A double focusing beta-ray spectrometer applied in heavy element studies

Iff S BH'II

lull

A DOUBLE FOCUSING BETA-RAY SPECTROMETER

APPLIED IN HEAVY ELEMENT STUDIES

A DOUBLE FOCUSING BETA-RAY SPECTROMETER

APPLIED IN HEAVY ELEMENT STUDIES

P R O E F S C H R I F T

TER VERKRIJGING VAN DE GRAAD VAN DOCTOR IN DE T E C H N I S C H E W E T E N S C H A P P E N A A N D E T E C H N I S C H E H O G E S C H O O L D E L F T OP G E Z A G V A N DE RECTOR M A G N I F I C U S IR. H. J. DE WIJS, H O O G L E R A A R I N D E A F D E L I N G D E R M I J N B O U W K U N D E , VOOR E E N C O M M I S S I E U I T D E S E N A A T T E V E R D E D I G E N OP D O N D E R D A G 2 M A A R T 1967 T E 16.00 U U R door W I L L E M L O U R E N S natuurkundig ingenieur ycborcn Ic Re O F F S E T D R U K K E R U

r-'^S

Dit proefschrift is goedgekeurd door de promotor

Prof Dr. A. H. Wapstra.

STELUNGEN

1. De vervanging van de scintillatie detector in een magnetische b e t a sp)ectrometer door een Si(Li) halfgeleiderdetector biedt üi het a l g e -meen geen doorslaggevend voordeel.

Dit proefschrift, hoofdstuk 4. •

2. Bij gebruik van de b e s c h r e v e n H a l l s t a b i l i s a t i e s y s t e e m a l s m e e t i n s t r u ment verdient het aanbeveling het gebruikte fasegevoelige d e t e c t i e s y s -teem te v ^ v a n g e n door een p i e k w a a r d e - d e t e c t i e s y s t e e m .

Dit proefschrift, hoofdstuk 6.

3. De meting van de d e s i n t e g r a t i e - e n e r g i e van 2 2 6 A C n a a r 2 2 6 i ^ zal, bij het beschikbaar komen van grote Ge (Li) d e t e c t o r e n , veel nauwkeuri-g e r kunnen worden uitnauwkeuri-gevoerd.

Dit proefschrift, hoofdstuk 9.

4. De door Valli geschatte intensiteit van de desintegratie van het 218 keV niveau in 217At over het 99 keV niveau is onjuist.

K. Valli, Acad. Sci. Fenn. n r . 165 (1964) 35.

5. Hoewel de door C o t h e m en Connor gemaakte opmerking, dat de keuze van de hoek waarop g e n o r m a l i s e e r d wordt voor hun a - Y hoekcorrelatie e x p e r i m e n t niet onjuist i s , moet het gebruik van hun methode van a n a -l y s e r e n ontraden worden.

C R . C o t h e m and R. D. Connor, Can. J o u m . of Phys Vol 42 (1964) 1805.

6. Het gedrag van de twee laagste 3 " niveaux in 86 Sr *), wat betreft hun desintegratie n a a r de twee l a g e r gelegen 2+ niveaux kan v e r k l a a r d w o r den door te v e r o n d e r s t e l l e n dat één 3 " , 2"*" p a a r het gevolg i s van n e u

-tronexcitatie en het andere van protonexcitatie. *) B.v.Nooijen e t al Nucl. P h y s . 6 3 ( 1 9 6 5 ) 2 4 1 .

B . v . Nooijen, p r i v . comm.

7. Het aanbrengen van een coïncidentie-voorwaarde in de l i n e a i r e poort van een analoog-digitaalomzetter, zoals gebruikelijk i s bij enkele m e e r - k a n a a l s impulshoogte-analysatoren,dient ten stelligste ontraden te worden.

8. Lippens concludeert uit de door hem geconstateerde c o r r e l a t i e tussen het watergehalte van boehmiet en de verlenging van de c - a s , dat twee e x t r a moleculen water in de eenheidscel een verlenging van 1.17*^A g e -ven. Deze conclusie is onjuist.

B . C . Lippens, d i s s e r t a t i e Delft 1961.

J . H . de B o e r , J . M . H . Fortuin, B . C . Lippens, W.H. Meijs J o u m of Catalysis 2 (1963) 1.

9. De detailhandel in elektrische en elektronische producten zal zich

meer moeten specialiseren in de reparatie van toestellen en het

verle-nen van goede "service",wil hij zijn positie t . o . v . de grote

warenhui-zen kunnen handhaven.

10. Gezien de beperkte mogelijkheden om leerlingen bij het middelbaar

on-derwijs vertrouwd te maken met de praktische zijde van de natuurkunde

zou een verrijdbaar laboratorium met deskundige begeleiding een

aan-trekkelijke oplossing bieden.

Aan mijn o u d e r s . Aan Ina, E s t h e r ,

CONTENTS Chapter 1 Chapter 2

Greneral introduction

General design of the s p e c t r o m e t e r 1. Introduction

2. The double focusing s p e c t r o m e t e r 3 . The type of double focusing s p e c t r o m e t e r 4. Conclusion

Chapter 3 P o l e - p i e c e s and fringing fields

11 14 18 3. 4. Introduction

Calculation of the shape of the pole-pieces 2 . 1 . General solution

2 . 2 . Application to the p a r t i c u l a r instrument Influence of fringing fields

Conclusion

Chapter 4 Construction of the s p e c t r o m e t e r 1. Introduction

2. P o l e - p i e c e s , central core and outer ring 3. Coils 4. Vacuum installation 5. Auxiliary equipment 5 . 1 . Source holder 5 . 2 . Geiger-MUller equipment 5 . 3 . Scintillation equipment 5 . 4 . Diaphragms Chapter 5 C u r r e n t stabilizer 1. Introduction

2. Electronical and mechanical realization 2 . 1 . Introduction 2 . 2 . Reference s y s t e m 2 . 3 . Amplifier s y s t e m 2 . 4 . Regulator system 2 . 5 . Protection s y s t e m 3. P e r f o r m a n c e 30 39

Chapter 6 A stabilizing system for magnetic s p e c t r o m e t e r s based

on the Hall-effect 46 3. 4. Introduction T e m p e r a t u r e stabilization 2 . 1 . Internal stabilization 2 . 2 . External stabilization The H a l l - g e n e r a t o r c u r r e n t Field regulator 4 . 1 . Introduction

4 . 3 . The influence of the magnet coil r e s i s t a n c e 4 . 4 . The influence of changes in amplification factor,

g e n e r a t o r c u r r e n t and b a s e - e m i t t e r potential 4 . 5 . Conclusion Stabilization set-up 5 . 1 . Block d i a g r a m 5 . 2 . Oscillator 5 . 3 . C u r r e n t - a m p l i f i e r 5 . 4 . Amplifiers 5 . 5 . Selective amplifier 5.6. P h a s e - s h i f t e r

5 . 7 . Phase sensitive detector and s q u a r e r 5 . 8 . C u r r e n t regulator and power supply Application

Chapter 7 Automatic operation of the s p e c t r o m e t e r 58 1. Introduction

2. Design considerations 3. Design description

4. Design of main operator and auxiliary equipment 4 . 1 . Main o p e r a t o r

4 . 2 . T i m e r

4 . 3 . Counter and p r i n t e r 4 . 4 . Mechanical step-counter

Chapter 8 Determination of the shape of the magnetic field 63 1. Method of field m e a s u r e m e n t

2. Application of the field-measuring method to some s p e c t r o m e t e r types

225 226

Chapter 9 Investigation of the decay of Ac and Ac 65 Introduction _„_

The decav of Ac

Instruments and source preparation 3 . 1 . G a m m a - r a y s p e c t r o m e t e r s 3 . 2 . B e t a - r a y s p e c t r o m e t e r 3 . 3 . Alpha-ray s p e c t r o m e t e r 3 . 4 . Coincidence s p e c t r o m e t e r 3 . 5 . Source p r e p a r a t i o n 4. Measurements and r e s u l t s „„, 4 . 1 . Alpha spectra (decay time of Fr) 4 . 2 . Electron spectrum

4 . 3 . The gamma spectrum

4 . 4 . a-Yangular correlation m e a s u r e m e n t s 5. Discussion

5 . 1 . Multipolarities

5 . 2 . a - Ydirectional angular correlation experiment 5 . 3 . Level scheme and spin assignment of "21pj, 5 . 4 . Spin and parity a s s i g n m e n t s in 217At and 213po

7. Instruments and source preparation

7.1. Instruments

7.2. Source preparation

8. Experiments

8.1. Electron spectrum

8.2. Gamma spectrum

8.3. The X-ray gamma coincidence experiment

8 . 3 . 1 . Introduction

8. 3. 2. Measurements and results

9. Discussion

9.1. The decay energy to 226^^

9. 2. The intensity of the decay to the groundstate of 226Ra

9. 3. Spin and parity for the levels in 226j{a and 226xji

9.4. Branching ratios in 6 ~ and E. C. decay

9.5. Groundstate of 226AC

Appendix

Summary

Samenvatting

References

Chapter 1.

