by the magnetic field, they travel in a straight line toward the image point. A brass vacuum box as shown in Figure 8 provides the enclosure for most of the distance from the spectrometer exit flange to the image position. At the image point, we wished to count the incoming particles with an R . C . A. solid state counter . Since the image point had not yet been found experimentally, means of moving the counter from point to point around the expected image position were necessary. The movement is obtained from a bellows section which allows verticaly motion, and by a more complicated assembly shown in Figure 9 which permits the position of the counter to be varied horizontally. The vertical bellows section is adjusted by three set screws, whereas the horizontal motion in the counter housing is achieved by adjusting a micrometer which, through a bellows section used for a vacuum seal, drives the shaft upon which the counter is fastened. The leads from the counter are brought out of the vacuum system through kovar seals. The vacuum system was designed to give a high pumping speed near the FIGURE 8 THE SPECTROMETER AND ITS COUNTING ASSEMBLY - 31 -target box and the analyzing apparatus . The fore pumping is done with a Welch Duo-seal rotary pump, which will pump the system down to less than half a micron with liquid air in its trap. For the high vacuum pumping, an Ultek "Evapor Ion" pump is used. The principle used in this method of pumping is to ionize the gas molecules and then combine them chemically with the titanium coating which is placed on the walls-of the pump. A large magnetic field is used as well as an electric field in order to make the path length of the ions, and electrons very long, and thus enabling them to make many collisions with other gas molecules on their way to the electrodes . These collisions ionize many more molecules, and thus speed up the pumping process. Because of this magnetic field, the pump cannot be placed too near the beam pipe, and in our system, it is about two feet below the beam height. Three valves are provided in the system: one to shut off the ion pump because exposure to high pressure or the atmosphere is detrimental to its performance; one to shut off the fore pump and its liquid air trap from the vacuum system, as one would wish when the system is under high vacuum and being pumped by the ion pump; and a third valve which shuts the fore pump only off from the system, but leaves the liquid air trap in the system. Tiiis valve is included because there are times when there are too many vapours in the system to let the ion pump work without liquid air. On the side of the last valve is a small valve through which one can let air into the system. The solid state counter is a large silicon junction diode, which is - 32 -employed in the reverse bias condition. When a charged particle loses energy in the charge depletion region of this diode, it frees carriers, which are swept out of the region, thus passing a pulse of charge from the battery. The amount of charge released is proportional to the energy lost by the particle in the charge depletion region, and if the bias is supplied through a large resistor, as in our case where ten megohms are used, a voltage pulse may be observed. This pulse is fed to a preamplifier directly on top of the counter housing, and from there to a main amplifier and to the kicksorter or scalers . The preamplifier^ , which was used here first by Mr. E . G. Auld, is shown in Figure 10. The amplifier is the Dynatron 1430 A amplifier used to drive the kicksorter and the sealers on the'main control panel. Before any experiment could be performed with the spectrometer, it first had to be aligned with respect to the point at which the target would sit, and have its resolution measured with an alpha particle source. In order that the focusing properties of a magnetic sector be utilized, the source or target must sit on one focal point of the sector. For this spectro— meter , this point is found six and one half inches perpendicular from the geo-metrical centre of the front side of the entrance flange. To align the source to this position, a plate