Some applications of the perturbed directional correlation technique in nuclear physics, solid state physics and radio chemistry

SOME APPLICATIONS OF THE

PERTURBED DIRECTIONAL CORRELATION TECHNIQUE

IN NUCLEAR PHYSICS, SOLID STATE PHYSICS

AND RADIO CHEMISTRY

S O M E APPLICATIONS OF THE

PERTURBED DIRECTIONAL CORRELATION TECHNIQUE

IN NUCLEAR PHYSICS, SOLID STATE PHYSICS

A N D RADIO CHEMISTRY

S O M E APPLICATIONS OF THE

PERTURBED DIRECTIONAL CORRELATION TECHNIQUE

IN NUCLEAR PHYSICS, SOLID STATE PHYSICS

A N D RADIO CHEMISTRY

PROEFSCHRIFT

TER VERKRIJGING VAN DE GRAAD VAN DOCTOR IN DE TECHNISCHE WETENSCHAPPEN A A N DE TECHNISCHE HOGESCHOOL DELFT, OP GEZAG VAN DE RECTOR MAGNIFICUS PROF.IR.B.P.TH. VELTMAN, VOOR EEN COMMISSIE A A N G E W E -ZEN DOOR HET COLLEGE VAN DEKANEN TE VER-DEDIGEN OP WOENSDAG 11 MAART 1981 TE

14.00 UUR

DOOR

ROBERT WILHELMUS HOLLANDER

natuurkundig ingenieur geboren te 's-Gravenhage

1981

Dit proefschrift i s goedgekeurd door de promotoren

PROF,DR.A,H,WAPSTRA

aan Erernien, Sandra en Ivette

CONTENTS

page

Chapter 1. INTRODUCTION 11 Chapter 2. EXPERIMENTAL SET-UP FOR g-FACTOR MEASUREMENTS 15

INCLUDING A 10T SUPERCONDUCTING MAGNET

2.1. Introduction 15 2.2. Some aspects of the design of the superconducting 15

magnet system

2.3. History of the magnet system 22 2.4. Some aspects of the mechanical design of the magnet 27

support system and the table for the radiation detectors

2.5. Design of shieldings for photomultipliers against 32 strong magnetic f i e l d s

2.6. The design of a peak s t a b i l i z e r 45 Chapter 3. THE INFLUENCE OF SOME PHYSICAL AND CHEMICAL CONDITIONS 57

OF THE RADIOACTIVE SOURCE MATERIAL ON THE ANISOTROPY OF THE DIRECTIONAL CORRELATION OF THE 208-113 keV YY-CASCADE IN 1 7 7H f 3 . 1 . Abstract 57 3.2. Introduction 57 3.3. Experimental set-up 59 3.4. Analysis 59 3.5. Experiments 62 3 . 5 . 1 . Solids 62 1. L u203 62 2. Lutecium metal 62 3. Lu(N03)3 64 4. LuC«,3 64 3 . 5 . 2 . Aqueous solutions 65 1. LuC£3 65 2. Lu(N03)3 66 3. LuC£3 + NH4C£ 67 3 . 5 . 3 . Acid solutions 67 1. L u203 in HC£ 67 2. L u203 in HN03 68

page

3. LuCJl3 in HC2. 68

4. LuC£3 in HC£ and HC£04, both with NaF added 69

3.5.4. Basic solutions 70

1. LuC£3 in NaOH 70

2. LuC^^ "in ammonia 70

3.5.5. LuC£3 in chelating agents 71

3.5.6. Lu£03 and LuC£3 in a decoupling magnetic f i e l d 72

3.5.7. Extrapolation to zero viscosity 73

3.6. Conclusion 75 3.7. Literature 76 Chapter 4. ON THE PROPERTIES OF THE 113 keV LEVEL AND THE 113 keV 79

TRANSITION IN 1 7 7H f

4.1. Lifetime experiment 80 4.2. L-subshell ratio measurement 86

4.3. {ye~^-Q)/{yy-Q) experiment 89 4.4. The gyromagnetic ratio of the 113 keV level in 1 7 7H f 93

