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Studies of supersonic beam formation at low temperatures for a polarized helium 3 ion source Vyse, Robert Norman 1967

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STUDIES OF SUPERSONIC BEAM FORMATION AT LOW TEMPERATURES FOR A POLARIZED HELIUM 3 ION SOURCE by ROBERT NORMAN VYSE B . A . S c . , U n i v e r s i t y of B r i t i s h Columbia, 1965 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department of Physics We accept t h i s t h e s i s as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1967 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y avaiJable f o r reference and s tudy, I f u r t h e r agree that p e r m i s s i o n - f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s , I t i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l ga in s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department of The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada Date .2 i . ABSTRACT The formation of a molecular beam using a miniature supersonic nozzle source i s discussed. The r e s u l t s of operation at room, l i q u i d nitrogen and l i q u i d helium temperatures of a supersonic nozzle system designed for use in a polarized helium? ion source are presented. It i s shown that heliunA beam intensities at 4.2% are approximately 1/8 of those at 300%. Factors upon which the beam intensity depend have been investigated experimentally and i t i s found that at room temperature and a distance of l6cm from the skimmer a heliunA beam intensity of 3x10-^ molecules/cm^/sec i s attainable under certain circumstances. This beam intensity i s an improvement by a factor of 10 over the original performance of the nozzle source. Assuming a 1+0% transmission through the magnet and a 0.25$ ionization efficiency an ion current of 0.02 microamperes i s estimated for the polarized helium^ ion source. i i . TABLE OF CONTENTS Page CHAPTER I - INTRODUCTION 1 CHAPTER II - SUPERSONIC MOLECULAR BEAM FORMATION 2 A. Fundamental Concepts 2 B. Summary of Kantrowitz and Grey's Original Theory . . 5 C. Review of Existing Experimental Results 9 D. The Nature of the Expanding Beam 10 E. Interaction with the Skimmer 13 CHAPTER III - THE POLARIZED BEAM APPARATUS 15 A. General Introduction 15 B. The Loxtf Temperature Beam Source 15 C. Testing of the Nozzle-Skimmer-Collimator System. . . 17 D. Analysis of the Experimental Results 19 CHAPTER 17 - INVESTIGATIONS INTO FACTORS AFFECTING BEAM INTENSITY 21 A. Nozzle-Skimmer Separation 21 B. Mechanical Alignment 23 C. Effect of Skimmer Diameter and Manufacture 25 1. Skimmer Diameter - 25 2. Skimmer Manufacture 25 D. Presence of Collimator 26 E. Background Gas Pressure 27 F. Nozzles 30 G. Summary 31 i i i . Page CHAPTER V - BEAM INTENSITIES AVAILABLE FROM THE POLARIZED He 3 BEAM SOURCE . 33 CHAPTER VI - POSSIBLE ION CURRENTS FROM THE POLARIZED He 3 ION SOURCE 35 BIBLIOGRAPHY . 36 i v . LIST OF TABLES Page 1. Dimensions of Supersonic Beam System 16 2. Selected Physical Parameters 19 3. Selected Experimental and Corresponding Theoretical Beam I n t e n s i t i e s follows p.19 4. Terminal Mach Numbers 28 V. LIST OF FIGURES To follow page 1. The Regimes of Gas Dynamics . . . . . . . . .\ . . . . 4 2. Schematic of Proposed Molecular Beam Source i n text p. 5 3. An Idealized Laval Nozzle i n text p. 6 4. The Temperature Ratio T ^ / T q as a Function of the Mach Number M. . 7 5. The Pressure Ratio P^/PQ a s a Function of the Mach Number M , 7 6. The V e l o c i t y of Mass Motion W and the Most Probable P a r t i c l e V e l o c i t y U as a Function of the Mach number f o r a Laval Nozzle Temperature of 2.2° K 7 7. Relative Transmission of He 3 P a r t i c l e s Through the Skimmer and Collimator as a Function of Mach number . 8 3 8. Relative Transmission of He p a r t i c l e s Through the Nozzle, Skimmer and Collimator as a Function of the Mach Number 8 9. T y p i c a l Supersonic Molecular Beam Performance f or Nitrogen . 9 10. Schematic Representation of Flow from an O r i f i c e i n t o an Evacuated Region . i n text p. 10 11. D i s t r i b u t i o n of Mach Number along the Axis of Symmetry ' of the Expanding Jet 11 12. Impact Pressure Downstream of the O r i f i c e 12 13. C o r r e l a t i o n of Asymptotic A x i a l Mach Numbers f o r Argon, Neon and Helium Jets . . . . . . . . 12 v i . To follow page 14. Ratio of Observed to Theoretical Intensity as a Function of Knudsen Number / Mach Number based on Free Stream Conditions 13 15. Shock at the Skimmer 13 16. Schematic Diagram Showing the Arrangement of the Compo-3 nents of the Polarized He Ion Source 15 3 17. The Low Temperature He^ Atomic Beam Source 15 18. Detail of Nozzle Assembly 15 19. The Magnet Assembly 17 20. Block Diagram of Beam Detection System . in text p. 18 21. Typical Chart Recording i n text p. 18 22. The Dependence of Beam Intensity on Temperature . . . . 18 23. The Ratio of Experimental to Theoretical Beam Intensi-ties as a Function of Knudsen Number to Mach Number . . 19 24. Adjustable Nozzle-Skimmer Apparatus 21 25. Turning Mechanism for Adjustable Nozzle-Skimmer Apparatus 21 26. Typical Results obtained from Adjustable Nozzle-Skimmer 27. Typical Results Obtained for Fixed Nozzle-Skimmer 28. Beam Intensity Results at 77° K 23 29. Beam Intensity Results at 300° K. . . . . . . . . . . . 23 30. Beam Intensity Results at 300° K. . 23 31. Correspondence between Nozzle and Nozzle-Skimmer Pressures at 300° K 23 To follow page 32. Correspondence between Nozzle and Nozzle-Skimmer Pressure 33. Alignment Assembly . . . . . . 24 34. Typical Results showing Effect of Poor Alignment.. , 24 35. Skimmer Manufacture. . . . . . . . . ..... . ; .26 36. Pumping System for Nozzle-Skimmer Region. . . . . . . . 26 . 37. • Beam Intensity Dependence on Background Gas Pressure 29 38. Beam Intensity Dependence on Background Gas Pressure 29 39. Beam Intensity Dependence on Background ;Gas Pressure 29 40. Beam Intensity Dependence on Background Gas Pressure 29 41. Beam Intensity Dependence on Backgroung Gas Pressure 29 42. Performance of 0.005" Tubing Nozzle 30 43. Performance of 0.0095" Tubing'Nozzle . . . . . . . . 30 44. Performance of 0.020" Nozzle . . . . . . 30 45. Room Temperature Intensities for 0.0095" Tubing -. . 31 46. Room Temperature Intensities for 0.0095" Tubing . . 31 47. Liquid Nitrogen Temperature Intensities for Oo0095'^ Tubing « « « » « » <> » • • • o • ©• o • ».» • • 31 48. Bundle of Capillaries used as a Nozzle . . ....... 31 49. Geometrical Arrangement of Multiple Capillary Device 31 50. Performance of Multiple Capillary Device . . . . . . 31 51. Comparison of Beam Intensities . ... . . . . . . . . 33 v i i i . ACKNOWLEDGEMENTS I would l i k e to thank my supervisor, Dr. M.K. Craddock, for his interest and help i n the work described in this thesis. I would also like to express my thanks to Dr. D Axen who built most of the existing polarized helium 3 beam apparatus and who was mainly responsible for the preliminary beam intensity measurements presented i n this thesis. I am grateful to Mr. G. Bloom and Mr. R. Turner for their technical assistance. I wish to thank the National Research Council for two scholarships held during the course of this work. 1. CHAPTER I Introduction Miniature supersonic nozzle systems have been shown to produce high intensity molecular beams. These beams besides being studied because of their own interesting properties have been used by various experimenters to investigate surface scattering, thermal relaxation, separation of gas mixtures, condensation phenomena, molecule - molecule collisions and many other physical phenomena. We need these intense beams for the successful operation of our polarized helium^ ion source. I n i t i a l sections of this thesis w i l l introduce some of the concepts used in discussing the gas dynamics of nozzle systems and then w i l l b r i e f l y review the original theoretical treatment of miniature supersonic nozzle systems. A summary of experimental results obtained by various investiga-tors w i l l be presented along with a picture of the expansion process as i t i s now understood. The nature of the skimmer interaction which limits the beam intensity w i l l be reviewed. With the above as background, we w i l l b r i e f l y discuss the polarized He3 b earn apparatus whose i n i t i a l design and construction has been reported by Axen (Ax 65) and then report on the performance of the supersonic nozzle system (shown schematically i n figure 2) which forms an important part of this apparatus. Later sections w i l l consider the experimental investigations into the nature of the beam expansion as required i n light of these preliminary results. The last section w i l l estimate the beam intensity one might hope to obtain from our polarized beam apparatus based on experimental results discussed in other parts of this thesis. 