fitting the entrance flange was made, and a brass spike was soldered at its centre, projecting six and one half inches from the entrance glange when the plate was bolted to the flange. Another brass spike was fixed to point directly upwards along the axis of rotation of the spectrometer. The point To preomp. Kova r ii Kovar ii Stee l Sha f t C o u n t e r b o x m a d e o f b r a s s B e l l o w s . ITIAAA/' Sol id state c o u n t e r UKfWV. FIGURE 9 THE SOLID STATE COUNTER HOUSING - 34 -of this spike was adjusted to be exactly forty-four and one half inches fromt he floor. The adjusting screws underneath the front of the spectrometer mounting and the large levelling screws were set so that the points of the two brass spikes coincided. Whenever a source or new target was to be used, this procedure had to be repeated, except one substituted the source or target for the vertical brass spike along the axis of rotation of the spectrometer, and aligned the spectrometer so that the spike suspended from the entrance flange just touched the centre of the source or target. - 3b -CHAPTER IV THE RESPONSE OF THE SPECTROMETER TO ALPHA PARTICLES FROM VARIOUS SOURCES The first source used to try to measure the resolution of the spec-trometer was a plutonium 239 isotope supplied by The Radiochemical Centre, Amersham, England. Because it was the first attempt to find an image point, a large one-half inch diameter solid state counter was used, since to find a small image point with the five square millimetre counters might be very hard to do. Particles were found, and an approximate image point determined. The small counter mentioned above was placed in position, and measurements taken of the count rate as a function of current. Unfortunately, this source^ was spread out over a ten millimeter.diameter disk, and its strength was not enough to get a large enough count rate to allow measurements to be taken in a reasonable reasonable time. Also, the large size of the source did not test the resolving capabilities of the instrument, since its size corresponded to a current width of two per cent, as determined from the dispersion of the magnet, I = 844 dl mm Since the image distance, 30.9 inches, is approximately twice the object distance, 15 inches, in calculating the dispersion, one must multiply the source diameter by the optical gain of the system , namely two. So, I = 844 = 42.2 dl ~20~ - 36 -so: _dl_ = .024 I Thus it became apparent that a stronger, small source was needed. The most convenient method of procuring a suitable source was by depositing polonium 210 on a piece of silver. The polonium 210 is in a hydrochloric acid solution, and will deposit on the silver only when the silver is very smooth and clean. A small disk of silver was glued on a glass rod and polished. Then a drop of the polonium solution was placed on the silver, and then taken off again and the silver washed. This procedure was repeated a number of times until a source whose intensity was measured to be 10,000 disintegrations a second was made . The measurement of the intensity was made with the one-half inch counter by placing the source right next to the counter. This source was then placed in the target chamber and the current profile curve shown in Figure 11, was obtained. This curve shows a sharp resolution of a main peak, but it is difficult to account for the smaller peak on the high energy side of the curve. The only explanation I can give is that the silver was not perfectly smooth, and the source was not uniformly distributed over the silver disk, which was about three millimetres in diameter. A three millimetre difference in positions between two active areas of the source would account for a displacement of the two peaks of dl = _6 52.2 = 0.4 amp. since the peaks are 0.5 amperes 844 apart, it seems that this might be able to explain the second peak. To test whether this peak was a peculiarity of the source, another source was made, this time by dipping the silver into the polonium for about twenty - 37 -seconds. A source measuring about 15,000 counts per second was the result. The current profile of this source is shown also in Figure 11. This