4 . 5 . The mixing ratio 61 1 3 and the penetration parameter 104

A1 1 3 of the 113 keV transition in 1 7 7H f

4.6. The determination of gK, gR, B(M1) and B(E2) and 117

comparison with theory

4.7. Literature 125 Chapter 5. THE g-FACTOR OF THE 279 keV LEVEL IN 2 0 3U 129

5.1. Introduction 129 5.2. Experimental set-up 132 5.3. Source preparation 134 5.4. Experimental results 138 5.5. Conclusion 143 5.6. Literature 144 Chapter 6. THE MAGNETIC FIELD STRENGTH Bg f f AT THE LUTECIUM 145

SITE IN L u2C o1 7 6.1. Introduction 145 6.2. Samples 145 6 . 3 . Analysis 145 6.4. Experiments 147 1. Lutecium metal 147 8

page

2. The intermetal1ic compound LUgCo^ 148

6.5. Literature 151 Chapter 7. TIME-DIFFERENTIAL AND TIME-INTEGRATED PERTURBED 153

DIRECTIONAL CORRELATION EXPERIMENTS ON DILUTE AQUEOUS SOLUTIONS CONTAINING H f+ AND F" IONS

IN LOW CONCENTRATIONS

7.1. Introduction 153 7.2. Time-integrated perturbed directional correlation 158

(TIPDC) measurements

7.3. Time-differential perturbed directional correlation 160 (TDPDC) measurements

7 . 3 . 1 . Samples with a time-dependent randomly oriented 163 interaction

7.3.2. Samples with a s t a t i c randomly oriented interaction 165

7.4. Conclusion 167 7.5. Literature 167

SUMMARY 169 SAMENVATTING 171

CHAPTER 1

INTRODUCTION

The purpose of the work described in this thesis was to acquire a thorough knowledge of the technique of the measurement of perturbed d i r e c -tional correlations. This complicated technique is of great importance since on the one hand i t i s applicable to many areas of physics (see below) and on the other hand provides a means to carry out investigations which are not possible with any other existing technique. The effects to be measured are generally extremely small which offers a great challenge to an experi-mental physicist and necessitates great care regarding s t a t i s t i c a l and systematical errors.

The theory underlying perturbed directional correlations is comprehen-sively and beautifully described by R.M.Steffen (73St). A review, even a con-cise one, would cover many pages and would be embarrassingly incomplete. Therefor only some r e s u l t s , which are relevant for the presented work, w i l l be given.

Let us r e s t r i c t ourselves to those cases in which the unperturbed direc-tional correlation function W(9) can be written as:

W(e) = 1 + A2P2(cos 9) (1.1)

where A2 i s the directional correlation c o e f f i c i e n t , P2 is a Legendre

poly-nomial and e i s the angle between the radiation detectors.

If a perturbation is caused by the interaction of an e l e c t r i c f i e l d gradient Vz z in a l i q u i d or in randomly oriented micro crystals with an

e l e c t r i c quadrupole moment of the nucleus in the intermediate s t a t e , then we find a time dependent directional correlation function:

W(6,V ,t) = 1 + G2(t)A2P2(cos 9 ) (1.2)

The perturbation i s completely described by a time dependent perturbation factor G2(t) (chapter 3 and 7).

If a s t a t i c magnetic f i e l d Bj_ is applied perpendicular to the plane in which the directional correlation is measured (in absence of an e l e c t r i c quadrupole i n t e r a c t i o n ) , then a perturbed directional correlation function W(6,Bj_,t) i s found due to the interaction of Bj_ and the magnetic dipole

moment of the nucleus in the intermediate state:

W(6,B1,t) = 1 + A2P2(cos(6-o)Bt)) (1.3)

The perturbation i s now described by a precession frequency ojg (chapter 5). If Bj_ i s applied in presence of a perturbing e l e c t r i c f i e l d gradient

Vz z > then we find a simple time integrated perturbed directional correlation

function in the case of liquids only (chapter 4):

For solids a complicated formula is found (73St), which can be approximated by (1.4) as long as G2 is close to 1 (chapter 6).

If a magnetic f i e l d B/( i s a p l l i e d in the direction of one of the

radiation detectors in presence of perturbing e l e c t r i c f i e l d gradients Vz z,

we find a time integrated correlation function identical to (1.1):

as long as the magnetic interaction frequency tog i s much higher than the e l e c t r i c interaction frequency Ug (chapter 3).