General introduction

The nuclear spectrocopist occupies himself with the study of level schemes and their p r o p e r t i e s . This includes the positioning of energy l e v e l s , the evaluation of their spins and p a r i t i e s and of the decay r a t i o s between these l e v e l s .

All the information yielded i s used to t e s t the validity of n u c l e a r models in various regions of the periodic s y s t e m . These models d e s c r i b e some a s pects of the nuclear f o r c e s , the s t r u c t u r e of the nucleus and s e v e r a l p r o -c e s s e s that -can take pla-ce in nu-clei.

The most useful models will be recalled h e r e .

The shell model: this model, which has some analogy to the atomic Bohr model, has been worked out by Goepert Mayer (Go .^O) and J e n s e n (Je 50). The point of d e p a r t u r e Is the occurence of special stability of nuclei con-taining c e r t a i n n u m b e r s of neutrons or p r o t o n s . In the physical theory a potential is a s s u m e d for the average force working on a nucleon, which in first approximation v a r i e s with the square of the distance from the centre of the nucleus. The Schrödinger wave equation can be solved in t e r m s of a - disturbed - harmonic oscillator. The solution gives energy levels with a good fit to the reality if a strong 1-s (spin-orbit) coupling is a s s u m e d . This shell model p r e d i c t s spins and p a r i t i e s of ground- and excited s t a t e s , especially of even-odd or odd-even nuclei in the environment of the magic n u m b e r s .

The shell model i s refined in the independent particle model which explains s t a t e s formed by the coupling of t h r e e , five. e t c . nucleons. Similarly, in oddodd nuclei coupling between the last neutron and proton o c c u r s ; the r e -sults a r e described by the "Nordheim" r u l e s . The behaviour of the even-even nuclei in the regions of magic n u m b e r s also can be explained by means of the independent particle model.

Collective model: s y s t e m a t i c s of the position of energy levels and their spins and p a r i t i e s in some even-even nuclei- e . g . in the r a r e e a r t h region - and of transition probabilities between them indicate the o c c u r r e n c e of collective motions of s e v e r a l nucleons.

These collective motions can be interpreted a s deformations of the nuclear surface; rotations and vibrations of various types (Bo 53). They will be most prominent in easily deformable nuclei. These t j ^ e s can be expected between closed shells both for protons and neutrons since the d e c r e a s -ing stability will cause l e s s rigidity a s is the case with closed s h e l l s ; h e r e , the nucleus will normally even be deformed in the ground s t a t e . In the regions 152 < A < 186 and A > 224 where the deformation can be l a r g e , the rotational s t a t e s a r e lower than the vibrational ones, w h e r e a s in the unde-formed regions the vibrational s t a t e s will be the lower ones.

In consequence of these considerations the intrinsic quantum n u m b e r s for the single p a r t i c l e in the nuclear shell model will not r e m a i n good quantum n u m b e r s . This is taken into account in the unified model: calculations have been performed considering a coupling of the i n t r i n s i c wave functions of the nucleons and a collective wave function of rotational or vibrational nature

(Ni 55).

Nuclear shell model and collective model have been tested in v a r i o u s r e -gions of the p e r i o d i c s y s t e m . In the region of i n t e r e s t , the independent p a r t i c l e shell model i s found to r e p r e s e n t well the e m p i r i c a l data n e a r the closed shells at Z = 82 and N = 126 (200 < A < 215), w h e r e a s the Nilsson model, v e r s i o n of the unified model, has been applied v e r y succesfully for m a s s n u m b e r s above 228.

F o r the intermediate region, the applicability of both models i s somewhat questionable. Availability of m o r e p r e c i s e experimental data in this region would be of g r e a t help.

This t h e s i s d e a l s with the study of two artificially p r e p a r e d isotopes 225AC and 2 2 6 A C and t h e i r daughter products which have partly a collective n a -t u r e , p a r -t l y (for lower m a s s ) single and many p a r -t i c l e n a -t u r e .

The study of these nuclei gives information about the nature of the energy l e v e l s in s e v e r a l nuclei, the decay branching r a t i o s between t h e s e levels and the a s s i g n m e n t of spins and p a r i t i e s to these l e v e l s .

The d i s c r e t e e n e r g i e s of the a - r a y s a r e of g r e a t advantage in the study of alpha emitting r a d i o active p r o d u c t s : they allow e a s y constructing of the level scheme of the daughter nucleus. Moreover the t r a n s i t i o n s p r o b a b i l i -t i e s of -the a - r a y s can be of help in -the a s s i g n m e n -t of quan-tum n u m b e r s -to the energy l e v e l s . The alpha s p e c t r a have been studied by the use of a s e m i -conductor d e t e c t o r when n e c e s s a r y .

A very useful tool in the study of the heavy elements is an e l e c t r o n s p e c t r o -m e t e r with a reasonable resolving power. This a p p a r a t u s is then used to study the conversion e l e c t r o n s p e c t r a which accompany the gamma r a y t r a n s i t i o n s between the excited levels in a nucleus. The e n e r g y differences between s u c c e s s i v e energy l e v e l s in these heavy nuclei a r e r a t h e r s m a l l .

Thus s e v e r a l g a m m a t r a n s i t i o n s between them exist often at r a t h e r low e n e r g i e s . Because each Y-transition yields a complex conversion e l e c t r o n s p e c t r a , a good resolution of the analyzing apparatus is highly d e s i r e d . A magnetic s p e c t r o m e t e r with a fixed r e l a t i v e momentum r e s o l u t i o n shows the b e s t r e s \ ü t s in the lower p a r t of the s p e c t r u m , w h e r e a s s e m i - c o n d u c t o r devices with a n e a r l y fixed absolute energy resolution - slightly i n c r e a s i n g with energy - a r e competative a t high e n e r g i e s ( > 1 MeV); s o m e t i m e s they a r e p r e f e r r e d because of t h e i r l a r g e r efficiencies.

The heavy e l e m e n t s a l s o show r a t h e r l a r g e e l e c t r o n conversion coefficients compared to the lighter nuclei, thus the study of gamma t r a n s i t i o n s - by observing K, L, M, e t c . conversion e l e c t r o n s in a magnetic s p e c t r o m e t e r - i s v e r y a t t r a c t i v e .

A u g e r - e l e c t r o n studies in this region a r e not so v e r y useful on accovmt of the l a r g e fluorescent yield which c a u s e s a s m a l l amount of Auger e l e c t r o n s . In t h i s t h e s i s the design and construction of a double focusing e l e c t r o n s p e c t r o m e t e r is d e s c r i b e d . The considerations concerning the choice of the type will be a l s o explained.

T h e r e a l s o will be paid attention to e l e c t r o n i c p r o b l e m s , a r i s i : ^ when e m -ploying t h i s type of s p e c t r o m e t e r .

In the c o u r s e of the investigations some other instrumentation was used; since t h e r e a r e no p a r t i c u l a r r e a s o n s to d e s c r i b e them in s e p a r a t e chap-t e r s , chap-they a r e menchap-tioned in chap-the chapchap-ter dealing wichap-th chap-the m e a s u r e m e n chap-t s (chapter 9).

Although the e l e c t r o n - s p e c t r o m e t e r proved very profitable in the study of heavy e l e m e n t s , this was not the motive for i t s construction. It was u n d e r -taken originally in o r d e r to gather experience for the construction of a much l a r g e r t\'pe of electron s p e c t r o m e t e r , which would be used for the study of neutron-capture g a m m a - r a y s , by studying their compton e l e c t r o n s . The development of the Ge(Li) s e m i - c o n d u c t o r s , which for the s a m e resolution have a much higher efficiency for Yray detection, gave cause not to c o m -plete the original p l a n s .

Chapter 2.

General design of the s p e c t r o m e t e r . 1. Introduction

The b e t a - r a y s p e c t r o m e t e r offers the possibility to get information about n u c l e a r decay s c h e m e s .

Several types of s p e c t r o m e t e r s exist; t h e i r quality depends on the kind of r e s e a r c h to which the tool will be applied. The Investigation of d i s c r e t e e l e c t r o n t r a n s i t i o n s e . g . conversion e l e c t r o n s and Auger e l e c t r o n s r e -(juires a good momentum resolution and a reasonable efficiency. The study of 6;continua and the possibility for coincidence m e a s u r e m e n t s between g and, e . g . Yrays, mainly r e q u i r e s a l a r g e efficiency at a reasonable r e s o -lution.