source was five millimetres in diameter, and the increased size is apparent in the increased width of the current profile. However, the absence of a subsidiary peak indicates that the smaller peak observed with the other polonium source was due to non-uniformity in the source, and not due to impurities in the polonium solution, since otherwise it would have showed up in the profile of the second source. The width of the peak for the second source was 0.9 amperes of 1.7 per cent. Considering the results of the current profiles of the first source, we see that the spectrometer was able to resolve a momentum group to within .3 amperes, or .57 per cent. To obtain results which would permit the resolving capabilities of the spectrometer to be tested, a beam of deuterons or protons should be scattered into the spectrometer. Because very high fluxes could be ob-tained, a very narrow slit of particles could be admitted and thus the broadening effect caused by a large source would not appear. As the beam deflection apparatus was not complete, scattered particle measurements of the resolution were not possible, so the next problem tackled was to determine the response of the spectrometer to particles emitted from a target such as would be used in the d(d, Y )He4 reaction. A brief introduction to the experimental details of the target assembly for the study of this reaction will now be given. A comprehensive treatment of the d(d,7)He reaction will be found elsewhere in the text. The smallest angle with respect to the beam direction to which the - W W I N P U T ® 0 1 / i f | ( — T - ® 0 U T P U T -o 3 0 0 v. o 3 0 0 v . Hammond > N I 0 8 4 I 6 7 L 6 0 FIGURE 10 THE PREAMPLIFIER - 39 -spectrometer can be aligned is ten degrees. Since the spectrometer accepts particles differing in direction from the central ray by up to five degrees, reaction products must be allowed to enter the spectrometer at angles from five degrees to fifteen degrees with respect to the beam direction. It is shown that by setting the incident deuteron energy appropriately, the alpha particles can be confined by kinematics to a cone with a half angle of twenty degrees. Thus, in polar direction with respect to the beam, the acceptance range of angles of the spectrometer covers most of the region in which alpha particles can be emitted. The target in this experiment will be a layer of heavy ice frozen on a copper surface. This surface will be inclined at five degrees to the beam direction, so that the beam will graze the heavy Ice target, and the alpha particles formed will be able to come off the surface and enter the spectrometer. It should be possible to converge the deuteron beam to a diamter of one millimetre with a quadrupole lens; this beam will spread into a strip twelve millimetres long when it hits the target. Thus it would be useful to know how the spectrometer would respond to such an emitting strip. A strip of silver was cut to the dimensions of the spot that the beam will make on the target and treated with polonium chloride solution to make a source which should approximate the target in the spatial spread of its emitted particles. The source was placed in the target chamber at five degrees to the beam direction, and a current profile taken. This profile Is shown In Figure 12. The half width of the peak was .9 amperes, giving a resolution of 1.7 per cent. - 40 -This means the image is dlspered over a length 1 = 844 . 017 = 14.3 mm. Thus, if we were to use a one-half inch diameter counter, nearly all of the alpha particles entering the spectrometer would be counted. In conclusion, this study has ended with the readying of the spectro-meter for the study of the EKD, Y)He4 reaction. The response to a target similar to that to be used in this experiment has been measured, and indicates that the • spectrometer will respond adequately to such a source of alpha particles. A discussion of this reaction will be found in Appendix D. M a g n e t C u r r e n t ( A m p e r e s ) FIGURE II CURRENT PROFILES FROM TWO POLONIUM 210 SOURCES (Amperes) 4 3 -APPENDIX A OPERATING INSTRUCTIONS FOR THE POWER SUPPLY Starting Procedure: 1. Turn on water and panel switch on the wall above the water tap. 2. Make sure that the supply cabinet door is closed. 