2. CHAPTER II Supersonic Molecular Beam Formation A. Fundamental Concepts In order to provide a basis for the discussion of nozzle systems i t w i l l be useful to define a number of common terms. These terms include r the characteristic length, boundary layer, free steam, Reynolds number, Knudsen number, Mach number, subsonic flow, transonic flow, supersonic flow, hypersonic flow, free molecular flow, transition flow, s l i p flow and continuum flow. Many dimensionless parameters make use of a characteristic length. This length may be simply related to the physical size of the object through which or around which gas flow occurs. For example, the dimension could be the diameter of a sphere or a piece of pipe. Under certain circumstances^ • however^the significant characteristic dimension i s often the boundary layer thickness. Often in flow over an object a velocity gradient perpendicular to the surface of the object i s set up. The velocity starts at zero at the sur-face and rapidly approaches a constant value. The region where the large velocity gradient exists i s known as the boundary layer while the region where the velocity gradient i s zero i s known as the free stream. In gas or f l u i d dynamics i t has been found that certain parameters are useful in describing the characteristics of flow experienced under varying conditions of pressure, temperature, velocity etc. The three common dimen-sionless numbers, namely: The Reynolds number-'- (Re), the Knudsen number (Kn), and the Mach number (M), are defined as follows: ^-Historical note: Reynolds while investigating f l u i d flow through similar pipes found that a c r i t i c a l value of this parameter predicted the onset of turbulent flow for varying flows, fluids and diameters of pipes. Reynolds number = Re — — • (1) V Mach number — M _ (2) ~ ~ O. Knudsen number _ Kn — -A- (3) Where V _ Particle velocity — Gas density \j- _ Viscosity CL _, Velocity of sound d _ Characteristic length X = Molecular mean free path In a great deal of work connected with gas flow through supersonic nozzles the ratio Kn/M is used as a parameter. This number can be related to the Reynolds number using a relation derived from kinetic theory (see for example Kennard (Ke 38)) H T (4) TT ^ Where ^ — Ratio of specific heats. Substituting (4) into (l) and using (2) and (3) one obtains: i^ Q ^ J — (5) M £t \ a Under most circumstances V is a constant so essentially Kn/M is simply an inverse Reynolds number. Two common schemes for the classification of flow problems are presented below: The f i r s t , based solely on the Mach number, i s as follows; The flow is described as subsonic i f the f l u i d or gas velocity i s less than the speed of sound in the medium (M< I ), transonic when the f l u i d or gas velocity i s com-parable with the sound speed (M~ I ), supersonic when the f l u i d or gas velo-city exceeds the sound speed (M7l ), and hypersonic when the f l u i d or gas 4. velocity i s much larger than the sound speed (M > I ). The other scheme uses both the Mach and Reynolds numbers to define four flow regimes. Within each of these regimes the characteristics of the flow can be described by one predominate mechanism. The flow regime appropriate to a particular situation can be conveniently identified by the values of the Mach and Reynolds number. These two numbers are used in figure 1 to characterize the flow regimes which one usually refers to as free molecular, transition, s l i p and continuum flow. To give a simple physical picture of the meaning of the various flow regimes consider the mean free path i n the gas. For free molecular flow the mean free path is much greater than the characteristic body length and thus molecules reemitted from a body surface do not collide with free stream molecules u n t i l far away from the body. For the transition regime the mean free path is about equal to the typical body dimension. Here surface collisions and free stream intermolecular collisions occur with equal frequency. For s l i p flow the mean free path is typically 1 to 10% of the boundary layer thickness or other characteristic dimension of the object. For continuum flow the characteristic length greatly exceeds the mean free path and thus free stream intermolecular collisions predominate over surface collisions. For continuum flow, the gas immediately next to a body i s essentially at rest, whereas in s l i p flow the layer of gas immediately adjacent to the solid is no longer at rest but has a f i n i t e tangential velocity. Rarefied gas dynamics refers collectively to the free molecular, transition and s l i p flow regimes. I O 3 IO £ io 1 10° io 1 io2- 1 0 3 IO4- IO5" IO6 IO7 R E Y N O L D S N U M B E R Figure 1. The Regimes of Gas Dynamics 5. B. Summary of Kantrowitz and Grey's original theory When Kantrowitz and Grey (Ka 51) proposed the use of a miniature supersonic Laval nozzle for a molecular beam source, they visualized a system consisting of a nozzle, skimmer, and collimator as shewn schematically in figure 2. Their theoretical treatment of this system was modified slightly Figure 2. Schematic of Proposed Molecular Beam Source. by Parker et a l (Pa 60) and a summary of the combined treatment i s presented below. Three c r i t i c a l assumptions are made: 1. The flow along the axis of the supersonic jet up to the skimmer entrance i s isentropic and may be treated by the methods of continuum gas dynamics. 2. The skimmer samples an undisturbed portion of the isen-tropic core. 3. Collisions between molecules downstream of the skimmer may be neglected. 6. With these conditions i n mind we can proceed i n the derivation of what is often referred to as the "theoretical beam intensity." An idealized version of a converging-diverging nozzle i s shown in figure 3. The mass flow through such a supersonic nozzle operating under RESERVOIR P I M P Figure 3. An Idealized Laval Nozzle. isentropic flow conditions i s given by Shapiro (Sh 53) as A" (6) where: G — Flow in mass/unit time A* zz Cross sectional area of nozzle throat = Molar mass R = Molar gas constant Po Pressure at nozzle entrance To Temperature at nozzle entrance and the velocity distribution in the Z direction, along the beam, is given by 1 2TT KT, where: U — Particle velocity in 2 direction -77t _ Particle mass 7. k = Boltzman's constant T| _ Internal temperature of gas W _ Average forward velocity of the particles (velocity of mass motion in the Z direction) f(u) represents the number of particles with velocities between U and U+du normalized so that f (u)du = 1 - o O The usual Maxwellian velocity distribution i s a special case of the above distribution when W = 0 . Other physical properties of the flow through an idealized Laval Ti_ P nozzle can be described by the ratio -r- , the ratio " ~ , the velocity 1 ° Po of mass motion (w), and the most probable particle velocity (U) as a function of the Mach number. These have been presented graphically for ^ — 1.66 i n figures l+} 5} and 6. T-^  and P-^  are the internal temperature and pressure of the beam, i.e. the temperature and pressure of the gas molecules with respect to a coordinate system moving with the beam. The Mach number, M, i s defined as M = — where W is the velocity of mass motion a of the beam and a is the velocity of sound at pressure P-^  and T-^  When one takes the skimmer and collimator into account the flow through the collimator i n atoms per second is given by ^ where: N-^  = Density of particles per unit volume at the skimmer entrance S-^  _ Area of skimmer aperture 1 -0 1.0 0.1 O..OI ,o0.| 0? \ Q T \ 0.001 O.01 I l l ' 1 1 < l 1 0.0001 i i i i i i i i ( • 0 2 + K A 6 8 IO M o 2 4 6 6 \0 l*\ Figure 4. The Temperature Ratio T 1/T Q as a Function of the Mach Number M Figure 5. The Pressure Ratio P-j/^o a s a Function of the Mach Number M Figure 6 . The Velocity of Mass Motion_W and the Most Probable Particle Velocity U as a Function of the Mach Number for a Laval Nozzle Temperature of 2.2°K (tor We1 <$a<0 8. S2 = Area of c o l l i m a t o r aperture D = Distance from skimmer to c o l l i m a t o r 0\o = V e l o c i t y of sound at nozzle entrance M _ Mach number of beam — W/Q. e r f = E r r o r f u n c t i o n For M?3 t h i s expression i s g i v e n approximately by F = N' S | S* a° M ( 3/? + ( 9 ) I t might be pointed out that the Mach number used i s that which charac ter izes the beam flow at the skimmer entrance.' For a f i x e d d e n s i t y and geometrical constants f i x e d i n equation 9 one can wri te a t ransmiss ion f u n c t i o n F , j f r r r P * 7 = ^ f l ^ d t e r f ^ T ) + - j ^ ( 2 t i M » ) ( i o ) CN,S,S2a.} J | + - ibi ' This f u n c t i o n i s p l o t t e d i n f i g u r e 7 and increases roughly as M^. The d e n s i t y N-^, however, i s a l s o a f u n c t i o n of the Mach number No ^ ^ T ^ p (11) where N 0 — d e n s i t y of p a r t i c l e s behind the nozzle . S u b s t i t u t i n g t h i s expression i n equation 10 the t ransmiss ion f u n c t i o n f o r the f low through the nozzle^ skimmer and c o l l i m a t o r becomes m ^ ) ^ « m + ( w £ ] e^l(12) This t ransmiss ion f u n c t i o n p l o t t e d i n f i g u r e 8 shows a broad maximum about M _ 2 . 5 . Thus f o r a given f l o w through the n o z z l e i t appears as i f the best t r a n s m i s s i o n would be obtained with low Mach numbers. It i s unfor tunate ly only i n s p e c i a l cases that i t i s p o s s i b l e t o f u l f i l the requirements mentioned at the beginning of t h i s s e c t i o n ; thus under most 1 2 4- 6 8 io I 2. 