Since the m a i n purpose of the i n s t r u m e n t under discussion will be the study of conversion e l e c t r o n s , a type of s p e c t r o m e t e r m u s t be chosen which c o m e s up to r e q u i r e m e n t s , stated f i r s t . A dquble focusing type of s p e c t r o m e t e r , p o s s e s s i n g an axially s y m m e t r i c magnetic field with a plane of s y m m e t r y p e r p e n d i c u l a r to the r o t a t i o n s y m m e t r y axis will be suitable for this p u r -p o s e .

2. The double focusing s p e c t r o m e t e r .

The theory of this i n s t r u m e n t h a s been discussed in the excellent review a r t i c l e s of K. Siegbahn (Si 65) and T. R . G e r h o l m (Ge 56) and will not be d i s -cussed h e r e in detail. We only will mention the points which a r e important in view of the instrument to be constructed. The principles of electron t r a j e c t o r i e s in an axially s y m m e t r i c field with a plane of s y m m e t r y a r e

developed by Svartholm (Sv 46) and Siegbahn. The magnetic field in the median plane i s expanded around a c e n t r a l - o r b i t (see fig. 1) a s :

B ^ ( r , o ) = B^ / l + ap + B p 2 + j (1) where

s/ / d B I „ ^ 2 / d ^ B \ P M r - r ^ ) / r ^ — V B J d F j r ^ ^ = ^o / B ^ ( - ^ j ^^ (In the median plane the r a d i a l component of the magnetic induction is zero)

In the case of double focusing (a = - j ) , see for instance Svartholm (Sv 46), the r a d i a l and axial focusing for p a r a x i a l r a y s takes place at an angle e of IT¥"2 r a d i a n s (see fig. 1).

When a does not have the p r o p e r value of - 5 , e . g . - ^ ( 1 - e ) , f o r p a r a x i a l r a y s in the median plane, according to Svartholm (Sv 49), an a s t i g m a t i c e r r o r in the image plane at e = ^ \^2 r a d will be introduced, c a u s i i ^ a line broadening of 6 <. = r sf eir V~2 where (f i s the r a d i a l a p e r t u r e angle. Shull and Dennison (Sh 47) have calculated in second o r d e r the image c o o r -dinates of an e l e c t r o n emitted at (r + A r) and A z at 9 = 0, at angles it»r and i)) z respectively to the tangent on the c e n t r a l orbit. T h e i r r e s u l t s c o m -bined with the d i s p e r s i o n found by Svartholm (Sv 46) for the double focus-ing s p e c t r o m e t e r fix the b a s e - l i a e resolution RQ a s :

R s w ^ 4 6 ^ 2 ^ 1 ^ o 4r 4 r ^^^2 6

8S-3

(2)

where s is source width; w is the defining slit of the electron detector, h i s and and r e p r e s e n t the a p e r t u r e angles.

source height,

The choice of 3 depends on the kind of aberation - with a chosen shutter system - one wants to s u p p r e s s . A choice 6 = 1/8 c o r r e c t s for defocus-ing caused by the radial opendefocus-ing angle.

fig. 1.

Symbols explained in the text

The value 6 = 1/4 is not used p r i m a r i l y to diminish aberations but only to achieve a field form which can be established easily with iron pole pieces of a conical shape (Sv 49), (Ar 55).

A value 0 = 3/8 m a k e s the resolution nearly independent of the axial opening angle.

It a l s o offers the possibility for double f o c u s i i ^ next other orbits than the central orbit (He 50), which is n e c e s s a r y for photographic recording of m o -mentum s p e c t r a o r the use of an a r r a y of semi-conductor d e t e c t o r s for r e g i s t e r i n g similtaneously on s e v e r a l o r b i t s . An even more ideal field for this purpose is suggested by Wild and Huber (Wi 57) namely a field varying

a s :

B(r) = B^ -1/2

The s e r i e s expansion of this field is B ( r , o ) = B

" ( ' •

ly^p + 3/8p^ - 5 / l 6 P ^ +

which uses for the first two coefficients the s a m e values a s considered b e -fore.

More arguments in favour of the value 6 = 3 / 8 a r e that the value contain-ing the source height is s m a l l e r than in the case B = 1/8.

Taking all of these factors into account we chose the value 3 = 3 / 8 . The relation between solid angle fi = i^ -tfe and fixed resolution Rg depending

TT

only on s p h e r i c a l aberations gives (Vr 60): 0 . 5 5 R ( 1 - 8 B ) (3fi - 3 ) - ^

s ^ ' 3

(3)

This relation does not indicate a c l e a r choice between 1/8 and 3 / 8 . In o r d e r to reduce the s p h e r i c a l a b e r a t i o n s further one can extend the e x -pansion (1) to third and higher o r d e r t e r m s . The realisation of the effect of this expansion depends greatly on the a c c u r a c y obtained with the f i r s t two t e r m s . Since the machining of the polepieces (see next chapter) n e c e s s a r y in o r d e r to obtain the d e s i r e d field c a u s e s already many p r o b l e m s it was not considered usefull to include higher o r d e r t e r m s .

3. The type of double focusing s p e c t r o m e t e r .

Based on the p r i n c i p l e s , mentioned before, many s p e c t r o m e t e r s have been constructed (He 50), (Ba 62), (Ch 64), (Gr 60) and (Si 64). They may be s e p a r a t e d into two main groups. In the f i r s t group - the iron free

i n s t r u m e n t s - the d e s i r e d field is r e a l i s e d with the aid of a combination of coils. In the second group - the iron containing i n s t r u m e n t s - the field i s obtained between iron pole p i e c e s of a suitable shape.

fig. 2a, 2b.

Double focusing magnets

^ ^ •q ^ r

i

v\

_^1

11

h^'^XK^

.-^M^

i

In the l a t t e r group the exciting coils a r e a r r a n g e d around a central iron core (fig. 2a) or inside an iron outer wall (fig. 2b). The f i r s t a r r a n g e m e n t has the advantage of easy accessibility to the vacuum tank; the second a good control of fringing fields.

The choice of the s p e c t r o m e t e r type suitable for our purpose depends for the g r e a t e r p a r t on the r o o m in which the instrument must be placed. A strong demand for an iron free instrument is the absence of iron in the environment of the s p e c t r o m e t e r .

We chose for the construction of an iron containing i n s t r u m e n t , since the r e q u i r e m e n t s demanded by an iron free s p e c t r o m e t e r could not be fulfilled. At f i r s t the intention was to build an instrument with a central c o r e , because of the good accessibility to the vacuum tank. However, calculations (see chapter 3) and m e a s u r e m e n t s (see chapter 8) showed a r a t h e r strong e d g e -effect for this type.

Finally a combination of the two depicted types of iron s p e c t r o m e t e r s has been chosen to get rid of the fringing fields, w h e r e a s the p o s s i b i l i t i e s of achieving a good field shape a r e g r e a t e r than in the case of a magnet excited by a single coil.

4. Conclusion.

The i n s t r u m e n t whose construction will be d e s c r i b e d in the following chapters is of the doublefocusii^ type with a field in the median plane satisfying the following equation:

B^(r,o) = B ^ / l - V ^ p + 3 / 8 p 2 ) {4, The field is r e a l i s e d by means of iron p o l e - p i e c e s , for which the

Chapter 3.

P o l e - p i e c e s and fringing fields. 1. Introduction.

In the preceding chapter the p r o p e r t i e s of a double focusing magnetic field have been outlined. The problem of obtaining this type of field with the aid of iron p o l e p i e c e s will now be d i s c u s s e d . Since the d e -rivation of the pole shape holds only for infinite a r e a , attention will be paid to edge-effects. This is n e c e s s a r y , since at f i r s t we had the intention to construct a s p e c t r o m e t e r with a central iron core. This type of spectroipieter has the disadvantage of hard to control fringing fields which can cause an intolerable influence on the d e s i r e d field shape. It will be seen in the conclusion that there a r e indications for such influences.

In the following discussion calculations of E l g e r s m a (El 62) a r e used. These calculations were c a r r i e d out to find a suitable field shape for a C o m p t o n - s p e c t r o m e t e r .

2. Calculation of the shape of the p o l e - p i e c e s . 2 . 1 General solution.

The d e s i r e d field shape p o s s e s s e s cylindrical s y m m e t r y around a z-axis and a l s o m i r r o r s y m m e t r y with r e s p e c t to a median plane (z = 0). F u r t h e r m o r e it is a s s u m e d that the iron has an infinitely large p e r -meability, so that the surfaces of the iron may be considered to be equipotentials.