3 . The null indicator power switch should be in the "ON" position, but if it is not, turn it to "ON". 4 . Make sure that the hellpot corresponding to "DIRECT" or "REMOTE", depending on which position the switch is in, is set at zero. 5. Press the "START" button. If the supply does not start, press the "STOP" button and hold it down long enough to allow the Variac to return to its zero position. Then press the "START" button again and the supply should start. 6. When the null Indicator has warmed up, set the current by turning the desired hellpot until It reads the selected current. The helipot must be turned slowly to prevent the variac from hunting. Shutting Down Procedure: 1. Turn the hellpot to zero, and wait ten seconds. 2. Press the "STOP" button. 3 . Shut off the water. - 44' -Precautions: 1. Make sure that the blower is running. It should come on automatically. 2. Do not change from "DIRECT" to "REMOTE" unless both helipots axe at the same position. 3. Do not shut the supply off until the hellpot has been set at zero. 4. In the case of power failure or other condition causing the magnetic breaker to open, the supply cannot be started until the Variac has been returned to Its zero position. To do this, press the "STOP" button and hold down for fifteen seconds. -4 5 -APPENDIX B SPECIFICATIONS OF CERTAIN COMPONENTS OF 1 . THE POWER SUPPLY Gneral Radio Variac Autotrans former. Model Number. W50H BB with 16 second traverse motor drive. See General Radio Catalogue "P" for maximum ratings, etc. Hammond Step Down Transformer. Special order from Hammond in December, 1959. Ratings; Maximum Current 100 amperes in secondary Maximum KVA 7.5 Primary Voltage Up to 220 volts, 60 c .p.s . Step down ratio 3.0 with puis or minus five per cent and ten per cent taps in the primary. Shielding: Two electrostatic shields brought out to separate taps. Hammond Heavy Current Choke: Special order from Hammond, May, 1960. Ratings: Inductance Five millihenries Maximum Current 100 amperes. Forty-two hundred Microfarad Filter Capacitors. Pyramid Electric Co., Type C Q M . , 100 V . D . C . " 4 5 -60° High Resolution Spectrometers Deflection or Sector 60° Radius of Curvature 15" Object Distance 15" Image Distance 30.92" Air Gap 0.75" Entrance Angle 56° 34' Exit Angle -32° 16' Solid Angle 5 .5° Maximum Induction 0.006 Steradlans Maximum Dispersion i_l_ p 844/mm S dp Stability: B/dB 1:104 Field Uniformity: Better than 1/1000 except at edge of gap. Momentum resolution: Magnet was designed for about 1/1500 but test results show about 1 /3000 Magnet Description: The magnet is a double focusing wedge shaped, uniform field magnet. It is provided with a base providing rotation about a vertical axis which runs through the target the target chamber. General Electric Rectifiers. Number 4JA6011AB1AB1. See General Electric Rectifier Handbook, High Current Silicon Rectifier section for ratings. - 47 -Minneapolis Honeywell Brown Null Indicator. See instruction book for circuit and specifications. Minneapolis Honeywell Constant Voltage Supply. See Honeywell information sheet number 5A for specifications. (S-900 series). - 48 -APPENDIX C SILICON CONTROLLED RECTIFIER TRANSIENT VOLTAGE SUPPRESSOR FOR THE SPECTROGRAPH SUPPLY a c . input f r o m 2 4 volt zener 2 2 0 f i - A A A — 0 4 - IN 1695 d i o d e s 8 2 0 n lO w. 2 2 0 f t 2 w. a . c . t o b r i d g e re c t i f i « r -0 This circuit, whose operation is described in the General Electric  Controlled Rectifier Manual, will limit the transient voltage on the input to the rectifiers to less than 150 volts. - 49 -APPENDIX D AN ESTIMATE OF THE MEASURABLE CROSSECTION FOR THE D (D, Y )He4 REACTION Introduction In the following pages, calculations are made which show that with the apparatus with which we are planning to observe the D(D, Y )He4 reaction, it should be possible to observe any total crossection which is greater than lCT^cm? for a counting rate of one count a minute. This estimate is made assuming the main contribution to the reaction is the S-wave component, and assuming that a fairly high