4 - 6 8 io M Figure 7 . Relative Transmission of He Particles Through the Skimmer and Collimator as a Function of the Mach Number Figure 8 . Relative Transmission of He Particles Through the Nozzle, Skimmer and Collimator as a Function of the Mach Number 9. circumstances one would not expect the Kantrowitz-Grey p r e d i c t i o n s to be f u l f i l l e d but they serve as a u s e f u l g u i d e l i n e i n assessing the performance of a nozzle beam system. In subsequent sect ions we s h a l l d iscuss why the assumptions made at the beginning of t h i s s e c t i o n are not i n general t rue and how these changes a f f e c t the molecular beam formation. C. Review of e x i s t i n g experimental r e s u l t s Perhaps the most i n s t r u c t i v e way to i l l u s t r a t e how p r a c t i c a l supersonic nozzle beams v a r y ' f r o m the i d e a l Kantrowitz-Grey p i c t u r e i s t o i l l u s t r a t e some sample experimental r e s u l t s . The most r e v e a l i n g of a l l experimental data presentat ions i s the dependence of beam i n t e n s i t y on the n o z z l e -skimmer d i s t a n c e . This dependence along w i t h the dependence expected from Kantrowitz and G r e y ' s theory i s shown i n f i g u r e 9 ( a f t e r Fenn and Deckers (Fe 63)). I t i s c l e a r the a c t u a l experimental r e s u l t s do not f o l l o w the p r e d i c t i o n s of Kantrowitz and Grey. The experimental curves can i n general be d i v i d e d i n t o 3 r e g i o n s : 1. For short nozzle-skimmer dis tance the beam f l u x decreases with i n c r e a s i n g nozzle-skimmer separat ion u n t i l a minimum occurs. 2. At l a r g e r nozzle-skimmer separations the beam f l u x increases u n t i l a maximum i s reached. 3. Further increases r e s u l t i n a decrease i n beam f l u x . One might point out that the three regions descr ibed above correspond roughly t o f low regimes at the skimmer which a r e : 1. Continuum 2. S l i p - t r a n s i t i o n 3. Free-molecular Needless to say the appearance of these 3 regions and the f a c t that the beam i n t e n s i t i e s i n many cases were s u b s t a n t i a l l y lower than p r e d i c t e d 0 Ul M J J in o o to 2 < L U m N I T R O G E N ROOM TEMP£RATOR.E NOZZLE DIAMETERS O.SKA MS SKIMMER DIAMETER = \ • G M MS SKlNAhAER-DETECTbR PrSTAMCg: 1 =• 10 cirv\ T H E O R E T I C A L P R E D I C T I O N S FENN AND P E C K E R (FBfc^ EXPERIMENTAL RESULTS-N O Z Z L E PRESSURES A . 10 MM HG S SO NAM 0 100 NANA O IO 2 © 3 0 AO 5 0 NOZZLE - SKIMMER SEPARATION fNOZZLE. D!MASTERS) Figure 9 . Typical Supersonic Molecular Beam Performance for Nitrogen 10. by the theory of Kantrowitz and Grey led people to examine the true nature of the supersonic jet they had produced. In the following section the nature of the expanding jet and i t s interaction with the skimmer i s considered with a view to explaining the experimental results presented here. D. The nature of the expanding beam The flow from a nozzle or hole into an evacuated region is shown schematically i n figure 10. The gas passing through the nozzle opening Figure 10. Schematic Representation of Flow from an Orifice into an Evacuated Region. expands isentropically i n a free jet unaffected by the background gas out-side the jet boundary. This expansion has been described theoretically for zz 1.4 by Owen and Thornhill (Ow 52) using the method of characteristics 11. and confirmed experimentally by Reiss (Fe 63) and Sherman (Sh 63). Their solution i s applicable to any jet, flowing into any external pres-sure, in that region bounded by the orifice and the f i r s t wavefront which registers the existence of an external pressure outside the jet. Ashkenas and Sherman (As 66) have extended Owen and Thornhill's solution to gases with V = 1.67 (e.g. Helium). They suggest the following f i t t i n g formula for the centerline Mach number of a free jet: M = A I - j ^ j - ( i i - t i - i - , H CI ~ ) (13) where x = distance from ori f i c e along centerline d = diameter of or i f i c e ^ — Ratio of Specific Heats A, C, and X Q are f i t t i n g constants for ^ =1.67; A = 3.26, C - 0.31, £° = 0.075 d _ This three term formula i s accurate for X ^/ d with maximum deviations from the characteristic data of ^ ± % of M. The calculated values are shown graphically i n figure 11. Another important parameter to know is the impact pressure as a function of distance downstream from the orifice. This i s the pressure one obtains experimentally upon inserting a Pitot tube, a small diameter piece of tubing with a pressure gauge attached to one end, into the beam so the open end of the tube points upstream. This pressure is essentially^ > V ^ whereis the gas density at the entrance to the Pitot tube and V is the particle velocity. Ashkenas and Sherman give the ratio of impact pressure to source pressure as a function of distance downstream from the orifice by means of the following f i t t i n g formula : o L I i « 1 1 1  O 4 3 12 )6 20 24-NOZZLE D I A M E T E R S FROM NOZZLE E X \ T Figure 11. Distribution of Mach Number Along the Axis of Symmetry of the Expanding Jet where Pi — impact pressure Po = pressure behind orifice Xo' and A are f i t t i n g parameters for )j = 1.67; X° _ 0.04, A = 3.26 d This formula which gives 1% or better predictions of the characteristic data for -j* ^ 2<5ls shown graphically in figure 12. The previous results are valid only u n t i l the expanding jet becomes aware of the background pressure. At this point, the Mach disk, the transition from isentropic continuum flow to nonisentropic free molecular flow occurs. A consequence of this transition i s the "freezing" of the thermal velocity and thus the Mach number. This terminal Mach number has been found by Anderson et a l (An 65) and Abuaf et a l (Ab 66) to obey in general the following relationship |\A T - 1.17 K n 0 (is) where Kn 0 is the ratio of viscosity-based mean free path in the nozzle stagnation chamber, that region upstream of the nozzle opening, to the nozzle diameter. Abuaf et a l (Ab 66) have found, however, that this formula overestimates the terminal Mach number in the case of helium. Their results for helium and other gases are shown in figure 13. Once the transition to free molecular flow has occurred the beam intensity, although continuing to vary inversely with the distance squared from the nozzle, is now scattered i n accordance with the usual attenuation factor (Ra 56) o./o 30 © ARGON • NEON / o 20 & HELIUM /do A / Q £ qfi^a© Q A . & &. M T -/ O 0 O 10 - M T - | . l 7 K f T ° ^ J> -/ QO -5 / % A ^ 0 & 1 • l 1 1 i 1 • . I i . i 1 1_ ZO Kn -1 o Figure 13. Correlation of Asymptoti c Axial Mach Numbers for Argon, Neon and Helium Jets 13. where ^ y = mean f r e e path f o r a beam molecule of v e l o c i t y V Jl = length of chamber E. I n t e r a c t i o n with the skimmer The expansion of the j e t up to- the skimmer i s f a i r l y w e l l understood and one might be l e d to b e l i e v e that a part of t h i s promising j e t could be skimmed o f f f o r use as a smal l narrowly c o l l i m a t e d intense molecular beam. The skimmer, however, i n t e r a c t s with t h i s beam and reduces, i n some cases, the i n t e n s i t y to l e v e l s obtainable wi th a simple oven beam. In t h i s case the skimmer acts as the o r i f i c e and the nozzle-skimmer r e g i o n acts as an oven. Fenn and Deckers (Fe 63) have c o r r e l a t e d the r a t i o of observed f l o w through the skimmer to the t h e o r e t i c a l f low p r e d i c t e d by Kantrowitz and Grey w i t h ' t h e dimensionless parameter Kn/M (the r a t i o of Knudsen number based on skimmer diameter and f r e e stream mean f r e e path at the skimmer entrance to the f r e e stream Mach number determined us ing the Owen-Thornhil l s o l u t i o n ) . This c o r r e l a t i o n , which has been confirmed by other groups, i s presented ( for ni trogen) i n f i g u r e 14. F igure 14 inc ludes the data of Fenn and Deckers (Fe 63) shown i n f i g u r e 9. They have proposed a mechanism to e x p l a i n , at l e a s t q u a l i t a t i v e l y , the shape of the curves obtained. Consider as i n f i g u r e 15 a normal shock i n f r o n t of the skimmer with M ^ , ^ , and T^ represent ing the Mach number, gas d e n s i t y , and temperature of the beam under f r e e stream c o n d i t i o n s . Free stream condi t ions are those that ex is t i n the r e g i o n s u f f i c i e n t l y f a r i n f r o n t . o f the skimmer so that the beam Figure 15. Shock at the Skimmer I.Oi O.I Q Q O Q Q o.oi Ac* / o A _! •* y o ' / A 4 I 1.0 10 0 , c* °-' Kn/H Ratio of Observed to Theoretical Intensity as a Function of Figure 14. Knudsen Number Over Mach Number Based on Free Stream Conditions. Open Points are From Fenn and Deckers for Nitrogen at Nozzle Pressures of 100 Torr (Triangles), 50 Torr (Circles), and 10 Torr (Squares) with a 1.6mm Skimmer Crossed Points are for Various Pressures with 0.4mm Skimmer. Solid Points are for Nitrogen from Scott and Drewry. The Single Square Solid Point is for Hydrogen from Becker and Biers Data 14. p a r t i c l e s are unaware of the skimmer's exis tence . As the beam passes through the shock r e g i o n i t s proper t ies are changed so that at the skimmer i n l e t they are b e t t e r represented by ¥.