Cylindrical coordinates will be used (r, 0 , z). The magnetic field is not a function of the angle 0 a s a consequence of s y m m e t r y p r o p e r t i e s and can therefore be described a s vector B ( r , z ) . This can be related to the magnetic s c a l a r potential $ :

B = - g r a d <t (1) B ^ ( r , z ) - - j j . (2)

B^(r,z) = - i l (3)

When there is no c u r r e n t in the space between the pole-faces the Max-well equations become:

div B = 0 (4) and r o t B = 0 (5) These equations give for the magnetic potential:

3 % ^

3 z 2

o r

3 r ^ 1

+ — _{r 3 r (6)}

The boundary conditions for the d e s i r e d field follow from the m i r r o r s y m m e t r y with r e s p e c t to the median plane and from eq. (2.4)

B (r,o) = 0 (7)

and

B , ( r , o ) = B^ n -\J2 P+ 3/8.1^1 (8)

The Laplace equation (6) with the conditions (7) and (8) a r e solved with a method given by Axner (Ax 55).

One looks for a solution in the form of a power s e r i e s in r / r with coefficients A that depends on z / r .

We define the following quantities:

=/r and r / r = "1 o We t r y the solution: n = k ^^^ ' J ' ( r , z ) = - B r ) a n A . ^ ^ ' ' o o ^—' n ' n(^ n = o (^) (9)

Subst. (9) in (6) and find: n = k - B r ) a o o L—I n n = o dA^(x) (n+1) Aj^(T) (2n+l) T -d x 2 ^ \ ( ^ ) + (1+T^) 2 — dT = 0

Hence A ^ ( T ) m u s t satisfy the differential equation: d"A ( T ) dA (,)

(1+T^) % (2n+l)T 2 + (n+l)^ A (x ) = 0 dx d x ^

(10)

with the conditions A (0) = 0

d A ^ dx

= 1 (12)

Eq. 3-10 is a h y p e r g e o m e t r i c differential equation. The solution can be given in a s e r i e s of even and odd powers of T .

A ( T ) = P

n^ ' c . j ' ^ Q

E

' 2 V + 1 C.X

V = o V = o

By substituting (13) in (10) we find the r e c u r r e n c e r e l a t i o n s : 2 (2 v - n - 1 ) "v-i-l (2v+2) (2v+l) (13) (14) and (2v-n)^ •v+1 (2v+2) (2v+3)

The power s e r i e s of (13) a r e convergent for IT I<1, or z / r < l . By using the boundary conditions (11) and (12) we find:

A (o) = 0 = P . c + Q. 0 = P.c = 0 n^ ' o ^ o

So P = 0 , or c = 0 and both of these conditions imply that

(15)

P E

1 = Q . c . Putting c = 1 and Q = 1 we find o o

for the solution of eq. (6):

( r . z ) = - B ( o^o l_^ ) ' ^ f e j n = o > ' n+1

-^

^(fl

c = 1 (19) n , o ' The coefficients A (x) have some p r o p e r t i e s , which r e q u i r e our

attention. By differentiating (10) we find: d^A (.) d^A ( T ) 2 ' ^ n ^ ^ ) (1+ T) (2n-l) X + n -^— = 0 (20) J 3 , 2 , d X d T dx By replacing n by (n-1) in (10) we find: . , 2. d \ _ i ( x ) d \ _ ^ ( , ) 2 ' ^ n - l ( T ) „ (1 + x ) 7. (2n-l)x 5 + n = 0 d x dx d x (21)

which is the same a s (20) if A i ( x ) = r -n - 1 dx

dA (x) n^ '

(22)

This m e a n s that if A (x) is known, A _-, (x) and A , i (x) a r e found by differentiation and integration respectively.

2.2 Application to the p a r t i c u l a r i n s t r u m e n t .

As stated before (Ch. 2) the magnetic field in the median plane has to obey the following equation:

B^(r,o) = B^ | l + ap + Bp^ + } (23) We want to approximate the field to the second o r d e r , so we a r e only

i n t e r e s t e d in t e r m s with 1, a and g . We can w r i t e (23) a s :

B^(r,o) = B ^ ( l - a - B ) + B ^ ( ( , - 2 g ) ( r / r ^ ) + B^g ( r / r ^ ) ^

According to (16) the magnetic s c a l a r potential b e c o m e s :

$ ( r , z ) = - B ^ r ^ ( l - a - 6 ) (r/r^)A^(T) - B ^ r ^ ( a - 2 B ) ( r / r ^ ) \ ( T )

- ^ 0 ^ 0 ( ^ / ^ o ) ' ^ 2 ( ^ ) (24)

We now calculate the value of A (x), A (x) and A (x).

The f i r s t value obtained with the°aid of (13), (18) and (19), is

By integrating relation (25) and by taking into account the determination of a p r o p e r constant, one finds A (x) to be:

A^(T) = - r - V s ^^ (26) On the other hand it i s s i m p l e r to determine A2(x) by m e a n s of the

r e c u r r e n c e relation (18) and equation (13).

The s a m e appear for A..(x), from relation (23) (see Axner) (Ax 55), we find:

Aj^(x) = 3/4 x U l + x 2 + l / 4 ( l - 2 x 2 ) In (x +\fü^) (27) or by using (18) and (13), this may be written in s e r i e s form:

A (x) = X- ( l / 3 ! ) x ^ + ( l / 5 : ) x ^ - ( S V D T ' ^ + ( 5 V 9 ! ) x ^ . . . (28) The e r r o r made by stopping the s e r i e s after the k t e r m is s m a l l e r than the (k+1)™ t e r m .

The s p e c t r o m e t e r whose construction will be described in the next chapter u s e s the following values for a and 8 .

a =-1/2 (29) g = 3/8 (30)

(The choice of these values has been elucidated in the previous c h a p -t e r ) . The cons-truc-tion design fixes -the cen-tral orbi-t -to be r = 25 cm. The maximum solid angle of about 1% of a sphere fixes the distance between the p o l e - p i e c e s at r = r = 2 5 cm to z = 7 cm.

In o r d e r to find the equipotential surface going through the point (25,7), we calculate $(25,7) by using (24), (25), (26), (27), (29) and (30). We find: $(25,7) = -0.5296 = 1.875 V r - 1 . 2 5 ( V r )2 .

[ 0 . 7 5 V r y i + f / r ) 2 + 0 . 25 / l - 2 ( ^ / r ) 2 I n / ^ / r +

*f^+^\ + 0.375(Vr^)2|Vr - ^/i^/vA

(31)

The z - c o o r d i n a t e s of the p o l e - p i e c e s have been calculated for d i s c r e t e values of r , a s indicated in table 1 by using eq. 3 - 3 1 .

Table 1. r z r 11.5 cm 5.074 cm 25.0 12.5 ' 13.5 ' 14.5 ' 15.5 ' 16.5 ' 17.5 ' 18.5 ' 19.5 ' 20.5 ' 2 1 . 5 ' 22.5 ' 2 3 . 5 ' 24.5 ' 5.208 ' 5.346 ' 5.484 ' 5.626 ' 5.768 ' 5.913 ' 6.058 ' 6.204 ' 6.350 ' 6.497 ' 6.642 ' 6.787 ' 6.929 ' 25.5 26.5 27.5 ' 28.5 29.5 ' 30.5 31.5 3 2 . 5 33.5 34.5 35.5 36.5 37.5 z cm 7.000 7.069 7.206 7.339 ' 7.467 7.591 7.708 7.818 7.921 ' 8.016 8.101 8.176 8.243 8.297 3. Influence of fringing fields.

In the introduction we mentioned that the calculation of the shape of the p o l e - p i e c e s holds only for infinitely l a r g e s u r f a c e s . Some information i s d e s i r e d about the effect of the pole-edges on the z-component of the magnetic field in the median plane.

We s t a r t with the Laplace eq. (6) 3 ^ * 1 3 $ S^*

+ + = 0 (6) 2 2

3r r 3 r 3z

In the p r e s e n t c a s e , however, we a r e only interested in the field n e a r the edge. Hence the second t e r m in (6) will be neglected; it is to the o r d e r (magnetic gap divided by the d i a m e t e r of the magnetic poles) s m a l l e r a s the other two t e r m s (Ro 38)

The equation

+ = 0 (32)

2 2 3r 3z

r e p r e s e n t s a two-dimensional c a r t e s i a n problem, the solution of which can be given by means of the use of complex v a r i a b l e s .