At f i r s t perturbations were regarded as a nuisance in nuclear physics experiments, l a t e r on these perturbations were acknowledged as an excellent p o s s i b i l i t y to measure magnetic dipole and e l e c t r i c quadrupole moments of short (10"9s) lived nuclear states or to determine magnetic f i e l d strengths

or e l e c t r i c f i e l d gradients at the s i t e of nuclei in an unknown surroundings. These aspects are reflected in this t h e s i s . Annoying perturbations are present in the determination of the unperturbed directional correlation c o e f f i c i e n t s of the 208-113 keV yy~ (chapter 3) and yej^-cascades (chapter 4)

in 1 7 7H f . A "perturbation" due to a magnetic f i e l d B,: i s used to restore the

"unperturbed" directional correlation of the 208-113 keV YY-cascade in 1 7 7H f

(chapter 3). The perturbation due to a magnetic f i e l d B^ is used to determine the nuclear g-factor of the 113 keV level in 1 7 7H f (chapter 4) and of the

279 keV level in 2 0 3TjI (chapter 5), and to determine the magnetic f i e l d

strength at the lutecium s i t e in the i n t e r m e t a l l i c compound Lu2Co^y (chapt.6).

F i n a l l y the perturbation due to an e l e c t r i c quadrupole interaction was used to investigate the chemical properties of solutions, containing hafnium and fluoride in low concentrations and to measure the asymmetric e l e c t r i c f i e l d gradient tensor at the hafnium s i t e in hafnium-fluoride complexes.

w ( e , BL, vz z) = 1 + G2A2P2(COS(6-G2Ù JBT ) ) (1.4)

w ( e , B „ , vz z) = l + A2P2(COS e ) (1.5)

A precise determination of the correlation function i s required in a l l these experiments since the effects of interest are hidden in usually small perturbations of the correlation function. It is sometimes possible to enlarge the effects by employing stronger perturbing f i e l d s . An experimental set-up with a 10 tesla superconducting magnet was b u i l t in order to obtain accurate nuclear g-factors of short lived (10"9s) nuclear l e v e l s , more

accu-rate than could be obtained with conventional electro magnets. Originally the introduction of such a system was the main purpose, but other experiments were started when the construction of the superconducting magnet took much more time than expected.

L i t e r a t u r e 73 S t R . M . S t e f f e n , T h e o r y of P e r t u r b e d A n g u l a r C o r r e l a t i o n s , i n : Nuc 1 ea r I n t e r a c t i o n s w i t h E x t r a n u c l e a r F i e l d s , P r o c e e d i n g s o f t h e XI W i n t e r S c h o o l on N u c l e a r I n t e r a c t i o n s , Z a k o p a n e 1 9 7 3 , p.105, P o l i s h S c i e n t i f i c Pub 1 . , Wa rszawa , 1974. a l s o : R . M . S t e f f e n , H . F r a u e n f e l d e r , The I n f l u e n c e o f E x t r a n u c l e a r F i e l d s o n A n g u l a r C o r r e l a t i o n s , i n : P e r t u r b e d A n g u l a r C o r r e l a t i o n s , ' P r o c e e d i ngs o f t h e U p p s a l a M e e t i n g o n ' E x t r a n u c l e a r P e r t u r b a t i o n s i n A n g u l a r C o r r e l a t i o n s ' , U p p s a l a 1 9 6 3 , P - 3 , N o r t h H o l l a n d Publ . C y . , A m s t e r d a m , 1 9 6 4 . H . F r a u e n f e l d e r , R . M . S t e f f e n , A n g u l a r D i s t r i b u t i o n s o f N u c l e a r R a d i a -t i o n , c r $ " Y Ray S p e c -t r o s c o p y , e d . K . S i e g b a h n , N o r -t h H o l l a n d P u b l . C y . , A m s t e r d a m , 1965 • R . M . S t e f f e n , A n g u l a r D i s t r i b u t i o n s a n d C o r r e l a t i o n s i n N u c l e a r S p e c -t r o s c o p y , i n : A n g u l a r C o r r e l a -t i o n s i n N u c l e a r D i s i n -t e g r a -t i o n , P r o c e e d i n g s o f t h e I n t e r n a t i o n a l C o n f e r e n c e o n A n g u l a r C o r r e l a t i o n s i n N u c l e a r D i s i n t e g r a t i o n , D e l f t 1 9 7 0 , p . l , W o l t e r s N o o r d h o f f P u b l . C y . , G r o n i n g e n , 1971.