^,^0^, and T^. The degree to which these proper t ies are changed determines how much the beam i s attenuated from the " t h e o r e t i c a l beam i n t e n s i t y " which assumes f ree stream condi t ions at the skimmer i n l e t . As the gas d e n s i t y i n f r o n t of the skimmer i s de-creased, the shock wave becomes t h i c k e r and the skimmer i n l e t i s penetrated f u r t h e r and f u r t h e r by the shock zone. Thus the gas a c t u a l l y enter ing the skimmer becomes l e s s and l e s s "shocked" u n t i l f i n a l l y at low enough d e n s i -t i e s the gas enter ing the skimmer i s i n the f r e e stream c o n d i t i o n . In f i g u r e 14 we see that as £2 or 1 increases and thus f r e e stream condi t ions M Re are approached the i n t e n s i t y approaches the " t h e o r e t i c a l i n t e n s i t y . " The ra ther abrupt departure at jj- *v | from the otherwise l i n e a r c o r r e l a t i o n has been shown by Fenn and Anderson (Fe 66) and Brown and Heald (Br 66) t o be due to s c a t t e r i n g of j e t molecules which otherwise would contr ibute t o beam i n t e n s i t y by background gas i n the nozzle exhaust- chamber. This model can a l s o be used to e x p l a i n the r e s u l t s of f i g u r e 9 showing observed i n t e n s i t y versus nozzle-skimmer s e p a r a t i o n . For very smal l nozzle-skimmer separat ion the shock i s swallowed i n t o the nozzle and the beam passes through unimpeded. As the separat ion i s increased s l i g h t l y the shock s t r u c t u r e abrupt ly appears i n the f r e e stream at the skimmer entrance thus reducing the beam i n t e n s i t y . The gradual a t tenuat ion of the e f f e c t of the shock with decreasing stream d e n s i t y as the n o z z l e -skimmer distance increases allows higher beam i n t e n s i t y u n t i l f i n a l l y the e f f e c t of s c a t t e r i n g of j e t molecules by background gas at s t i l l l a r g e r distances i s f e l t . 1 5 . CHAPTER I I I ' The Polarized Beam Apparatus A General In 1963 Warren, Klinger and Axen (Wa 63) proposed a means of pro-3 ducing an intense beam of po l a r i z e d He^ p a r t i c l e s . A schematic presen-t a t i o n of the scheme along with t h e i r expected molecular flows at various locatio n s i s shown I n figu r e 16 . He^ gas cooled to 2 . 2 ° K passes through a supersonic Laval nozzle-skimmer co l l i m a t o r arrangement to produce an intense narrowly collimated beam. This beam enters a hexapole magnet i n which the two nuclear spin states of the He 3 are separated and one discarded. The p a r t i c l e s are then ionized and accelerated thereby producing a polarized 3 He beam. B. The Low Temperature Beam Source Figure 17 shows the design of the low temperature He^ atomic beam source. The He^ gas precooled to 7 7 ° K passes through a s p i r a l heat exchanger before entering the l i q u i d He^ " bath at 4 . 2 ° K. The gas then passes through a helium bath maintained at 2 . 2 ° K before entering the Laval nozzle. Figure 18 shows i n d e t a i l the nozzle-skimmer-collimator arrangement and table 1 summarizes the relevant dimensions necessary i n c a l c u l a t i n g the expected beam f l u x . He° Atoms Polarized He3 Atoms *" Polarized He0 Ions tt HG 45 4IOO 100 Figure 16. Schematic Diagram Showing the•Arrangement of the Components of the Polarized He Ion Source. The Designed Beam Intensities are Given in Atoms/sec. and the Maximum. Allowable Background Pressures in mm.Hg. 4 To He Recovery System Transfer Tube (fozzle Assembly Bel Iows To LeyboId Pump Bel lows f+— He3 Inlet Transfer Tube 3 •Transfer Tube Z Heat Shield NeKapole Magnet Bel lows 3 Liqui Nitrogen ITTTt To PMC 4100 Bel I owz Scale 1:6 rzrza Figure 17. The Low Temperature He Atomic Beam Source Figure 18. Detail of Nozzle Assembly > 16. TABLE 1 Dimensions of Supersonic Beam System Diameter Area Nozzle throat 0.2 mms 3.24x10-4 cm2 Skimmer 0.4 nuns 12.6 xlO"^ cm2 Collimator 0.1 cms 7.85xlO - 3 cm2 Magnet entrance 0.3 cms 7 . 0 7 x l 0 " 2 • cm2 Skimmer-Collimator distance 3 cms Nozzle-skimmer distance 0,63 cms Skimmer-magnet distance 15 cms With a nozzle pressure of 15mm and assuming a Mach 4 beam Axen (Ax 65) calculated that 6 .5x l0 1 5 particles per second would enter the magnet. Assuming a 40$ transmission through the magnet and a 0.25$ (Ve 64) ionization efficiency this would be sufficient to produce an ion beam of one microampere intensity. I n i t i a l testing of the nozzle using He^ " gas carried out be Jassby (ja 64) at room temperature and the nozzle-skimmer-collimator by Axen (Ax 66) at room and liquid nitrogen temperatures showed discrepancies i n both beam intensities and Mach numbers from those expected from theoretical considerations assuming an idealized Laval nozzle system as proposed by Kantrowitz and Grey (Ka 5l). In spite of these deficiencies i t appeared that beam intensities adequate for the successful operation of the polarized He3 beam source were available. 17. C . T e s t i n g of the Nozzle-Skimmer-Coll imator System. In order t o c a r r y out a more complete examination of the performance of the atomic beam source a s e r i e s of measurements using He -^ gas at room, l i q u i d n i t r o g e n and l i q u i d helium temperatures was undertaken. Measurements were made w i t h the magnet and i o n i z e r chamber i n place t o examine at an e a r l y stage any alignment or vacuum problem that might a r i s e so that modi-f i c a t i o n s could be made t o improve the o v e r a l l performance of the system. F i g u r e 17 and 19 show the r e l a t i v e l o c a t i o n of the var ious components. The pressure i n the nozzle-skimmer r e g i o n was measured with a P i r a n i gauge attached to a piece of t u b i n g i n s e r t e d j u s t below the nozzle-skimmer axis as shown i n f i g u r e 18. The pressures i n the magnet entrance and i o n i z i n g regions were determined by use of i o n i z a t i o n gauges. The beam i n t e n s i t y was measured w i t h a d i f f e r e n t i a l P i r a n i detector (DPD) s i m i l a r to one whose c o n s t r u c t i o n and c a l i b r a t i o n i s descr ibed by Jassby ( ja 64). The DPD upon c a l i b r a t i o n was found to have a s e n s i t i v i t y of approximately 12 2 4x10 molecules/cm / s e c ^ v o l t . The output from the DPD was measured us ing a Hewlett Packard Model 425 A DC Micro volt-ammeter capable of measuring 1 /10 'of a m i c r o v o l t . The s i g n a l from the DPD was a m p l i f i e d by a Hewlett Packard micro volt-ammeter and used t o d r i v e a Moseley Model 680 chart recorder to provide an e a s i l y read record of the beam i n t e n s i t y . The beam was chopped a f t e r every reading t o determine the reference back-ground s i g n a l l e v e l . A block diagram of the recording system i s shown i n f i g u r e 20.' A t y p i c a l recording from the chart recorder i s shown i n f i g u r e 21. F i g u r e 22 presents the r e s u l t s of beam opera t ion at room, l i q u i d n i t r o g e n and l i q u i d helium temperature p l o t t e d as a f u n c t i o n of the pressure i n the nozzle-skimmer r e g i o n . Figure 19. The Magnet Assembly 18. D I F F E R E N T I A L PlRAMI 0 E T E C T O B . MlCfcO" VOLT ANVPAETER. C H A f c X R E C O R D E R , Figure 20. Block Diagram of Beam Detection System. BEAM CHOPPED Figure 21. Typical Chart Recording. The nozzle-skimmer pressure measured i n the location shown in figure 18 i s used as an ordinate i n plotting beam intensities as i t is assumed that this pressure is simply related to the nozzle pressure. That this i s in fact true, under certain conditions, is shown in figure 32. It is also assumed that the nozzle-skimmer pressure is an indication of free stream conditions just upstream of the skimmer. That this may in fact not be true is also shown in figure 32 where i t shows that the relation between nozzle pressure and nozzle-skimmer pressure is roughly independent of nozzle-skimmer separation. One would expect the free stream pre-skimmer conditions to depend on the nozzle-skimmer separation and thus would expect a different relationship for each separation. o UJ to o o 2 4 2 . 0 S K I M M E R DETECTDPv D I S T A N C E ' 7 6 C M H /-si CO z L U 1-< LLi CD X o o tux xx xx K X X ft R O O M T E . M P E R A T O R E . X <x 1*. X rt LIQUID NITROGEN TE.MPERA.TU R E 00 L I Q U I D H E L I U M T E M P E R A T V > I * E -I i i i—i— 50 too ISO V 2 0 0 P R E S S U R E |K NOZZLE - S K I M M E R R E G I O N ( M I C R O N S ^ Figure 22. The Dependence of Beam Intensity on Temperature 19. D. Analysis of the Experimental Results In order to assess the performance of our beam source i t i s useful to calculate the expected "theoretical beam intensity" using equation 9. If one uses the physical dimensions of the nozzle-skimmer system given i n table 1, the Mach number as determined from figure 11, the physical con-stants given i n table 2, and the fact that the DPD was 76 cm from the skimmer one obtains for selected nozzle-skimmer pressures the expected intensities tabulated i n table 3. TABLE 2 Selected Physical Parameters For Helium 4 Gas. a 0 = 5.9 x 10 3 N ft? cm/sec. 1.67 M i = 9.66 x 10 1 8 molecules/cm3 To* X = 5.85 x IO" 5 cms M - 6.5 Nozzle-skimmer separation =3.1 Nozzle diameters We have correlated in figure 23 the observed to theoretical beam intensities with the dimensionless parameter Kn/M (the ratio of Knudsen number to Mach number). Our Knudsen number is based on the skimmer diameter and the mean free path calculated using the temperature of the gas before i t passes through the nozzle and the previously described nozzle-skimmer pressure. The Mach number is the free stream Mach number given by the Owen and Thornhill solution i n figure 11. Our correlation i s similar to that of Fenn and Deckers (Fe 63) shown in figure 14 except that their Knudsen number is based on the free stream TABLE 3 SELECTED EXPERIMENTAL AND CORRESPONDING THEORETICAL BEAM INTENSITIES TEMP. NOZZLE-°K SKIMMER PRESSURE EXPERIMENTAL BEAM INTENSITY Atoms/cm^/sec. THEORETICAL k BEAM INTENSITY M Atoms/cm^/sec. s/D F2exp. F2theor. 300 77 25 microns 0.72x10^ 3.43x10^ 2.7 0.21 50 1.07 7.1 1.3 .15 75 1.37 10.5 0.9 .13 100 1.66 13.8 .67 .12 125 1.83 18.3 .54 .10 150 1.98 22 .45 .09 175 2.1 24.7 .38 .085 200 2.17 28.2 .33 .077 25 0.5 7.15 .69 .07 50 0.6 15 .35 .04 75 0.73 20.9 .23 .035 100 0.8 26.6 .17 .03 125 0.87 34.8 .13 .025 150 0.95 43.2 .11 .022 175 0.96 48 .10 .02 42 50 0.22 55 .02 .004 0.