In o r d e r to get a simple problem, we f i r s t make some a s s u m p t i o n s : ' the curve of the pole-pieces is neglected

' ' the p o l e - p i e c e s a r e a s s u m e d to be infinitely thin

' ' ' the p o l e - p i e c e s a r e r e p r e s e n t e d a s two semi-infinite planes at a distance 2d. (fig. 3)

1

t = id G

$ = ï ,

t=-idG

fig. 3

Map of the t-plane for infinite thin p o l e - p i e c e s separated at distance 2d. The direction of transformation i s given by a r r o w s .

We introduce a complex variable t = r + iz.

The complex t-plane - chosen a s shown in the figure - i s now con-sidered to be a degenerate polygon to which the method of conformal mapping can be applied by means of the Schwartz transformation. Furtiier a potential f is introduced which is conjugeted to the a l -ready known -potential *. The lines of force a r e given by H" = con-stant. F u r t h e r m o r e we introduce another Laplace equation:

? 9

d W 3 W Sr^ Sz^ with

W = 4» + i* (33) For 'i' and * we have the Cauchy-Rlemann relations

di) 3$ — = (34) 3 r 3 z and 3i); 3 $ 3 z 3 r (35) The p o l e - p i e c e s a r e two equipotential s u r f a c e s with potentials +* and

- $ , respectively a s is shown in the figure.

By a metiiod of conformal mapping known a s the Schwartz-Christoffel transformation (Mo 53), (Ko 27) we t r a n s f o r m the tplane into a w -plane in which the poles form the whole r e a l a x i s , the i n t e r i o r and e x t e r i o r of the p r o b l e m is transformed to the w-plane. (coordinates). At the same time we t r a n s f o r m the complex W-plane = t + i $ to the w-plane (potentials).

The transformation for the coordinates is a differential equation:

a

d t <. I I _ __n

— = Cj I ; w - w ) Ti (36) dw " "

where a and w a r e suitable r e a l constants.

n n

We take the t r a n s f o r m a t i o n path a s i s given in fig. 3 and find for the e x t e r i o r angles a ;

^ n

a = - IT, "o "^ " ^'^d ",, = - I I .

We a s s i g n the c o r n e r on each pole the value w = i 1 and to the value t = oo + id we a s s i g n w = 0 .

Thus the transformation in this case b e c o m e s : dt w ^ - l

(37)

dw w

C i s a constant defined by the boundary conditions. By integrating we find:

t = C (iw^ - In w) + c ' (38)

The constants C and C a r e determined in the following way:

t = id — > w = 1 t ^ i d > w =-1

1 fT Substituting these values for t into (38) gives with w = - 1 = e :

2d ƒ 2 ) = — < | ( w - 1) - In w + |iTT I

M ƒ

(39) The transformation from the W-plane into w-plane is simple because we have only two equipotential s u r f a c e s with one e x t e r i o r angle a = TI and the value of W in this point is t r a n s f o r m e d to w = 0 so w = 0 . The t r a n s f o r m a t i o n b e c o m e s :

dW ^B_ dw w

with boundary conditions (ti=+<i> a t w = j ^ l Integrations of (40) gives: ° (40) W = B In w + B W = B In I + B . i . a r g w + B (41) 25

and b e c a u s e W = 'P + i * we find for B and B respectively: 2*

and

B=--2 (42)

B ' = i * o (43) We now consider W = 'J' + 1 * . Differentiating with r e s p e c t to t gives:

dW 3 $ 3 $ dt 3 r 3 r

using the Cauchy Riemann relations (34) and (35) we find: dW 3 $ 3 *

= + i = - B - iB dt 3 r 3 r ^ ^

F r o m ^ = • ^ • • ^ ' s u b s t i t u t i i ^ (40) and (37) and using (42) we get:

$ 1

B + IB = - 2 . ^ - (44)

We a r e only i n t e r e s t e d in the r e a l p a r t of (44) so we substitute for w

i V ^ = iv (v is a r e a l variable) (45) * 1

and find B = 0 and B = - — . (46) ^ ^ d v+1

We use (45) also for substitution in (39) and get:

z = 0 , r = - ^ (v + l + lnv) (47) With (46) and (47) we obtain a magnetic field in the median plane n e a r

the edge a s given in fig. 5 curve a. (d = 7 cm).

In o r d e r to refine the calculations we can also take into account a finite thickness of the p o l e - p i e c e s b .

The way of conformal mapping for the coordinates i s now given in fig. 4, see also Kottler (Ko 27).

ï = i ,

m

Tw:

:S

Map of the t-plane for pole-pie ces with thickness b s e p a r a t e d at distance 2d. The direction of t r a n s f o r -mation is given by a r r o w s .

The e x t e r i o r a i s l e s a r e a , = -ITI , a„ = -ITT , an ^ '" < " 4 ^ " i ' " ^^'^ a = - è " , the transformation to the w-plane i s p e r f o r m e a in such a way that for t = jf id we get Wj^ - + X and for t = j ^ (d+b)i

w b e c o m e s Wjj = i y .

The Schwartz-Christoffel transformation gives:

2,è

dt ( W ' - A " ) ^ ( W ^ ' - U ^ ) ^

— = C

dw w With the boundary conditions we find for C: C The integration of (48) than y i e l d s :

-2d.

(48)

t = r + iz = id iU(^ -W ) (y -W ) j O 2, , 2 2, ^ '''^ d.

In + A yd In ^y^ -w + yl/u -w (49)

The transformation of W is the same a s in the previous problem and i s : dW dW Integration of W = _ B w (50) yields: In w + 1* (50) 27

dW

Using the derivation for -TT- we find with (48) and (50)

*o 1

B 7 + i B _ = - — 1 ( H M n 11

^ dv V(A -w'^) (y -w"^) (51) The values for A and y a r e found by means of the following eq.

2 /2d+b\ 2

y + A = 1 (52)

and

/2 b \ 2

U - A = (53) These equations a r e foimd in considering the conformities in the t - and

w-plane at w = 0 and w = + ~ .

The e x p r e s s i o n s for B^ and t a r e found with the substitution of (45) in (49) and (51). d n " {v+u ) (v+A ) for t we find: Q-|-Q i / \ 7 - i - i i -4- \i xr-1-^ t = id - d \ / ( v + y ^ ) (v+A^) - — i n , ^ — ^ - , - ^ - ^

d+b yv+y + \Jv+X

\f^-\P

and find for r :

\ I ; ;- d+b \ / v T 7 +\/v+ A^

r = -d\/(v+y^) (v+A^) l n , \ , .y „ +

V 'T yv+y"^ -Uv+ A'^

. ! , „ v\/t^v^x]fWv

The relation between B and r i s shown in fig. 5 curve b . (d = 7 cm, b = 1 c m . ) .

fig. 5

r(cm)

Deviation from homogeneity caused by edge-effects curve a: F o r infinite thin pole-pie ces

curve b : F o r p o l e - p i e c e s with finite thickness. 4. Conclusion

The d i a g r a m s of fig. 5 a r e related to an originally homogenous field shape. In reality the field has to d e c r e a s e about 2%/cm towards the outside. This can be derived with the aid of eq. 2 . 1 by differentiating this gives:

AB

= a p +

Substituting a = - g and neglecting the second t e r m gives the mentioned value.

The field shape i s realized by curved p o l e p i e c e s . The distance b e -tween the pole faces is not a constant. F o r the calculations of the edgeeffect we used the average pole distance, however, the e d g e -effect will possibly l a r g e r than calculated in this way. Thus the following conclusions have to be considered a s lower l i m i t s . The d i a -g r a m s show in the re-gion of i n t e r e s t (21 cm to 29 cm) a d e c r e a s e of the field with an average of 0.15%/cm. This value is 7.5% of the d e s i r e d value and will probably add to the calculated d e c r e a s e . Thus we expect a roughly 10% too high r e a l i z e d value of a . M e a s u r e m e n t s , mentioned in chapter 8, have confirmed these expectation. The c a l -culations and the m e a s u r e m e n t s caused a divergence of the original plans. A s p e c t r o m e t e r which will not p o s s e s s the inconvenient fringing fields and which has some possibilities for c o r r e c t i o n s of the field shape will be d e s c r i b e d in the next chapter.

Chapter 4.

1. Construction of the s p e c t r o m e t e r . 1. Introduction

The motivation of the choice of the s p e c t r o m e t e r is given in chapter 2. At f i r s t a s p e c t r o m e t e r has been constructed consisting of a central core and p o l e - p i e c e s enclosing a chamber in which the focusing of the e l e c t r o n s can take p l a c e . However, after completion of this s p e c t r o m e t e r p r e l i m i n a r y m e a s u r e m e n t s showed a too strong ec^e-effect, which spoiled the demanded field distribution (chapter 8). It was decided to entirely surround the m a g n e -tic gap with iron by adding an iron wall between pole faces at the outside of the s p e c t r o m e t e r .