CHAPTER 2

EXPERIMENTAL SET-UP FOR g-FACTOR MEASUREMENTS INCLUDING A 1QT SUPERCONDUCTING MAGNET.

2.1. Introduction.

The nuclear g-factor of short-lived nuclear levels can be deduced from the rotation of the directional correlation pattern, when a magnetic f i e l d i s ap-plied perpendicular to the plane of the radiation detectors (65Fr). A high accuracy was aimed at. The accuracy can be increased by using stronger magnets. A 10T superconducting magnet system was introduced (section 2.2. and 2 . 3 . ) . Very stable mechanical and electronical devices are not less important. The mechanical construction of the support system for the magnet and the radiation detectors i s described in section 2.4. The shielding of the detectors from the strong stray f i e l d s of the " a i r " c o i l s is described in section 2 . 5 . The design of a "peak s t a b i l i z e r " is described in section 2.6.

The description of the system is restricted to those items, which are im-portant in respect to the desired high accuracy, but many other indispensable subsystems as:

- a "stand-alone" hardware data acquisition system, - a CAMAC-based software data acquisition system,

- a system for automatic and independent positioning of three detectors, - a CAMAC-based interface for a LABEN multi-channel analyser,

- an automatic r e f i l l system for l i q u i d nitrogen,

- two magneto meters based on the magneto resistance- and Hall p r i n c i p l e , were made. Computer programs were developed to monitor the s t a b i l i t y of the set-up, to analyse the data and to make isomeric plots of the spectra.

The method of data acquisition in two-dimensional coincident energy spectra was revised for g-factor measurements and i s described in chapter 4.

2.2. Some aspects of the design of the superconducting magnet system.

"Many g-factors have been measured by using powerful electromagnets delivering f i e l d s of up to 5.5T The development of superconducting c o i l s for the production of very high magnetic f i e l d s w i l l make i t possible to measure g-factors of even shorter-lived states (less than 10"9 s e c ) .

Super-conducting magnet c o i l s are p a r t i c u l a r l y suited for this purpose, since the physical size of the required f i e l d s i s small".

This was the situation in 1965, described by Frauenfelder and Steffen (65Fr p. 1163). In February 1967 Dr. Van Nooijen of the Nuclear Physics group at Delft took the i n i t i a t i v e to b u i l t an experimental set-up for g-factor measurements including a superconducting magnet. The "Integral Rotation Perturbed Directional Correlation" technique (65Fr) should be used, which requires a strong magnetic f i e l d perpendicular to the (horizontal) plane of the radiation detectors. About at that time Dr. Hesselink of the same group b u i l t a r e l a t i v e l y small superconducting magnet (72He) to be used in a-Y directional correlation experiments. From his experience i t was decided to buy a complete system, cryostat and power supply included, and not to. try to make one by ourselves.

The following manufacturers of superconducting magnets were invited to make a quotation for a complete system:

AVCO-EVERETT BRITISH OXYGEN Cy.

COMPAGNIE GENERAL d'ELECTRICITE GARDNER CRYOGENICS

GENERAL ELECTRIC MAGNION

OXFORD INSTRUMENTS Cy. PHILIPS PLESSEY RCA SIEMENS THOMSON CSF WESTINGHOUSE

The magnet had to meet the following s p e c i f i c a t i o n s :

a f i e l d strength of 1IT or more at the source position in the centre, - 8 conical radial access ports at 0°, 90°, 135°, 150°, 180°, 210°, 225°

and 270°, having an aperture of 30° for the detectors, - a homogeneity of better than 1% over a 1 cm3 source volume,

- a s t a b i l i t y of 1% or better.

The source in the centre of the magnet had to be at room temperature. This should require a bore of the magnet of about 20 mm.

The cryostat should have a l i q u i d helium and l i q u i d nitrogen storage capacity and a b o i l - o f f rate such, that the system could be used for 18 hours without a r e f i l l .

The power supply should be protected in such a way, that the power supply could not damage the magnet and vice versa. A quench of the magnet should not damage the c o i l s , nor the power supply.