-7r Figure 23. The Ratio of Experimental to Theoretical Beam Intensity as a Function of Knudsen Number to Mach Number. y -z. UJ >-t -Z UJ h z © ° ROOM TEMP. o © A ZL UJ _J < o UJ o U J A LIQUID N l T R 0 6 E ^ J H ^ R . 0 1 0 .003 • LIQUID H E L I U M TEMP. J I I M i l l I I I I M i l l I I I I .Of O.I 20. pressure and temperature just upstream of the skimmer entrance rather than the pressure and temperature we chose. It should be clear that the Knudsen number used i n figure 14 based on free stream conditions i s not directly comparable with the one used i n figure 23. From figure 22 we see that the beam intensities decrease with tempera-ture for a constant nozzle-skimmer pressure rather than increase as expected from the theory of Kantrowitz and Grey (Ka 51). It had been expected that the beam at liquid helium temperatures would be about ten times more intense than the room temperature beam; the sad fact was however that the beam was about ten times less intense.' The correlation i n figure 23 shows that we obtain only a fraction of the f u l l "theoretical beam intensity" for low Kn/M ratios but obtain an increasing fraction of the theoretical for higher Kn/M ratios. This i s attributed to the fact that lowering of the gas temperature increases the gas density thus lowering the mean free path and hence Knudsen number at the skimmer entrance. This results i n the gas being more severly "shocked" •at the lower temperatures than at the higher temperatures with a subsequent attenuation i n beam intensity. The fact that the actual beam intensity at li q u i d helium temperature is about 100 times less than expected led to a reassessment of the f e a s i b i l i t y of the polarized beam experiment. It was decided that an improvement in beam intensity by a factor of 10 would be necessary to produce a polarized beam of useful intensity. With this i n mind a program was undertaken to re-examine a l l aspects of our nozzle system and to consider alternate means of improving the beam intensity. The results of these efforts w i l l be des-cribed in the next section. 21. CHAPTER IV Inves t iga t ions i n t o f a c t o r s a f f e c t i n g beam i n t e n s i t i e s In reviewing the performance of our molecular beam system with a view to i n c r e a s i n g the beam i n t e n s i t y we have examined many aspects of the beam format ion . Some of the main points i n v e s t i g a t e d i n c l u d e : The e f f e c t of pressure and temperature The e f f e c t of nozzle-skimmer dis tance The e f f e c t of skimmer diameter and manufacture The e f f e c t of a c o l l i m a t o r The e f f e c t of background pressure i n the nozzle-skimmer r e g i o n The e f f e c t of var ious types of beam forming devices Some of these points have been u n s a t i s f a c t o r i l y i n v e s t i g a t e d or have g iven i n c o n c l u s i v e r e s u l t s but i n most cases have i n d i c a t e d i n a general f a s h i o n the s i g n i f i c a n c e of the e f f e c t on beam i n t e n s i t y . A . Nozzle-skimmer separat ion In order to examine the e f f e c t of nozzle-skimmer distance on beam i n t e n s i t y i t was f i r s t necessary to devise a means of e a s i l y a d j u s t i n g the nozzle-skimmer d i s t a n c e . The scheme chosen i s shown i n f i g u r e s 24 and 25. In t h i s arrangement the skimmer-coollimator dis tance i s f i x e d to ease con-s t r u c t i o n . The nozzle-skimmer dis tance i s adjusted by r e v o l v i n g the skimmer-coll imator c a r r i a g e on a screw thread (26 threads per inch) cut on the main nozzle assembly. The gear on the end of the skimmer-collimator car r iage i s connected by means of a gear chain system t o a rod which passes through the vacuum chamber w a l l us ing an 0- r i n g s e a l thus a l l o w i n g the rod to be rotated from outside the vacuum system. One complete r e v o l u t i o n of • O - RINGS gure 24. The Adjustable Nozzle-Skimmer Apparatus. 64 COG GEAR ON END OF ADJUSTABLE NOZZLE - SKIMMER- APPARATUS PINION S T O C K W I T H S C O G G E A R O N E N D 8 COG GEAR o-RING MOVEABLE SEAL V A C U U M PEEO T H R O U G H HANDLE ure 25. Turning Mechanism for Adjustable Nozzle-Skimmer 0 C H A I N o 22. this rod corresponds to 1/8 of a revolution of the skimmer-collimator carriage which increases or decreases the nozzle-skimmer separation by .0048 inches. The skimmer is prevented from being forced against the nozzle by means of a collar which presets the "zero" revolution nozzle-skimmer distance at any desired value. The vacuum seal between the various diffe r e n t i a l l y pumped regions is effected by means of two 0-rings built into the skimmer-collimator carriage. Thus under room temperature opera-ting conditions i t was possible to f i x the nozzle pressure then adjust the nozzle-skimmer distance by turning a handle on the outside of the vacuum system. Some typical results obtained from the adjustable arrangement are shown i n figure 26 for several nozzle pressures. Figure 27 shows the results one obtains by fixing the nozzle-skimmer distance then varying the nozzle imput pressure. The results obtained are similar to those obtained by other experimenters and can be explained by the mechanism discussed previously. A l l results with the adjustable nozzle-skimmer arrangement have been made with a skimmer-detector distance of about 16cm. Obtaining similar results at li q u i d nitrogen temperatures i s not as simple because the neoprene rubber 0- rings freeze and i t i s impossible to rotate the skimmer-collimator carriage. We have considered teflon 0- rings but as yet have not been able to obtain any for testing purposes. However, results can be obtained by fixing the nozzle-skimmer separation at room temperature then cooling the system to liquid nitrogen temperatures and then observing the beam intensity for varying values of input pressure. After obtaining one set of results i t is then necessary to warm the entire system to room temperature, reset the nozzle-skimmer separation and repeat the procedure. If one selects several nozzle-skimmer separations i t 3 £000 0^00 4000 1000 o O C T O B E R Z5~(t<f6G -—*-2 .4xlO , f c atort\s|cm 2/sec ROOM TEMPERATURE O-Oie" SK'MMEP. NO COLLIMATOR ttZ.ERC/ ^ . O O / f i - " <2> X <b — X H0Z.ZLE P R E S S U R E 0 /O M M A 3 4 M M X S 3 M M 0 140 MM XX SoooK* 2ooct~ & Q x © A * . 0 4 AS J 0 0 0 5 0 5 . A A © * * 8 * A 3 a Q Q O D Q D D Q Q D j s ; \i0 • Q O K /4-O 6 16 24 32 40 49 56 64-N O Z Z L E - S K I M M E R S E P A R A T I O N NUMBER OF TURNS FROM * ZERO" Figure 26. Typical Results Obtained From Adjustable Nozzle-Skimmer Apparatus. O C T /i<36£ A / O Z Z L E - S K I M M E R SEPARATION ^ IS REVS 5"000 v- Z x IO l f e a±oms.|Cfn 1/sec s Aooo — X * X / TV £ * * * —• X 3000 —^  *• X x Z.000 — < \ooo o X 1 1 1 1 o 5"0 /OO /6"0 Z O O N O Z . Z L E P R E S S U R E . CfV\ M H G ^ Figure 27. Typical Results Obtained for Fixed Nozzle-Skimmer Separation. 23. should be possible to get an idea of the dependence of beam intensity on nozzle-skimmer distance at liquid nitrogen temperatures. Just such a procedure was used i n obtaining the results shown i n figure 28. Room temperature results are included i n figure 29 and 30 for comparison. In order to compare these results with earlier'results plotted on the basis of nozzle-skimmer pressure figures 31 and 32 have been compiled using the results associated with figures 28 and 30 for several selected nozzle-skimmer separations. The results i n figures 26 — 30 show clearly the effect of nozzle-skimmer separation on beam intensity and point out the advantages of optimum separation for a given nozzle pressure and total gas flow. The later item is extremely important as most beam sources have a limited pumping capacity. For example figure 26 shows for a fixed nozzle pressure that the beam intensity can be varied by a factor of 3 by mearly changing the nozzle-skimmer separation by 0.04 inches. Figures 28 and 30 il l u s t r a t e how one can obtain a higher beam intensity, especially at lower temperatures, by keeping the nozzle-skimmer separation i n the region before the minimum or valley shown i n figure 29. Although such features as the exact location of the peak and valley shown i n figure 26 and the value of the peak to valley ratio depend on the particular skimmer and possibly nozzle that one has in their system, this data should be extremely useful i n serving as a guide in designing a system with maximum beam intensity and minimum total gas flow. B, Mechanical alignment Many of the d i f f i c u l t i e s involved with molecular beam systems are associated with the actual mechanical alignment of the nozzle-skimmer-collimator system. The physical alignment of these components of the L/QUip NITROGEN TEMPERATURE II HIU \CLcooo, » . 