The machining of the p o l e p i e c e s m u s t be c a r r i e d out very carefully, b e -cause these p a r t s of the s p e c t r o m e t e r determine the shape of the magnetic field (see chapter 3). The quality of the s p e c t r o m e t e r depends a g r e a t deal on these p a r t s . The construction of the iron p a r t s of the s p e c t r o m e t e r i s described in section 2.

The magnetic field is generated by m e a n s of coils fed by a well regulated d i r e c t c u r r e n t . The construction of the coils will be considered in section

3. and the regulation of the c u r r e n t in chapter 5.

The electron momentum analysis has to take place in a vacuum, so it must be possible to evacuate the chamber between the poles. The vacuum c h a m -b e r and s y s t e m a r e descri-bed in section 4. Finally in section 5. we will pay attention to the s o u r c e - h o l d e r , adjustable diaphragms and counter s y s t e m s .

2. P o l e - p i e c e s , central core and outer ring

Before starting with a description of the construction, we first have to e v a -luate some dimensions. The dimensions of the lathe on which the pole-pieceg had to be machined allowed a maximum pole face d i a m e t e r of 75 cm. This value caused some trouble since calculations of the fringing fields (chap. 3. 3.) indicated that a l a r g e r value would be favourable. The occuring e d g e -effects a r e now compensated by the use of the iron wall mentioned in the above introduction.

Since we want to use a s little iron a s p o s s i b l e , because of the weight, we now calculate the minimum thickness of the pole-plates at the edge and at the place of the central c o r e .

The values for the radius of the central core and the height of the p o l e - p i e c e s at the edge and near the core have to be established in such a way that the maximum p e r m i s s i b l e induction of about 0.8 \V/m^, in t h e ' i r o n to be used (Armco), never will be exceeded.

The s p e c t r o m e t e r will be designed to focus e l e c t r o n s up to an energy of 4 MeV. F o r t h i s energy the induction at the central path has to be 6.10"2 W / m 2 .

The following calculations have been c a r r i e d out for the original s p e c t r o m e t e r . Although they a r e not completely applicable to the p r e s e n t s p e c t r o m e t e r they give useful information about the magnetic fluxes in the iron p a r t s and in the gap.

The evaluated dimensions will not differ much in both types.

We have calculated (chapter 3) the fringing field for a polepiece which is 1 cm thick at the edge; we will now check whether this value can be tolerated at the l a r g e s t inductions used.

In chapter 3 eq. 51 we found for:

! ^ = ^ z - iB^ = - \ l ' 2 2], 2 \ (1) I 71 d w (A - w ) (y - w ) At the edge: $ 1 ^ t = ^ r = " ^ \ ƒ, 2 2, , 2 2, • (2> nd \ / ( w -A ) (u -w )

The average value of B i s :

y y

/

1"^

(4)

Using eq. 52 and 53 of chapter 3 we find: _ 2'$

B = — 2 l n / w (5)

^ 7Tb

With the same equations it follows from b = 1 cm and d = 7 cm \? = 0.540

The value for d a t the edge is about 8 cm.

F o r the maximum induction of 6.10~2 W/ni2 we find for * the value: o

* = 48.10"'^ W / m o

With eq. 4-5 we find: B = 0 . 1 6 W / m 2

r

which i s 5 t i m e s lower than the limiting value of 0. 8 W / m 2 .

Nevertheless the value of b = 1 cm m u s t not be diminished since the induction is probably somewhat higer at the s h a r p e d g e s .

The outer i r o n - r i n g with the added outer coils will compensate the calcu-lated s t r a y flux. The thickness of the outer ring thus have to a g r e e with that of the p o l e - p i e c e s .

The construction even demanded a somewhat thicker wall (16 m m ) , b e c a u s e of a good fit of the junction between o u t e r - r i n g and p o l e - p i e c e s .

In o r d e r to calculate the values for core d i a m e t e r and pole thicknesses at the core we neglect the stray flux at the outside of the poles and find for the flux, generated by the central coils: " c e n t r a l " flux = flux through the edge + flux through the inside of the p o l e s .

This flux has to p a s s through the central core and the poles n e a r the c o r e . So we have for the c o r e :

0 . 8 i i r ^ ^ / 6 . 1 0 " ^ T , ( R ^ - T^)l + 0.16 2iTRb (6) where r is the r a d i u s of the core in m e t e r s , and R is the radius of the

p o l e - p i e c e s .

F r o m (6) follows: r > 0.11 m.

We took a value of 11.5 cm, since a l a r g e r value combined with the d i m e n -sions of the exciting coils around the core would take away space from the focusing c h a m b e r .

F o r the thickness h of the p o l e - p i e c e s at the central c o r e :

0.8 . 2 i i r h > 6.10~^Ti(R^-r^)+ 0.16 . 27iRb (7) Substituting the known values we find for h:

h > 0. 052

We choose the value of 6 cm.

U s i i ^ these values for h and r we have constructed p o l e p i e c e s and core a c -cording to the coordinates of table 1.

For the construction of the s p e c t r o m e t e r Armco iron was used with the fol-lowii^ impurity analysis a s specified by the manufacturer:

C: 0.015%; Mn: 0. 028%; P : 0. 005%; S: 0. 025%; Si: 0. 03%. After machining the iron m u s t be annealed. It i s heated relatively fast to 840'' C and then allowed to cool slowly over a period of 8 h o u r s . The annealing took place in a hydrogen-nitrogen a t m o s p h e r e . After annealing the magnetic p r o p e r t i e s were determined to be a s follows:

Initial permeability = 250 Maximum permeability = 7000 Permeability (at H = 50 A/m) = 2000.

The poles were machined to within 5 y m of the calculated coordinates. The machining was performed on a lathe with the aid of a model. Care was taken to a s s u r e that the upper and lower face of the p o l e - p i e c e s were p a r a l l e l . Special attention was also given to the finishing of the m e t a l . The two pole faces a r e joined to the core by m e a n s of t h r e e bolts on each end of the c o r e . The toppole has a facility for fastening a hook for a puUy, so that this p a r t can be removed easily. The two p o l e - p i e c e s constitute the upper and lower enclosure of the vacuum c h a m b e r , which will be described below.

3. Coils

The d e s i r e d maximum field of 6.10~2 VJ/refi and the a v e r s e pole distance of 14 cm r e q u i r e 7500 a m p e r e - t u r n s for the c e n t r a l - and outer coil each. Neglecting the magnetic r e s i s t a n c e of the i r o n , this value is calculated roughly from:

where 2d i s a v e r a g e pole d i s t a n c e , nl the number of a m p e r e - t u r n s and y = 4 71.10-".

o

The maximum c u r r e n t of the available supply is about 30 A. Thus the n u m -b e r of coil windings has to -be a-bout 200.

table 2. number of coils number of t u r n s dimensions of the windings r e s i s t a n c e max. d i s s , power outer coil 6 180 10 mm x 0 . 1 mm 0.65 ü 585 W. central coil 6 220 5 mm x 2 mm 0.50 fi 450 W.

The c e n t r a l coils w e r e constructed in four p a i r s , with one coil on each side of a cooling box, within the specifications given in table 2. The winding direction was chosen so that the inside t e r m i n a l s of each p a i r of coils could be connected together, w h e r e a s the outer t e r m i n a l s form the interconnection between the p a i r s . The coils a r e all connected in s e r i e s . The t e m p e r a t u r e imder working conditions can be determined by the c u r r e n t through a s m a l l platinum r e s i s t a n c e , which is cemented to one of the middle coils. The coils w e r e connected together and to the cooling p a r t s by means of Araldit r e s i n at a t e m p e r a t u r e of 120^ C. The whole coil packet can be lifted from the core when the upper pole is removed, since the waterpipes a r e connected by an O-ring to the cooling system of the s p e c t r o m e t e r .

In the course of the construction of the s p e c t r o m e t e r the outer coil a s s e m b l y was placed at the inside of the iron outer ring a s shown in fig.6.

These coils a r e connected in s e r i e s to the central coils. Since outer and inner coils differ in the number of windings respectively 180 and 225 and an equal amount of a m p e r e turns is demanded the inner coil is shunted by a r e s i s t a n c e which value i s determined e m p i r i c a l l y (about 2 ft ). The s p e c i -fications of this coil a r e also given in table 2.