beam intensity are used. The apparatus which will detect the reaction is arranged as follows: any alpha particles produced by the reaction are emitted in a forward cone into a double focusing magnetic spectrometer, where their momenta are analysed, and at the appropriate place above the spectrometer a solid state counter detects all particles with a given momentum, and gives out a pulse proportional to the energy of the particle . This reaction has heretofore been almost impossible to detect, because all previous attempts have involved a search for the gamma ray emitted, rather than for the alpha particle. The other reactions produced by the deuteron beam, D(D, n )He^ and D(D,p)H^ are much more prolific than JD(D, 7)He4; neutrons are emitted and make it almost impossible to detect the gamma rays, whose flux is about a million times less than that of the neutrons. With our apparatus, - 50 -there should be no background from these other reactions because the momenta 3 o of the H and He0 particles are quite different than that of the alpha particles, and thus all except the alpha particles will be bent away from the solid state counter. This counter is insensitive to neutrons and gamma rays which could be present around the apparatus, and therefore should produce no extraneous counts. The deuteron target will be of heavy ice, deposited on a polished copper block from a vapour squirt. The block is inclined at a grazing angle to the beam of five degrees . Theory When a beam of deuterons interacts with a target of deuterons, three reactions occur. These are D(D, n)He3, D(D,p)H3 and D(D, y )He4. Consider the selection rules operating in these three reactions. In the first two, the S-wave deuterons can react with the target. However, in the third reaction, which we are studying, since each deuteron has spin 1, when they combine to form the alpha particle, either 0, 1, or 2 units of angular momentum must be carried off by the gamma ray. By conservation of charge, the reaction cannot proceed if 0 angular momentum is to be carried away. If the gamma ray is to carry away 1 unit of angular momentum, it must be magnetic dipole, which is very weak . If 2 units are to be carried off, parity considerations require the radiation to be electric quadrupole, which is of stronger intensity than the magnetic dipole, so this is the way that S-wave reaction would occur. - 51 -The P-wave contribution to the crossection will be very small, since 18 for electric dipole radiation to occur, we must have an isotopic spin change of 1 So the P-wave reaction must involve magnetic quadrupole or electric octopole radiation, which is highly forbidden. The D-wave could proceed by electric quadrupole. Higher waves would have to emit higher order multipole radiation, so they would not contribute . Therefore, we can assume our reaction is due to S and D waves alote , and we will consider the S wave contribution primarily. The fact that electric dipole radiation is not allowed makes the D(D, Y )He4 much less prolific than the other two, and explains why it has been hard to detect. Energetics The reaction D(D, y )He4 has a large positive Q value and thus can occur at low energies. The mass difference is A M = 2 M D - M Q = 2(2.01473) -4.00389 = .02557 a.m .u. This is equivalent to Q = (9.31)X102 x (.02557) = 23.9 Mev. With a bombarding energy E j ^ , since the masses of target and bombarding particles are equal, the energy available in the centre of mass system is 1/2 E^]-, . So in 18; This is explained in the paper by Telegdi and Gell Mann, Phys. Rev. 91., 169( - 52 -the centre of mass system, the energy of the alpha particles is E - _Q'2 where Q* = Q + 112 E l a b 2Mc 2 = 80Kv approximately. In considering the problem in the laboratory system, it is desirable to use as high a bombarding energy as possible to narrow the cone of particles produced in the reaction. Therefore in the following calculations which deal with the variation of the energy of the alpha particles with scattering angle, I have assumed a bombarding energy of 3 Mev. Maximum laboratory scattering angle: / ray D e u t e r o n Beam a par t icHe From conservation of momentum, we