F i n a l l y , in February 1970, OXFORD INSTRUMENTS Cy., PLESSEY, RCA and THOMSON CSF were w i l l i n g to offer quotations for a system according to our specifications. Then RCA closed their superconducting magnet d i v i s i o n , PLESSEY and THOMSON CSF were not able to make both the magnet and the cryostat and were looking for partners. Only OXFORD INSTRUMENTS Cy. was able to deliver a complete system at that time and we did not want to run into problems of mis-matching components. Moreover, this company successfully b u i l t and tested a system very similar to ours ( f i g . 2.1.) for the University of Bonn in Germany. The group at Bonn started their negotiations with the OXFORD INSTRUMENTS Cy. later than we d i d , however, they were so lucky to get the money e a r l i e r than we d i d .

A survey of "price sensitive" specifications was presented by the author at the International Conference on Angular Correlations in Nuclear Disinte-gration at Delft in August 1970 (71Hol). From a comparison of many.quotations i t was found, that besides the maximal f i e l d strength the distance between the two c o i l s of the " s p l i t p a i r " magnet was very important too. This d i s -tance is influenced by the height of the source, the required vertical aper-ture for the detectors and the thickness of high-Z shielding claddings of the conical radiation ports. Claddings of 2-5 mm thick were found to be necessary to reduce the amount of scattered radiation from the magnet in a test experiment on a model of the magnet (71Hol). The eight conical radiation ports were replaced in the f i n a l design by three ports of a more or less rectangular shape, having a vertical aperture of 25° tangential to a central c i r c l e with a diameter of 3 mm and a horizontal aperture of 85° tangential to a central c i r c l e with .a diameter of 5 mm. The vertical aperture, however, proved to be tangential to a 2.8 mm c i r c l e at delivery. The spacer blocks and the central cheeks of the c o i l s were made from one piece of a "heavy"-alloy consisting of sintered tungsten and copper with a s p e c i f i c gravity of

16.8 gem"3. This material can be machined very w e l l , has a s u f f i c i e n t

mechan-i c a l strength at a temperature of 4.2 K as w e l l , and shows a good absorptmechan-ion of gamma radiation. Moreover, the parts of "heavy"-alloy could be made as thick as 7.5 mm or more. Ho additional high-Z claddings were necessary then. The lower part of the cryostat with the magnet f-'-^cu is shown in f i g . 2 . 1 . in the f i n a l design.

11 mm

Fig. 2. 1. Cross-section of the lower part of the cryostat with the magnet. There are six aluminium radiation windows between the source in the centre of the cryostat and the radiation detectors outside the cryostat with a total thickness of 3.2 mm.

1- "split-pair" magnet 2- liquid helium storage (251) 3- liquid nitrogen storage (501)

4- vaauum space for thermal insulation 5- aluminized mylar super-insulation 6- thermal r a d i a t i o n shield at 77K 7- fabric reinforced phenolic resin

spacers

8- aluminium centering discs 9- "heavy"-alloy central spacer

block, and coil cheeks 10- non-inductive copper

magneto-resistance probe

11- high radial field zones near the centre and the outer edge of the magnet

The central f i e l d strength was reduced from 1IT to 10T to obtain the best system quality ( f i e l d strength and apertures (71Hol)) for the money. Later we found out, that a central f i e l d strength of 10T was already very hard to obtain with a " s p l i t - p a i r " magnet at that time. Much higher f i e l d strengths could be obtained with the same type of superconductor in straight solenoids, however, in such single c o i l magnets the f i e l d strength in the central win-dings is about the same as the maximal central f i e l d strength, while in our " s p l i t - p a i r " magnet the f i e l d strength in the central windings is about 25% higher than the central f i e l d strength. This percentage can only be reached i f a l l available space in the centre of the magnet is used for windings. This area is most e f f i c i e n t in producing a central f i e l d . The OXFORD INSTRUMENTS Cy. designed c o i l s consisting of several tapered wound modules, separated by spacers of reinforced epoxy resin with channels for the coolant. The superconductor was copper s t a b i l i z e d Nb3Sn tape, 0.25 inch wide.

The mechanical stress in the tape was found to be very high, probably due to the conical shape of the c o i l formers. This problem was not recognized by the manufacturer at f i r s t and was the reason for several repairs later on. Lots of superconductor in the central modules had to be replaced by stainless steel reinforced tape.