The outer coil a s s e m b l y consists of six coils of copper ribbon which a r e self-supporting. Each of these coils can be excited separately. The con-struction was p e r f o r m e d using wooden moulds because the entrance holes for source holder and counter s y s t e m s both demanded a sophisticated design. During the winding cold-sticking Araldit was use^ to cement the windings and to maintain the d e s i r e d model.

fig. 6

The coils a r e connected to the outside of the outer wall, so t h e r e exist a good heat exchange with the surroundings.

The c u r r e n t r e q u i r e d by the coils is supplied from a stabilizing and regu-lating s y s t e m which is described in chapter 5.

4." Vacuum-installation

The vacuum c h a m b e r of the s p e c t r o m e t e r c o n s i s t s of the p o l e p i e c e s t o gether with two cylindrical w a l l s , the innerone made of 14 mm thick a l u -minium, the outer-one of 16 m m iron. The vacuum sealing is performed by four neoprene g a s k e t s which w e r e fabricated from neoprene tubes, carefully cemented together.

The vacuum tank i s provided with two lock s y s t e m s , one for the source inlet, the other for counter a s s e m b l i e s . The chamber is evacuated by m e a n s of an oil diffusion pump (Edwards) boosted by a m e r c u r y diffusion pump (Leybold Hg 3), which has its outlet in a buffer vacuum v e s s e l .

P r e - e v a c u a t i o n of tank and v e s s e l i s performed by a two stage rotation pump (Edwards).

The minimum p r e s s u r e of the s y s t e m i s 10"^ m m Hg and a p r e s s u r e of 10"3 mm Hg can be reached in 20 ijiinutes.

The connections of the vacuum s y s t e m a r e shown in fig. 7. In all connec-tions neoprene O - s e a l s a r e used.

The p r e s s u r e in the vacuum tank is m e a s u r e d by an ionisation gauge (Philips PW 7900) which is able to indicate p r e s s u r e s between 10"l m m and 10~5 m m Hg.

fig. 7

V a c u u m - s y s t e m OIL OIFF PUMP MERCURY OIFF PUMP

5. Auxlltary equipment 5 . 1 . Source holder.

The sources are attached to aluminium rings which can be fitted into the source holder.

The sources can be moved radially in the plane e = 0 by m e a n s of a s c r e w construction a t the back of the source h o l d e r . A pinhole construction is p r o -vided for a reproducible v e r t i c a l positioning of the s o u r c e . The coupling between lock and s o u r c e holder i s performed by the a t m o s p h e r i c p r e s s u r e only. Tabs a t the source holder slip over projections at the lock to e n s u r e that the position of the source does not change (fig.8).

Lock S o u r c e holder

Source holder and source lock

5 . 2 . Geiger-MUller equipment

F o r the d e t e c t o r we u s e d a c o m m e r c i a l l y available Philips G. M. tube type 18504. The types 18505 and 18510 can a l s o be used. The l a t t e r has the a d -vantage of an a c c e s s o r y guard ring tube, which s u p p r e s s e s background d i s c h a r g e s in the main tube by using it in an anti-coincidence mode of ope-r a t i o n .

The tubes can be mounted in a lead block by means of a d a p t o r s n e c e s s a r y since the tubes have d i v e r s e d i a m e t e r s . The lead block is used a s a s h i e l -ding against Y - r a d i a t i o n from the source and against background radiation

(now 10 c / m ) . F u r t h e r m o r e , it s e r v e s f o r the v e r t i c a l and r a d i a l p o s i -tioning of the coxmters in the plane T I ^ r a d i a n s . The counters a r e filled with a self quenching g a s m i x t u r e and provided with mica windows of about 2 mg/(>m2 t h i c k n e s s . The windows a r e constructed for use under a t m o s -p h e r i c conditions, so because of the g a s -p r e s s u r e of 30 cm Hg -precautions have to be taken for u s e imder vacuum conditions.

The window i s normally bent inside to withstand the a t m o s p h e r i c p r e s s u r e , t h i s position of the window must be maintained under vacuum, otherwise the window i s easily damaged. This is achieved by a b r a s s support foUowii^ the curve of the mica window.

A slit in the m a s k s e r v e s a s the defining slit of the coimter. In o r d e r to e x -tend investigations to lower e l e c t r o n e n e r g i e s , provisions have been made to install a contineous flow-counter with changeable windows. The self quenching c h a r a c t e r of the g a s m i x t u r e in all counters allows the ommission of a e l e c t r o n i c quenching c i r c u i t . The p u l s e s of the detector a r e r e c o r d e d by a combination of Hewlett P a c k a r d counting xmits, which p e r m i t automatic

r e a d - o u t . The d e t e c t o r s a r e capable of handling coimting r a t e s of 2000 c / m with only about 1% l o s s .

5 . 3 . Scintillation equipment

It i s also possible to detect e l e c t r o n s by the use of an anthracene c r y s t a l . Scintillations in the c r y s t a l a r e then amplified by a photo multiplier tube mounted outside the s p e c t r o m e t e r in o r d e r to reduce the influence of the magnetic field on the focusing p r o p e r t i e s of the multiplier.

The optical coupling of the scintillation d e t e c t o r , which is situated at the central orbit, and the light s e n s o r , which is at a distance of about 50 cm from the c r y s t a l , i s performed by a Incite lightguide. In o r d e r to achieve optimum light collection the rectangle c r y s t a l ( 2 x 0 . 6 x 0 . 6) cm3 is mounted in the Incite lightguide a s shown in fig. 9.

fig. 9

Scintillation d e t e c t o r and lightguide Aluminized

b)-»}'}///^/^///^^. _{////////////////////A}

To get maximum reflections in the direction of the m u l t i p l i e r , the front end of the lucite tube is given a s s p h e r i c a l shape. Both this p a r t and the half cylindrical p a r t a r e covered with evaporated aluminium. F u r t h e r light c o l -lection i s performed by total ref-lection. Except for the front p a r t the whole lightguide is surrounded by an aluminium cylinder. The lucite lightguide i s positioned in this tube by m e a n s of two O - r i n g s , which a l s o s e r v e a s a vacuum s e a l .

A magnetic shielding of the photo-multiplier is provided, f i r s t by m e a n s of a soft iron shielding, secondly by a y - m e t a l foil wrapp)ed roimd the tube; these p r e c a u t i o n s proved to be sufficient.

The e l e c t r i c a l pulses from the multiplier a r e fed into an amplifier; the a m -plified signals go to a s i n g l e - c h a n n e l - d i s c r i m i n a t o r , in o r d e r to have the possibility to d i s c r i m i n a t e between pulses caused by radiation and by s y s t e m

The signal to n o i s e - r a t i o is diminished considerably by the use of the light-guide. which has a t r a n s m i s s i o n of 30%.

F u r t h e r m o r e in spite of the s m a l l dimensions of the d e t e c t o r the amount of background radiation in the analyzed p u l s e s is considerably higher than in the case of the G. M. detector. This fact is caused by the much higher d e n s i ty of the anthracene c r y s t a l compared with that of the g a s m i x t u r e . The d e -t e c -t o r is capable of measuring e l e c -t r o n s down -to energy of 100 keV.

Although the detection of l o w e r e n e r g y e l e c t r o n s is p o s s i b l e , t h e i r m e a s u r e -ment is not v e r y reliable because of the influence of noise.

The advantage of this kind of detector is that it is capable to handle large counting r a t e s and that it can be employed in coincidence m e a s u r e m e n t s where a G . M . tube is not p r a c t i c a l , because of the r a t h e r l a r g e r i s e time of i t s e l e c t r i c a l p u l s e s . The defining slit for the detector i s mounted on the flat p a r t of the lightguide. A set of adjustable diaphragms is provided, so that counter s l i t widths of 0. 5 till 3 mm may be used.

5 . 4 . Diaphragms

Use of a s p e c t r o m e t e r of this design (with second coefficient in the s e r i e s expansion for the magnetic field i s 3/8) r e q u i r e s an adjustable opening angle in the r a d i a l direction» As indicated in chapter 2 the opening angle in the v e r t i c a l direction does not have much influence on the resolution of the s p e c t r o m e t e r . Two diaphragms w e r e therefore provided with radially a d j u s -table s h u t t e r s . The adjustment of the d i a p h r a g m s can take place outside the s p e c t r o m e t e r , without disturbing the vacuum.

The opening of the s h u t t e r s can be r e a d from the outside by means of a "helipot" dial.

The axial opening angle is fixed so that no scattering of e l e c t r o n s can take place at the point where the electron b e a m has its widest a p e r t u r e . The m a x i m u m axial opening angle <)> zm can be calcidated from

d = To * z m l ^ (He 50) (9) where the values for d and TQ a r e 7 and 25 cm respectively.

The m a x i m u m value for the r a d i a l opening angle i s fixed by the effective width of the pole-gap in the same way a s :

d ' = r o * r m V T (10) The value d i s 5 cm.