may write: M D V D = M a v a c o s A + n " c o s c O = M g V ^ i n A - hi/ sin C (2) c When sin C = 1, sin A assumes its maximum value, and alpha particles cannot be emitted at an angle greater than A. The energy h v of the gamma ray is approximately 23.9 Mev., since very little of the energy available for the reaction - 53 -is given to the alpha particle. Since the velocities of the alpha particles are much less than that of light, we can say that Mv = sjl ME (3) so, working in the M . K . S . system of units, we substitute (3) into (1) and (2), and putting sin C = 1, we get 23 .9 x 106 x 1.6 x 10"1 9 = / 2 x 4 1.67 X 10"2 7 X E A m a x sin A m a x 3 x 108 (4) Since at A ^ ^ , cos C = O, then (1) becomes ^ 2 x 2 x 1.67 x 10' 2 / x 3 x 10° x 1.6 x lO""1^" =/2 x 4 x 1.67 x 10 - 2 7 E Amax cos A (5) max Dividing (5) by (4) we have -20 cot A m a x = 5.65 10 1.30 10-20 and Amax = 13 degrees, Variation of alpha particle energy with scattering angle: A t Amax' consider (5). Cos A m a x is .974. then 5.65X10 - 2 0 = V 8 x 1.67x10"^' E~7 .974 Amax a n d EAmax = 1-572 Mev. When A=.0, E can have two values, depending upon whether cos C is 1 or -1 Let these values be £ Q and E respectively. - 54 -£ 0 = (5.65 - 1.30) ^ 1 0 ~ 4 ° = .887 Mev. — 8 X 1.67 X 10-27 x 1.6 X 10" 1 9 and E 0 = (6.95)2 X 1 0 " 4 ° = 2.26 Mev. 8 X 1.67 X 10" 2 7 X 1.6 X 10" 1 9 In the experiment, we will have the spectrometer centred 10° from the axis of the beam; i.e. , A = 10° . The half acceptance angle in the polar direction of the spectrograph is 5 ° , so we must find the energy of the alpha particles emitted at 5° to determine the energy spread of the particles entering the counter. For A = 5 ° , we must determine the angle C of the gamma rays in order to calculate the energies of the two groups of alpha particles emitted. From (1) and (2) we get 1.30X10" 2 0 sin C = ^8 X 1.67 X 10" 2 7 £ o sin 5° 5 5.65X10" 2 0 = / 8 X 1.67 X 10" 2 7 X E 5 o X cos 5° + 1 .3 10"20cos C, So we have 5.65Y10'2 0 = 1.3 X 10" 2 0 cot 5° sin C + 1.3 10" 2 0 Cos C Let sin C = x cos C = 1 - x 2 then we have 4 .34 - 11.47 x = 1 - x 2 (6) solving for x, we get the value that satifies the equation (6): x = .296 Thus C = 1 7 . 3 ° This the one of the two values of C gained from squaring (6) which satisfies (6). So, as before, let £ 5° and E-o have their previous meaning. —D - 55 -And 2 E 5 o = (5.65+ :i .24) X 10" 4 0 8 X 1.67X1G" 2 7 X 1.6 X 1CT 1 9 = 2.20 Mev. E 5 o = (5.65 - 1.24) 2X 10" 4 0 8X1.67*10-27x1.6x10-19 = .911 Mev. The window thickness of the solid state counters is about 700 Kev, so the lower energy group is probably too low in energy to resolve accurately. So let us consider the higher group. Those particles entering the spectrometer with angles from 5° to the maximum angle of 13° will have an energy spread of 628 Kev. It is now necessary to calculate the dispersion in the magnet caused by this energy spread. We have the relation p 2 = 2ME from mechanics. Therefore p dp = M dE and dp_ = M dE p 2 ME = 1/2 dE E So _d£_ = 1/2 X 628 103 p 2.23 106 = 1.35 10"1 From the specifications of the magnet, we are given that the dispersion of the spectrometer is p_ = 844 /mm . dp So the dispersion for the higher energy group of alpha particles is - 56 -1.35 X 10 X 844 = 12.2 cm. For a finch diameter solid state counter, we can have a momentum spread of only 1.27 cm., so an energy spread of 60 kev is all that the spectrometer could be focused on at one time. Thus there is a loss in transmission of a factor of ten. q Calculations similar to the above show that scattered deuterons, He and H particles will have very different momenta than the alpha particles for angles in the vicinity of 5° from the beam direction, so the spectrometer current should be set to focus alpha particles entering at these angles, and thus having energies from 2.20 Mev to 2.14 Mev. Since the solid state counter gives out pulses proportional to the energy of the impinging particle, any of the uninteresting particles mentioned above which could have momenta to be focused would have very different energies than the alpha particles with the same momenta. Thus the background count should be