2 W 0 ' 6 atoms/crn/sec N O Z Z L E - SKJM MER SEPARATION • . — ^ >t «. «... r-« ^ » ^ v\ ^ ^ ll 5 3 4000 >-^ 3000 CO .3 o G3 4 K E V S F R O M * Z E f 3 0 " = 3 NOZZLE P / A M E T E R S X /0 V v • = T /-- a — a — — Q - — 0 f O O O f - / — 0' ^ -A — "~ ~ — A - - - , -_ • A. 1 SO IOO ISO N O Z Z L E PRESSURE ( M M HG) zoo Figure 28. Beam Intensity Results at 77°K 10/28/66 u o UJ < Lu CD 5"ooo — 3000 o 2 x /o'6ato/ns|cmz/sec 10 /© AO' O A / © loco 1 12. R O O M T E M P E R A T U R E 0 . O I 8 " S K l M M E R NO COLLIMATOR vVZEfcO" R E V S ^ <O0S" 44 I-0 I S 1 I*7 I NOZZLE PRESSO&E C /0<9 M A i A / 6 0 M M 3 0 J N D Z L Z L E DlA*S. 0 8 /6 32 40 4 8 & 6 > N O Z Z L E - S K I M M E R S E P A R A T I O N ( T U R N S FROM x X ZEfcO") Figure 29. Beam Intensity Results at 300°K. lp ER S E P A R A T I O N /^)OM TE/VI P££ AT ORE. > £ 0 0 0 ^ Q 4- R E V S FROM 3 NOZZE DIAMETERS 10 7 " • 0 18 v v' /2 v 44 ^ • £ 7 * 07 < CQ - - u * - _ ~ _ 0 _ - a - f 2000 / ^ - O Q (opo / ' A - _ ' / © ^ A ~ 4 - 41 I I - J I £0 /OO t€0 2 0 0 NOZZLE PRESSURE ( M M H$) Figure 30. Beam Intensity Results at 300°K. NOZZ .LE-SKIMMER. SEPARATION) 0 4 REVS A |£ REVS Q IS R E ^ x 44 REVS £OOM TEMPERATURE. ta AT 0 • 1 (Z> o 5"o /OO /SO £ 0 0 N O Z Z L E P R E S S U R E . ( M M BG^ 2 C O Figure 31. Correspondence Between Nozzle and Nozzle-Skimmer Pressures at 300°K. Z O O -z. a 3 ISO oL /OO 0/ I LU —I N o O N o Z Z L E - S K I M M E R S E P A R M t o N A /0 RtVS • 18 KEVS X 44 REVS 1 LI&VIP NITROGEN! TEMPERATURE 4 0 d O 50 too NOZZLE PRESSURE (tAM H O /50 ZOO Figure 32. Correspondence Between Nozzle and Nozzle-Skimmer Pressures at. 77°K. 24. system is extremely important because of the relatively small diameters of the various apertures. Because of this i t is necessary to follow an alignment procedure each time the beam assembly is dismantled. We shall discuss below the procedure used specifically in setting up the adjust-able nozzle-skimmer apparatus but the procedure used i s essentially the same as used with the fixed nozzle-skimmer apparatus. The overall alignment set-up i s shown schematically i n figure 33. The framework which holds the nozzle and skimmer-collimator carriage i s f i r s t inserted i n the collet of the Colchester "student" lathe then inspected by means of an accurate d i a l indicator and adjusted until f i n a l l y the inner surface on which the skimmer-collimator carriage runs i s true to. better than .001" when the collet is rotated. Following this the Wild Model T2 theodolite i s focussed on the nozzle and the collet rotated. The nozzle i s adjusted by means of four adjusting screws unt i l there is no vi s i b l e asymmetry upon rotating the collet. The skimmer-collimator carriage i s then inserted into the main framework. Holding the main frame-work fixed, the carriage i s rotated manually by means of the gear on the end. The skimmer i s viewed through the theodolite and adjusted to minimize as much as possible, any vis i b l e asymmetry. The theodolite is then adjusted i n the horizontal and vertical directions u n t i l i t s axis is coincident with the nozzle-skimmer axis. Finally the collimator i s inserted and i t s position checked i n the same manner as the skimmer. If the alignment is not correct the beam intensity i s no longer a smooth function of nozzle-skimmer separation as i n figure 26 but now exhibits oscillations every 8 revolutions. Figure 34 is an example of very bad align-ment. Some misalignment can also be detected i n the 83mm Hg readings i n figure 26. 4 1 © 0 \ Q IV I \ I I o \ o I \ © I I O o < b 0 OftQtfeO 6 0 o d > 0 o 8 f& /vozZLE -SKIMMER SEPARATION REVS PRO(v\ W i E R O " 2 4 i 6 Figure 34. Typical Results Showing Effect of Poor Alignment. LATHE O Z Z L £ - $ K I M M E R " \ C O L L E T ; r ^ S s E l A B L r THEODOLITE DIAL INDICATOR Figure 33. Alignment Assembly. 25. C . E f f e c t of skimmer diameter and manufacture The e f f e c t of skimmer diameter and manufacture on beam i n t e n s i t y has been i n v e s t i g a t e d under rather l i m i t e d c o n d i t i o n s . We s h a l l t r e a t each separa te ly i n the f o l l o w i n g paragraphs. 1. Skimmer diameter The o r i g i n a l t h e o r e t i c a l treatment of Kantrowitz and Grey p r e d i c t s the beam i n t e n s i t y as a f u n c t i o n of the diameters and separations of the skimmer and c o l l i m a t o r , the pressure , the temperature, and the Mach number. As we have mentioned the t h e o r e t i c a l and a c t u a l beam i n t e n s i t i e s appear to be r e l a t e d through the parameter Kn/M where the Knudsen number, Kn, i s a f u n c t i o n of pressure , skimmer diameter and temperature. I f one takes the case of constant temperature, Mach number, and pressure the observed i n t e n s i t y should increase roughly as the skimmer diameter. Thus i f we double the skimmer diameter the beam i n t e n s i t y should a lso double . N a t u r a l l y there i s a l i m i t to t h i s l i n e of reasoning but i t was thought u s e f u l to increase the skimmer s i z e and see i f any increase i n i n t e n s i t y r e s u l t e d . No s i g n i f i c a n t dependence of beam i n t e n s i t y on skimmer s i z e was found. Pi i s probable that the l a c k of c o n t r o l of skimmer q u a l i t y obscured a p o s s i b l e dependence. It should be noted that Campargue (Ca 66) reports an increase i n beam i n t e n s i t y of 30% upon i n c r e a s i n g the diameter of h i s skimmer from O.k to 0.8mm. 2. Skimmer Manufacture Once one has determined the i n t e r i o r and e x t e r i o r angles f o r the skimmer (see Axen (Ax 65)) i t appears as i f the only parameter, other things being equal , that could a f f e c t the extent to which the beam i n t e r a c t s wi th the skimmer i s the sharpness and smoothness of f i n i s h of the skimmer edge. The manufacture of the skimmers and our observations as to the e f f e c t of 26. skimmer edges on beam i n t e n s i t y w i l l be discussed below. The general procedure f o r manufacturing the skimmer i s as f o l l o w s . The i n s i d e cone i s machined out of the end of a piece of rod stock. A small h o l e , the diameter of the skimmer, i s d r i l l e d i n t o the stock us ing the i n s i d e cone as a center ing device . This cone i s then attached to a mating s e c t i o n thus a l l o w i n g the m a t e r i a l to be machined from the opposite d i r e c t i o n . The outside cone i s then machined o f f u n t i l the surfaces of the two cones meet. F igure 35 shows the general arrangement and what i s meant by the " t u n n e l " . The skimmers r e s u l t i n g from t h i s procedure i n general leave much to be d e s i r e d as the t h i n edge tends to break up or a t u n n e l i s l e f t at the end. Results from many skimmers of v a r y i n g q u a l i t y do not show any s i g n i -f i c a n t trends and i t has not been p o s s i b l e to a t t r i b u t e some ra ther abrupt increases and decreases i n beam i n t e n s i t y t o the q u a l i t y of the skimmer. I t i s p o s s i b l e , however, that the l e a d i n g edge on the best of our skimmers i s of such poor q u a l i t y that a reduct ion i n skimmer beam i n t e r a c t i o n and a r e s u l t i n g increase i n beam i n t e n s i t y are s t i l l p o s s i b l e . Although not g r e a t l y a f f e c t i n g the beam i n t e n s i t y the amount of " t u n n e l " has been observed to change the character of the nozzle-skimmer separat ion versus i n t e n s i t y r e s u l t s . D. Presence of C o l l i m a t o r In order t o reduce the number of f a c t o r s upon which the beam i n t e n s i t y could depend we have removed, f o r many measurements, the c o l l i m a t o r from our beam system on the assumption that i t should not a f f e c t the beam i n t e n -s i t y . I t has however been our experience, at l e a s t w i t h the adjustable nozzle-skimmer apparatus, that the beam i n t e n s i t i e s wi th the c o l l i m a t o r i—r BUTTERFLY VALVE , VA/V/v "PUMPlKS LIN E NOZZLE-SKIMMER. fcCeioN-- L E Y 6 0 L D M O D E L M E R C U R Y E J E C T O R P l » M P Figure 36. Pumping System for Nozzle-Skimmer Region. 27. removed are 2 to 3 times more intense than with the c o l l i m a t o r i n p l a c e . This must mean one of two t h i n g s ; e i t h e r the c o l l i m a t o r i s misal igned or the pressure i n the skimmer-coll imator r e g i o n i s too h i g h . The f a c t that the skimmer-coll imator separat ion i s 3 cm and the c o l l i m a t o r diameter i s 1 mm makes i t improbable that the small p h y s i c a l misalignments that could conceivably e x i s t a f t e r our c a r e f u l alignment could cause an at tenua-t i o n of the s i z e observed. It i s , on the other hand, qui te conceivable because of obst ruct ions associated w i t h the adjustable nozzle-skimmer arrangement that the pressure i n the skimmer-coll imator r e g i o n i s excessive . Unfortunately with our present experimental apparatus we are unable to measure t h i s pressure. We see no reason why our present pumping system should be incapable of handl ing the e x i s t i n g gas f low and thus f e e l that wi th s u i t a b l e m o d i f i -ca t ions we w i l l be able t o reduce the pressure i n the skimmer-coll imator r e g i o n to an acceptable l e v e l . This means we w i l l assume that beam i n t e n s i t i e s a t t a i n a b l e without a c o l l i m a t o r are f o r a l l i n t e n s i v e purposes a t t a i n a b l e with a c o l l i m a t o r . E . Background gas Pressure In an e a r l i e r s e c t i o n we presented an o v e r a l l d e s c r i p t i o n of the expansion process from a nozzle i n t o an evacuated r e g i o n . This treatment suggests that the a c t u a l j e t molecules upstream of the Mach d i s k remain unaware of the background gas i n the nozzle-skimmer region because of the presence of a shock wave which acts as a b a r r i e r t o outside i n f l u e n c e s . Downstream of the Mach d i s k the beam can e a s i l y be bombarded by the back-ground molecules . With these thoughts i n mind i t was considered u s e f u l to determine experimental ly the e f f e c t of the background gas i n the n o z