The shape of tape is not the best shape of a superconductor in a " s p l i t -pair" magnet. In some parts of the c o i l s , especially near the centre and the outer edge of the magnet ( f i g . 2 . 1 . ) , the angle between the f i e l d direction and the surface of the tape is rather large, much larger than in a straight solenoid, due to the large radial component of the f i e l d . This unfavourable condition requires extra s t a b i l i z a t i o n of the superconductor in these areas and thus a further reduction of the superconducting to total volume r a t i o .

The helium b o i l - o f f proved to be another problem. The evaporation rate of the system shows a time constant of several hours ( f i g . 2.2.) to f a l l to a reasonable level after a r e f i l l . This steady state is strongly influenced by the cross-section of the copper current leads, running from the top of the cryostat to the magnet. The leads are cooled by the s t i l l cold helium gas, before this gas leaves the cryostat. The contribution to the b o i l - o f f due to a current of 192 A through the leads, necessary for a central f i e l d

strength of 10T, depends on this cross-section too. This contribution :ribution could be measured separately from the contribution of a current through the magnet since the magnet is provided with a superconductive switch across i t s terminals.

time after a r e f i l l in hours *

Fig. 2.2. Helium evaporation of the oryostat with the cross-section of the copper current leads as parameter. The contribution due to 192A through the current leads is also shown.

It should be possible now to optimize the cross-area of the leads, but aspects as: the use of the magnet in the persistent mode1), the time required

to energize the magnet or the number of f i e l d reversals per day, are not considered y e t . The magnet can only be used in the persistent mode i f the decay rate of the f i e l d strength i s low, for instance less than 1 tesla per 24 hours starting at 10T. The decay rate was measured before and after many repairs of the magnet ( f i g . 2 . 3 . ) . The resistance of the magnet can be de-duced from the decay rate of the f i e l d and from the inductance of the magnet, which i s 6.0 H. This resistance i s rather high and depends strongly on the f i e l d strength. The f i e l d dependent part of the resistance i s probably caused by minute cracks in the very b r i t t l e Nb^Sn tape near the interconnections of the modules. These cracks are caused by the high stresses in the superconduc-tor due to the high f i e l d strength and the conical shape of the modules.

) The magnet i s u s e d i n t h e p e r s i s t e n t mode, when t h e s u p e r c o n d u c t i v e s w i t c h a c c r o s s t h e t e r m i n a l s o f t h e magnet i s c l o s e d , a f t e r t h e magnet i s e n e r g i z e d , a n d t h e e x t e r n a l l y s u p p l i e d c u r r e n t i s r e d u c e d t o z e r o .

I ' I I I I I I I I L

0 1 2 3 4 5 6 7 8 9 10

Fig. 2.3. The decay rate of the magnetic field strength and resistance of the magnet as a function of the magnetic field strength.

Cracks were also found near the j o i n t s with the thick copper current leads, which interconnect both halves of the magnet. The r e s i s t i v e spots are well cooled, since they do not cause a quench of the magnet.

The f i e l d "independent" part of the resistance is mainly caused by the about 100 soldered j o i n t s in the magnet. This resistance i s not completely independent of the f i e l d strength due to the magneto resistance effect in normal conductors ( f i g . 2 . 3 . ) .

We have the strange s i t u a t i o n , that the magnet can produce a central f i e l d of 10T at an evaporation rate of less than 1 l i t r e helium per hour when used in the persistent mode, however, i t is not possible to maintain a f i e l d of 10T at an evaporation rate of less than 1 1/hr. The decay rate of the f i e l d at 10T is too high for the magnet to be used in the persistent mode; on the other hand the helium b o i l - o f f is too high for the magnet to be used at 10T with the required current continuously supplied externally. The high resistance of the magnet is the reason for both i m p o s s i b i l i t i e s and not

the normal heat input through the cryostat and the copper current leads. After many repairs of the magnet by the OXFORD INSTRUMENTS Cy. and later on by the INTERMAGNETICS GENERAL CORP. the resistance at 10T remained I2\iti or higher and we f i n a l l y decided to use the system in the persistent mode at a lower f i e l d strength, between 9 and 9.5T.

The cross-area of the copper leads was taken 5 mm2 as a compromise; the

area is small enough to keep the b o i l - o f f low when the magnet is used in the persistent mode, and the area is large enough to keep the extra b o i l - o f f due to an external current in the leads reasonably low, when the magnet is used in the "external" mode.