The d i a p h r a g m s a r e placed in the vacuum tank of the spectrometer a s i n d i -cated in the g e n e r a l drawing of the i n s t r u m e n t fig. 6.

They a r e in the planes 6 = 27. 5° and 9 = 227. 5 ° .

The other fixed d i a p h r a g m s , also indicated in the drawing, a r e used to p r e -vent detection of s c a t t e r e d e l e c t r o n s .

Chapter 5.

C u r r e n t Stabilizer 1. Introduction

Since the magnetic field is generated by a c u r r e n t , stabilizing and regulating devices can p r i m a r i l y be applied to the c u r r e n t . In the spiectrometer c o n s i -d e r e -d , c u r r e n t regulation i s not a sufficiently a c c u r a t e solution; in the next chapter a field regulation i s d e s c r i b e d which does meet the r e q u i r e m e n t s . The r e a s o n for still using a c u r r e n t s t a b i l i z e r i s found in the possibility to automize the equipment without many difficulties which i s f a r l e s s simple with this field r e g u l a t o r (see chapter 6, 7). The c u r r e n t s t a b i l i z e r has been designed with the following considerations.

1. The magnet c u r r e n t m u s t have a range of 0 . 1 - 30 A in o r d e r to enable the s p e c t r o m e t e r to focus e l e c t r o n s from 5 keV to 4 MeV. n . The determination of line positions with a p r e c i s i o n of 1 p a r t in 10"*

a s s o c i a t e d with a resolution of about 0 . 1 % r e q u i r e s a long t e r m s t a b i -lity of the o r d e r of about 5 p a r t s in 10^.

i n . Line broadening due to field fluctuations has to be v e r y s m a l l ; a short t e r m stability of 1 p a r t in 10'^ is demanded, when using a resolution of 0 . 1 % .

The power supply should not take too much maintenance and m u s t a c t p r o -p e r l y during a long t i m e ; f u r t h e r m o r e , it must not take much s-pace. Our choice was a t r a n s f o r m e r with a r e c t i f i e r to supply the d. c. voltage. The b a s i c r e g u l a t o r i s adopted from equipment proposed by Brog and Milford

(Br 60); we used also the experience of Garwin et al (Ga 59) in constructing the s t a b i l i z e r . The used circuit i s known a s a s e r i e s - r e g u l a t o r . Since the c u r r e n t in the load v a r i e s from v e r y s m a l l values up to 30A, the power r e -q u i r e m e n t s on the r e g u l a t o r t r a n s i s t o r s a r e very e x t r e m e . When the load c u r r e n t i s z e r o , they m u s t a b s o r b the total supply voltage. When the load c a r r i e s a l a r g e c u r r e n t , the t r a n s i s t o r s have to be able to handle this c u r -r e n t . The maximum dissipation in the -regulato-r happens when the load i s c a r r y i n g glniax at a voltage of i V m a x . Thus the w o r s t dissipation condition for tiie r e g u l a t o r i s 1/4. Pmax- Equipment which comes up to these demands i s d e s c r i b e d in the following. The p r i n c i p l e s applied in the above mentioned s t a b i l i z e r s w e r e used a s a guide in constructing the s e t - u p .

2. Electronical and mechanical realization 2 . 1 . Introduction

Fig. 10 shows a block d i a g r a m of the r e g u l a t o r s y s t e m .

The needed power i s supplied by a twenty-four phase t r a n s f o r m e r - r e c t i f i e r combination. (66V - 50A, o r 33V - lOOA). The supply introduces a ripple with a frequency of 1200 Hz and with an amplitude of about 0.7V at an output voltage of 66V. The ripple i s filtered by a IT f i l t e r , shown in the d i a -g r a m . F u r t h e r re-gulation i s performed electronically.

The p r i n c i p l e s of the e l e c t r o n i c s involved a r e a s follows, (fig. 10) The magnet c u r r e n t develops a c r o s s the reference r e s i s t a n c e a voltage which is compared to a v e r y stable r e f e r e n c e voltage. Fluctuations in

RR « R«f rtfsistonc» HC « MognHcoil

fig. 10

Block d i a g r a m of the s t a b i l i z e r .

the magnet c u r r e n t , which may be due to variations in the line-voltage or to variations in the load, cause changes in the comparator output. This e r r o r signal is applied to a d . c . amplifier s y s t e m . The amplified e r r o r signal i s fed into the main r e g u l a t o r , consisting of a compounded t r a n s i s t o r - s t a g e . F r o m the simplified equivalent r e g u l a t o r circuit of fig. 1 1 , the major p a r t s in the s y s t e m can be recognized and the points to which one h a s to pay attention can be found.

[ ^ ^

",

Pj^^fe'bl

If

L

ke ^

The gain r e q u i r e m e n t s for the d . c . amplifier to fulfill stability d e m a n d s , a r e derived a s follows.

Using small signal notation ( e . g . for AV = v, and A I = i), we have for the r e g u l a t o r stage (represented by one t r a n s i s t o r ) :

V. = h.gij^ ( 1 ^ ^ i s n e g l e c t e d ) (1) and i = h . i, + h V (2) c fe D o e c E l e m i n a t i n g i, w e find: ^ f e / • v.. + h _ v ^ (3) 1 = fe / ^ I . . le c "^I'h. 1 o^ c W h e n s u p p l y v o l t a g e c h a n g e s (v ) a r e c o n s i d e r e d f i r s t we find ( s e e a l s o n e x t c h a p t e r ) v . = R i A (4) 1 r c ^ ' B y s u b s t i t u t i n g (4) i n t o (3) we find: h o e v i I A h , r f e , i = C — — (5) c 1 + R A h , ' ^ h. le S i n c e V = V - I R c s c m w e find b y d i f f e r e n t i a t i n g V = v ^ - i R _ (R = c o n s t a n t ) (6) c s c m ^ m ' ^ ' B y s u b s t i t u t i n g (6) i n t o (5) we find i h c _ oe V 1 + R h + R A . h , / h . s m o e r fe l e w i t h 1 + R h <<R A . h , / h . we h a v e : m o e r fe le i h h . c o e le (7) (3) v R A h , s r fe W h e n l o a d f l u c t u a t i o n s a r e c o n s i d e r e d we find: V = - I A R „ - i R (9) c c m c m ^ ' T h i s e x p r e s s i o n i s found b y d i f f e r e n t i a t i n g V = V - I R B y s u b s t i t u t i n g (9) a n d (4) i n t o (3) we find: ^ s c m 4 1

i h

" - °^ . A R / R (10) I 1/R^ -Ih, / h . U R / R I A + h

c m ( fe ief[ r m; oe

the t e r m s l / R and h can be neglected, compared to the t e r m

[V^e)-(V^m\^^'^'i^^^i^'*

i h h. R AR

c _ o e i e m m „... I h , R A R

c fe r m

With the aid of eq. 5-8 and 5-11 the gain of the difference amplifiers can be calculated by substituting the m e a s u r e d t r a n s i s t o r p a r a m e t e r s :

h.^ = lo'^^ h , = 10^

fe

h = 0 . 5 S oe

The value of R^ i s 5 . 1 0 " S2; we find with a stability demand of i / v = I . I O " ^ with eq. 5-8

c s ^

A = 10^ (12) This amplication factor put into eq. 5-11 with Rj^ = i n gives for

AR / R = 100%. This demand can be fulfilled easily.

m m •' 2 . 2 . Reference s y s t e m

The stability of the r e f e r e n c e voltage m u s t be beyond all doubts. The reference voltage is taken from a 40-turn helipot, fed by a c u r r e n t from a reference element, consistir^ of two voltage r e g u l a t o r diodes. Potentiometer and reference element a r e placed in an oil-bath, which is kept on constant t e m p e r a t u r e by a t h e r m o s t a t . The t e m p e r a t u r e can be regulated within O.l^C.

The stability of the reference s y s t e m was tested and established a s b e t t e r a s 10 p . p . m . , both s h o r t and long t e r m stability.

A l a r g e value of Rj. improves the stability, a s seen from 5-8 and 5-11 but on the other hand a too large value causes dissipation p r o b l e m s . The r e f e r e n c e r e s i s t a n c e was composed of a set of manganine r e s i s -tances of 5.10~2 ^, which can be connected either in p a r a l l e l or in s e r i e s , thus providing the opportunity to use a s m a l l e r o r l a r g e r scale in analyzing e l e c t r o n s p e c t r a .

The manganine r e s i s t a n c e s a r e placed in a box filled with k e r o s i n e . It i s possible to m e a s u r e the t e m p e r a t u r e of the liquid by m e a n s of a