z l e -28. skimmer region on the beam intensity. The location of the Mach disk for many gases is given by equation 15. For helium, Abuaf (Ab 66) presents results (figure 13) which give for the same Knudsen number lower terminal Mach number than equation 15. TABLE 4 Terminal Mach numbers Nozzle diameter = 0.2 mm Nozzle Pressure Xmm Kn Mm = 1.17X T Kn-°.4 Nozzle diameters Abuafs Nozzle diameter T r300°K ° 100mm 1.75xlO"3 8.7xlO"3 7.8 3.8 5 2 40 4.4xl0- 3 2.2xl0~2 5.4 2.4 3.5 1.5 10 1.75xl0-2 8.7xl0 - 2 3.1 1 No data -T0=77°K 100mm 0.45xl0~3 2.25xl0"3 13.5 8.2 10 5.5 40 1.13xlO - 3 5.6xlO - 3 9.3 5 7 3.5 10 0.45xl0~2 2.25xl0~2 5.3 2.2 3.5 ' 1.5 T0=4°K 100mm .023xl0" 3 0.12xl0" 3 43.7 » 3 0 28 >25 40 .059xlO" 3 0.29xlO~3 30 »30 19 14 10 .023xl0 - 2 0.12xl0" 2 17.4 12.5 13 8 Table 4 gives the values of the terminal Mach number determined by both equation 15 and Abuafs results for several selected nozzle pressures. Using the results of Ashkenas (figure l l ) we have assigned a nozzle-skimmer separation corresponding to these terminal Mach numbers. From these results i t i s apparent that scattering by background molecules w i l l be of importance at least at room temperature for almost a l l nozzle-skimmer separations and operating conditions that we wish to consider. Naturally the transition 29. between continuum and free molecular flow is not sharp and these results are only indicative of the approximate region where one might expect this mechanism to become of consequence. Experimentally the dependence of beam intensity on background pressure in the nozzle-skimmer region was determined by constricting the pumping line to this region and thus increasing the background pressure. It was only possible to examine a limited range of background gas pressures because of the limited pumping capacity available and the conductance of the pumping line. Figure 36 shows the location of the pump, the valve, the pumping line and the nozzle-skimmer region. Figures 37 - 41 show some typical results obtained by constricting the pumping line to the Leybold Hg 45 diffusion pump. Each figure presents results obtained using selected fixed nozzle pressures and a constant nozzle-skimmer separation. These results show how the expanding jet i s protected from background gas scattering u n t i l the transition to free molecular flow occurs at the Mach disk. In figures 38, 39 and 40 an increase i n background gas pressure reduces the beam intensity consider-ably whereas i n figure 37 the beam intensity i s slightly reduced for the 12 and 41 mm case and unaffected by the background gas intensity i n the 100 mm case. As the results i n table 4 show, however, the Mach disk should appear upstream of our nozzle-skimmer separations for a l l pressuresif one uses Abuaf's results and for a l l except'the 100 mm 4 nozzle-diameter case i f one uses formula 15. The important thing to note here is the trend which shows clearly that for nozzle-skimmer separations considerably downstream of the Mach disk attenuation of beam intensity due to background gas scattering i s considerable. The increase i n beam intensity at large background pressures i s the Sooo k J A ooo > Sooo V C/> tu L_ 2ooo Q3 /ooo NOZZLE-SKIMMER SEPARATION! = 4 R£V5 = 3 NOZZ.LE. DIA*?-ROOM TEMPERATURE £3QQ N O Z Z t E PRESSURE - 102 MM _ - a Q . Q - C I -0 _ NOZZ .LE PRESSURE =41 M NA _ _ e f i f e c a ^ > « a - - _ - - - -13 ^ PRESSURE s /2MNv _^ — 4-VALVE COMPLETELY CLOSED 100 ZOO 306 400 500 £ 6 0 700 QOO 9 0 0 \0<>O PRESSURE |N NOZZLE-SKIMMER REGIO N CKMCfcoN^) Figure 37. Beam Intensity Dependence on Background Gas Pressure. O > 4^00 — _ 1000 < US CQ N&Z.ZLE. - SK\ M M ER. SEPARATION ~ IO f?£VS £oof\A T E M P E R A T U R E (2) VA-LVE C O M P L E T E L Y C L O S E D \ \ Po - lOOMfW S ^ j r - ? 0 - 47lV\NA X — " S x * X. — — - — K J L 1 1 2 > J L J I |0O 2 0 O 300 400 5 3 0 70O Qoo 7 0 0 / 0 0 0 P R E S S U R E IN N O Z Z L E - S K I ^ ^ E R R E G I O N ( M I C R O N S ^ ) Figure 38. Beam Intensity Dependence on Background Gas Pressure. SoOoi *-Zxio,b atomsjcma/sec \n 4ooo tr 3 3006 h JOOO o O A/0ZZ.LE - S U M M E R . S E P A R A T I O N - REVS =. /2 NOZZLE. P / A S . N O Z Z L E P R E S S U R E © V A L V E C O f A P L E T E L L V C L O S E D \oi N\r\\ x*x 42 »NArA , , . 12 lAfsA O i f I K / 0 — © , L*£v ~~ - Q _ _ — — . < » ' . * J L o too Zoo 3 0 O 400 Soo ton 7 0 0 fioO 900 /ooo PRESSURE. IM N O Z Z L E - S K l M W A E f c . RE<3\0|S* C MlC R.ON)S) Figure 39. Beam Intensity Dependence on Background Gas Pressure. 5000 I/O I-- J o A 4000 2000 — I0O0 • 2* /o'featoNvs/c.fY\*/sec N02--ZLE -SKIMMER S E P A R A T I O N = N O Z . 2 L E P R E S S U R E /o/ M M x x x 40 MM . . • 12 MM 44 £ E v s 2 7 NOZZLE D/AS. ROOM TE/v\pEP-ATOP.E VALVE COMPLETELY CLOSED k * \ . — — r ** K X i 100 ZOO 300 400 500 600 700 80o 90o PRESSURE IH NOZZLE ~ S K I M M E R R E G I O N 6M IC RONS') /000 Figure 40. Beam Intensity Dependence on Background Gas Pressure. 3 0 0 0 2ooo LJ |OOO o > A y 3000 •z. 2000 1000 < L U CQ o -\.Z xiO , f c cx±orfts,|ctt\2/sec NOZZLE - SKIMMER. SEPARATION = l8 REVS NOZZLE PRESSURE " '2 N.D. /OO M M • VALVE COMPLETELY CLOSED « ' - /2/v\M _ — — — o — ~"" LtQUtt> A/JTROGEN T E M P E R A T U R E f X © GO - - o ©OK N 0 Z . Z L E - S K I M M E R . SEPARATION = 10 REVS - 7 N.D-LIQUID N I T R O G E N T E M P E R A T U R E - X -? o - ^ 3 6 _ M r A _ _ 100 200 30O 400> 5"00 ^00 70O 8 0 O 900 I00O P R E S S U R E IN NOZZLE. - S K I M M E R . REGION ('MICRONS^ Figure 41. Beam Intensity Dependence on Background Gas Pressure. 30. r e s u l t of the skimmer producing a simple oven beam. For la rge enough nozzle-skimmer ( i . e . oven) pressures the beam i n t e n s i t y produced by t h i s mechanism i s qui te l a r g e and appears, i n some cases, t o exceed that ob-t a i n e d with the nozzle beam but one must remember the extremely high gas pressures i n the nozzle-skimmer r e g i o n which are necessary t o produce t h i s s o r t of i n t e n s i t y . The oven beam could be u s e f u l i f the t o t a l gas f low to the system was not excessive as i t might e l iminate the need f o r a r e c i r c u l a t i n g He 3 system. F . Nozzles The nozzle used i n most of our experimental i n v e s t i g a t i o n s has been descr ibed by Jassby ( ja 64). I t was thought u s e f u l to consider two a l t e r n a t e beam producing d e v i c e s . The f i r s t was a s i n g l e channel c a p i l l a r y d e v i c e , whi le the second was a m u l t i - c h a n n e l c a p i l l a r y device . The r e s u l t s obtained w i l l be discussed below. For devices of the s i n g l e c a p i l l a r y type we used three d i f f e r e n t diameters . Two, 0.005" and 0.0095" i n s i d e diameter, were simply sect ions of s t a i n l e s s s t e e l tubing while the t h i r d , 0.020" I . D , was a hole d r i l l e d i n a piece of brass . The tubing was mounted by means of epoxy cement onto a holder which was then i n s e r t e d i n the same l o c a t i o n as our usual n o z z l e . The r e s u l t s obtained f o r the two diameters of t u b i n g and one d r i l l e d hole are shown i n f i g u r e s 42, 43, and 44 f o r s i n g l e f i x e d nozzle-skimmer separa t ion . Because of the u n c e r t a i n t y i n nozzle pressure , vary ing l e n g t h s , imprecise nozzle-skimmer separations and u n c e r t a i n alignment no conclusions other than apparent beam i n t e n s i t y and general nature of the curves should be extracted from the r e s u l t s . Later r e s u l t s with the adjustable n o z z l e -2000 1/7 > laoo >-400 — u .0O5 1' TUBING N O Z Z L E A / O Z Z L £ - S K I M M E R SEPARATION ^ 3 T^B/NG D/AM.ETERS TUBE LEMGTH ~ Zo T U B E P/A/V\ETERS ROOJNA T E M P E R A T O R E . •OI8" SkitwrvAES + C O L L I M A T O R . 0 0 0 D O ? 0 G O o 0 20 40 PRESSURE. 60 ao 'OO /20 /40 160 /80 IN N O Z Z L E - S K I M M E R REGION /MICRONS') 200 Figure 42. Performance of 0.005" Tubing Nozzle. 2000-I GOO-y- izoo u UJ BOO I— - 0 . 8 x l 0 1 6 0 atonvslen^kec G O © 0 0 0 O , 0 0 9 5 T U B I N G T U B E L E N G T H » P l A M E T E R O F T U B E N O Z Z L E - S H I M M E R S £ PA RATION ^ 3TOBE R O O M T E M P E R A T U R E DIA-• 018" S K ' / M M E R T C O L L . / M A T O R . UJ 400 Q 0 o 0 1 1 O 2 0 4o 6 0 P R E S S U R E IN 8 0 /oo 120 /40 160 NOZZ L E - S K I M M E R R E G I O N f M l C R O N S ^ Figure 43. Performance of 0.0095" Tubing Nozzle. in > I Goo->-/20O — L U 800 I— < CD 400 O Q 0 0 © © . 0 2 0 " HOLE LENGTH OF H O L E ^ fO x p i A M E T E R NOZZLE- S K I M N V E R P I T T A N C E ^ 3 X P I A M E T E R ROONA T E M P E RATT0RE • 0 I 8 " - S K I M M E R -F- C O L L I M A T O R . 0 0 O © 0 O 20 40 60 8 0 /OO /2o 140 160 180 200 P R E S S U R E I N N O Z Z L E - S K I M M E R R E G I O N ^ M / C R O / s / S ) Figure 44. Performance of 0.020" Nozzle. 