negligible, since only alpha particles can have the right energy and momenta to be identified as coming from the D(D, 7)He4 reaction. Estimate of Lowest Measurable Crossection We are now ready to proceed with calculating the number of counts cor-responding to a given total crossection. We must calculate the beam intensity, the target thickness, and the efficiency of our measuring system. Since we are assuming symmetry in the centre of mass system, the differential crossection in the laboratory system will have its largest values near the axis of the beam, since rj o(smQll A) = const sin A' and since when A' = O, A = O, "(ToT s i n A - 57 -the crossection has a large value for small A. For our experiment, as was mentioned earlier, the transmission was reduced by a factor of ten by the fact that the solid state counter was only \ inch in diameter. To get the efficiency of the system, we first calculate the total solid angle subtended by the cone of alpha particles. The total solid angle subtended by the cone of alpha particles is •M3 ° sin A dA = 2IT {I - .974) = . 18 steradians . J P Since the transmission solid angle of the spectrometer is .006 steradians and this is reduced by a factor of ten, the efficiency of the system is .0006 = .33 per cent. .18 Target Thickness We will try the experiment first with a thick 50 Kev target. From Whaling's article in Handbuch der Physik. XXXIV. p. 193, we find the stopping crossection of heavy ice for deuterons is 25y\0~^-^ e.v-cm^ we assume this is a constant over the range of energy lost in the target. The stopping crossection is defined as S = 1 dE N dx where N is the number of molecules of a substance per cubic centimeter. Let us assume the density of heavy ice is about 1 gm/cc. Then, since one molecule of heavy water weighs 20 >1.67*10"24 gm., then the number of molecules per cc is N = 1 20 X 1.67 X 10"2 4 - 58 -So the thickness of a target which absorbs oO Kev is x = dE = 20 X 1.67 X 10"9 X 10 3 cm. N S 25 2 So the number of molecules per cm in the target is Nx Nx = 2 X 101 8 18 Since in each molecule, there are two deuterons, there are 4*10 deuterons per square centimetre. Beam Intensity: We will use a 10 microampere beam, and converge it to a diameter of 1 millimetre. So the flux is F = 10X10"6 1.6X10" iy i HT 2" 4 15 2 = 8x10 particles/sec/cm Total Crossection: The total crossection for a reaction is defined to be the number of reaction particles produced for one target nucleus and for unit beam intensity. This is = __N F X (No. of target nuclei) -2 i o The number of target nuclei are IT X 10 X 4 X 10 ° , F is the beam flux, 4 and N is the number of alpha particles produced per second. N = counts /sec efficiency So the total crossection for one count per minute is - 59 -atof = 1000 60 X 3.3 8 X 10 1 5 X 4 X 101 8 X 7T 10"2 = 2.01 X 10"3 2 cm 2 . - 60 -BIBLIOGRAPHY Blatt, J. M . , and Weisskopf, V. F . , Theoretical Nuclear Physics, New York, Wileya..d Sons, 1958. Bromley, D. A . , and Bruner, J. A . , "The Design of a Focusing and Analyzing System for the Twenty-seven Inch Cyclotron Beam". Physics Department, University of Rochester, Rochester, New York, 1954. (Unpublished). Camac, M . , Rev. Sci. Instr. 22, 197 (1951). Cross, William G . , Rev. Sci. Instr. 22, 717, (1951). Enge, Harald A . , "Combined Magnetic Spectrograph and Spectrometer", Massachusetts Institute of Technology, Cambridge, Mass. (Sub-mitted for publication in Rev. Sci. Instr) Garwin, Richard L . , Rev. Sci. Instr. 29, 223, (1958). • Garwin, Richard L . , et_. aJL , Rev. Sci. Instr. 30, 105, (1959). General Electric Controlled Rectifier Manual, First Edition, General Electric Company, Liverpool, New York, 1960. Johnson, S. D . , and Singer, J. R. , Rev. Sci. Instr. 29, 1026 (1958). Meier, Otto Jr., et. a l . , Rev. Sci. Instr. 29, 1004 (1958). Stephens, W. E . , Phys. Rev. 45, 513, (1934). Stoltzfus, Joseph C . , "The Development and Testing of a Magnetic Spectrometer", Doctoral Dissertation, State University of Iowa, Iowa City. Telegdi, V. L . , and Gell-Mann, JVL, Phys. Rev. 91, 169 (1953). Whaling, W., Handbuch der Physik XXXIV, p. 193. 

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