31. skimmer assembly f o r a 0.0095" section of tubing at room and l i q u i d nitrogen temperatures are shown i n fi g u r e s 45, 46, and 47. These r e s u l t s show that the tubing produces a beam with properties s i m i l a r to those of our Laval nozzle. The bundle of c a p i l l a r i e s shown i n f i g u r e 48 consisted of many i n d i -v i d u a l tubings about 0.005 inches i n diameter. For t h i s set of measure-ments the skimmer and collimator openings were made by simply c u t t i n g round holes i n t h i n metal sheets. The dimensions of the tested assembly are shown i n f i g u r e 49. The r e s u l t s obtained are shown i n f i g u r e 50. Although the i n t e n s i t i e s obtained are a t t r a c t i v e l y large the large diameters of the skimmer and collimator allow an excessive flow of gas i n t o the skimmer-coll i m a t o r and magnet regions of our apparatus. G. Summary In our investigations i n t o the properties of beam formation by minia-ture supersonic nozzle systems.we have been guided by the desire t o obtain highly intense yet narrowly collimated helium beams at low temperatures. The beam i n t e n s i t y from our nozzle system was found to decrease considerably upon cooling of the gas and beam assembly t o low temperatures. The e f f e c t of nozzle-skimmer separations on beam i n t e n s i t y has been investigated i n considerable d e t a i l and the advantages of optimum nozzle-skimmer separation are demonstrated. Background pressure i n the nozzle-skimmer region has proven to have considerably a f f e c t on beam i n t e n s i t y providing the skimmer entrance i s downstream of the "Mach disk". The beam i n t e n s i t y was found to be very dependent on actual p h y s i c a l alignment of the nozzle-skimmer-c o l l i m a t o r system. Results obtained by varying the skimmer diameter were inconclusive. No p o s i t i v e r e s u l t s as to the e f f e c t of the sharpness of -009b" TOBlNG ROOM TEMPERATURE 5006 4000 bo 3000 (— — 200Of 5 ioool_ 6 o 2xio,fc NOZZLE P R E S S U R E x.x.x, — |57 M M , ZO^ > M M * Z - E R O " - O-OZT1' N O C O L L I M A T O R .018" S K I M M E R X / 13 <7 22 27 3 2 I N O Z Z L E D I A M E T E R S O 8 /6 24 3 2 4o 4.3 N O Z Z L E - S K I M M E R S E P A R A T I O N C REVS FROM vZERO , , v) Figure 45. Room Temperature Intensities for 0.0095" Tubing. .009S" TURING N O Z Z L E - S K I M N A E R SEPARATION* SOW— 0 "V REVS = 3 N O Z Z L E DIAMETERS A IS REVS - 1 2 . ^ * Q 22. REVS = 17 ^ " R O O M T E M P E R A T U R E N O C O L L I M A T O R #018" S K I M M E R 4000 *-o > 3ooo H £ 0 0 0 | 21 LU I— . z ; loool <c m O .'-ZERO1' -O.027" a -a U - T I L 1 I I I L O /4o 160 2 0 4 0 60 80 100 (2o N O Z Z L E PFLE -SSORE Figure 46. Room Temperature Intensities for 0.0095" Tubing. (80 2 0 o ,009S" TUBING LIQUID N / T R O G E N T E M P E R A T U R E -si © r u Z £ " f c O ' N O Z Z L E - S K ' I M M ER S E P A R A T I O N - O . O 2 . 7 NO C O L L / M A T O R O . 0 I 8 " S I < I M M E R /.6x fc>'6 Qtomsjcrrfjsec ,"3000f b <" 2ooo|— z looof 2 < U J CQ o _ - © — - O - - © - — _ J I I I I L J 1 I I 1 I 1 L _ J L _ i O 20 40 &0 BO /OO 12.0 I 140 /60 N O Z Z L E P R E S S U R E . f M M ^ IQO 200 Figure 47. Liquid Nitrogen Temperature Intensities for 0.0095" Tubing. S C A L E " . I CM = O.I IY\M Figure 48. Bundle of C a p i l l a r i e s used as a n o z z l e . -BUNDLE OF CAPILLARIES DIFFERENTIAL plRAN I SK IMMER ^ — C O L L I M A T O R PETEGTOfc-^ 4 I i . 5-" 15 % IT T 16 Figure 49. Geometrical Arrangement of M u l t i p l e C a p i l l a r y Device . 7200 _ CAPILLARIES ROOM TEMP. G400 S60O X ASoo X — X X 4000 X X — X h ^ 3200 X _ X X y 24oo — X 1 X ^ 800 C Q JL X 1 I 1 1 I I I < j IO 2 0 3 0 40 SO 60 70 P R E S S U R E IN M O Z Z L E - S K I M M E K REGION 6 A IC RONS') Figure 50. Performance of Multiple Capillary Device. 32. the skimmer edge were obtained although i t i s quite l i k e l y that the majority of our skimmers were so poor that any trends were obscured. Use of d r i l l e d holes and c a p i l l a r y tubing as nozzles showed that these devices produced beams of a s i m i l a r nature and i n t e n s i t y to those produced by the Laval nozzle. 33. CHAPTER V Beam intensities -available for the polarized He^ beam source In order to compare the results of beam intensity measurements made at various stages of development of the beam source i t i s necessary to relate the intensities to a common parameter. We have used the results in figure 31 to relate measurements made on the basis of nozzle-skimmer pressure to those based upon nozzle pressure. We have used the fact that beam intensity is inversely proportional to the square of the distance from the skimmer to relate intensities obtained with the d i f f e r e n t i a l pirani detector at different distances from the beam source. Using these conversion techniques we have plotted selected results on figure 51. The* results indicated with the symbols and CD show the values of intensities obtained during the original testing of the nozzle source at room tempera-ture. The results indicated by © , X, and Q are-representative of the intensities one can now reliably obtain at a nozzle-skimmer separation which keeps the tot a l gas flow into the skimmer-collimator region reasonable. These results are typically 2 - 3 times greater than those originally obtained. The results i^d.icated by are an example of results one can obtain with certain skimmer and nozzle arrangements. As can be seen from the figure these are approximately 10 times larger than those attainable for the same nozzle pressure with the original nozzle skimmer apparatus. Other results, not shown here, give beam intensities without a collimator approaching those corresponding to a DPD signal of SOOO t^t volts for certain nozzle-skimmer configurations at room temperature and for nozzle pressures less than 100 mm Hg. Unfortunately we are unable, as- yet, to reproduce 5ooo 4ooo 3000 2ooo looo — CX)oRlG/NAL N O Z Z L E S E T - U P DPD |6 C M F B - O M S K I M M E R . ® ORIGINAL NOZZLE S E T - U P RESULTS WITH DPD 76 CM FP.OM SKI M M £ R SCALED B Y 2 2 - 5" X ADJUSTABLE N O Z Z L E - S K I M M E R R E S U L T S F I6ORE 30 f4f*.evs") N O C O L L I M A T O R . 0 .009£""TUBIN& \ft/|TH COLLIMATOR. ( N - S SEPARATION ABOUT . 0 2 5 " ) C3 . 0 0 9 5 " " TUB/tf& CMODIFIEP^ NO COLUMATOR (N-S .SEPARATION ABOUT • O25"'0 th. .00 .95"" TUBING NO COLLIMATOR f N - S .SEPARATION O . O O l " ) ^ A ROOM TE(v\p. — 2KlOyfcatorrNS|Clr?-Kec. A K o o 00 1 o c 0 0 © 2S £"0 75" /OO /2£ ISO 175 ZOO N O Z Z L E P R E S S U R E ( M M HG") Figure 51. Comparison; of Beam Intensities. • 34. these i n t e n s i t i e s i n a r e l i a b l e fashion although there appears to be no reason why we should not eventually expect to achieve them. 35. CHAPTER VI 3 Possible Ion Currents from the Polarized He^ Ion Source From the r e s u l t s presented so f a r i t i s possible to estimate an 3 approximate ion current from our Polar i z e d He-' i o n source. I f we assume that the beam i n t e n s i t i e s are of the same magnitude f o r He^ and He^ we can o p t i m i s t i c a l l y assume that we w i l l have a beam corresponding approxi-mately to a DPD s i g n a l of 5000Revolts i n t e n s i t y at room temperature. From f i g u r e 22 we see that the beam i n t e n s i t y at l i q u i d helium temperature (/V/4°K) i s reduced from the room temperature i n t e n s i t y by a f a c t o r which i s approximately proportional to the square root of the temperature r a t i o ( i . e . s| 4/300 ). Thus, assuming the beam does not condense upon expansion, at 4°K we s h a l l assume that the beam i n t e n s i t y i s approximately 1/8 of the room temperature beam i n t e n s i t y . We s h a l l take the d i f f e r e n t i a l P i r a n i 12 o detector c a l i b r a t i o n to be 4x10 molecules/cm^/sec^/Uvolt and the area of -2 2 the magnet opening to be 7x10 cm . We w i l l assume the beam i n t e n s i t y to be constant across the magnet opening. I f we assume that 40$ of the beam a c t u a l l y passes through the magnet (50$ eliminated because of undesired spin and 10$ losses) and that our i o n i z e r , described by Vermette (Ve 64), has an e f f i c i e n c y of 1/4 of 1$ we f i n d a f i n a l ion current of approximately 0.02^t amperes. This assumes that we are able to extract from the i o n i z e r a l l those p a r t i c l e s ionized, and focus them i n t o a u s e f u l beam. 36. BIBLIOGRAPHY Ab 66 N. Abuaf, J.B. Anderson, R.P. Andres, J.B. Fenn and D.R. Miller, 5th International Symposium on Rarefied Gas Dynamics, Oxford (1966) In press An 65 J.B. Anderson and J.B. Fenn, Physic of Fluids 8, 780 (1965) As 66 H. Ashkenas and F.S. Sherman, 4th International Symposium on Rarefied Gas Dynamics, Volume 1 (Academic Press, New York 1966) Ax 65 D. Axen, Ph.D. Thesis, The University of British Columbia (1965) Br 66 R.F. Brown and J.H. Heald, 5th International Symposium on Rare-fied Gas Dynamics, Oxford (1966) In press Ca 66 R. Campargue, 4th International Symposium on Rarefied Gas Dynamics, Volume 2 (Academic Press, New York 1966) Fe 63 J.B. Fenn and J. Deckers, 3rd International Symposium on Rarefied Gas Dynamics, Volume 1 (Academic Press, New York 1966) Fe 66 J.B. Fenn and J.B. Anderson, 4th International Symposium on Rarefied Gas Dynamics, Volume 2 (Academic Press, New York 1966) Ja 64 D. Jassby, M.Sc. Thesis, The University of British Columbia (1964) Ka 51 A. Kantrowitz and J. Grey, Rev. Sci. Instr. 22, 328 (l95l) Ke 38 Kennard, Kinetic Theory of Gases, (Mc Graw - H i l l , New York, 1938) Ow 52 P.L. Owen and C.K. Thornhill, Report and Memoranda #26l6 Aero-nautical Research Council (1952) Ra 56 N.F. Ramsey, Molecular Beams (Oxford University Press, 1956) Sh 53 A.H. Shapiro, The Dynamics and Thermodynamics of Compressible Fluid Flow (Ronald Press, New York, 1953) Sh 63 F.S. Sherman, 3rd International Symposium on Rarefied Gas Dynamics, Volume 2 (Academic Press, New York, 1963) 37. Ve 64 C. Vermette, M.A.Sc. Thesis, The University of British Columbia (1964) Wa 63 J.B. Warren, W. Klinger and D. Axen, Progress i n Fast Neutron Physic, ed. by G.C. Ph i l l i p s , J.B. Marion, and J.R. Rissner (Rice University Semicentennial Publications) 335 (1963) 

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