The f i e l d was reversed once in 24 hours for practical reasons. One rever-sal takes about 75 minutes. This time is lost for the measurements. An exter-nal current i s running through the copper leads during a f i e l d reversal causing an extra evaporation of l i q u i d helium. F i e l d reversals thus reduce the time between two r e f i l l s of the helium reservoir. The magnetic f i e l d shows some hysteresis, but the extra b o i l - o f f caused by this effect is low enough to be neglected. The s t a b i l i t y of the total measuring system was good enough to reverse the f i e l d only once a day.

Summarizing; i t was possible to operate the system for 18 hours in the persistent mode at a mean f i e l d strength of 9.2T and for 6 hours with zero f i e l d with one r e f i l l of 25 l i t r e s of l i q u i d helium and 35 l i t r e s of l i q u i d nitrogen per day. This frequency i s very-convenient, p a r t i c u l a r l y i f one realizes that several months of continuous operation of the system i s some-times required.

2.3. History of the magnet system.

The decision to buy a complete system was based on our experience with a small superconducting magnet system. We wanted a 10T superconducting magnet system to be used as a tool in our nuclear research programme. Making such a large system would have taken some years of research on superconducting magnets and large cryostats. It was not possible for us to predict how long this research period would be and how much the system would f i n a l l y cost. Now, about ten years l a t e r , we can say, that the decision was r i g h t . However, we did not get the easy to operate system as we expected then. The system proved to be very d i f f i c u l t to make and, when the system was f i n a l l y delivered, i t needed many modifications and repairs to meet the original s p e c i f i c a t i o n s . Thus, we did not save as much time by ordering a complete system as we had

h o p e d f o r .

I w i l l try to give some insight in the kind of problems that had to be solved. Most of the modifications were related to an i n s u f f i c i e n t accuracy, mechanical as well as e l e c t r o n i c a l ; the repairs to a marginal design p h i l o -sophy. The lack of mechanical accuracy was most troublesome in the centering of the magnet. Moreover, the centre of the magnet was 22 mm higher than the centre of the thin aluminium radiation windows in the cryostat when the system was f i n a l l y delivered. This was most probably due to several changes in the design of the magnet after the cryostat was f i n i s h e d . A larger ' t a i l ' for the helium reservoir was milled to f i t the magnet exactly and a new set of fabric reinforced phenolic resin and aluminium spacers was made ( f i g . 2 . 2 . ) . The magnet was rotated around a vertical axis over some degrees with respect to the mounting holes in the cryostat.

The accuracy of the magneto resistance magnetometer was 0.5% according to the s p e c i f i c a t i o n s , but only for a short time after c a l i b r a t i o n . The s t a b i l i t y was rather poor. This was caused by the read-out system of the magnetometer and not by the magneto resistance probe, which consists of two non-inductive c o i l s of thin copper wire near the centre of the magnet ( f i g . 2 . 1 . ) . A new read-out unit was made based on a Thomson-bridge. The total accuracy and s t a b i l i t y of this system is now better than 0.25% at 10T.

We also b u i l t a magnetometer using a special axial Hall-probe (type ALMK). This probe, developed by the Institute of E l e c t r i c a l Engineering of the Slovak Academy of Sciences in B r a t i s l a v a , shows a very linear response between 2 and 15 tesla and can be used at room temperature and 4.2 K as w e l l . The accuracy is better than 0.5% and the s t a b i l i t y i s better than 0.1%, both at 10T. Both magnetometers were calibrated applying a rotating c o i l magnetometer (Rawson Lush type 829M12 with an accuracy of 0.1% at 10T), which was recently c a l i -brated against NMR standards.

The marginal design philosophy can be i l l u s t r a t e d by the repairs of the power supply. Many components had to be replaced: a l l the power regulation t r a n s i s t o r s , power s e r i e s - r e s i s t o r s and power r e c t i f i e r diodes, and 18 mis-cellaneous components including capacitors, voltage s t a b i l i z e r s and opera-tional amplifiers. Line-interference suppression f i l t e r s were i n s t a l l e d . We also modified the power supply to reduce the noise and ripple and to make the output " f l o a t i n g " .

These modifications and repairs were made in our laboratory. The repairs of the magnet however, had to be carried out by the manufacturer, f i r s t in

England and later on in the USA. The problems with the magnet were very serious and abundant and might have diverted the attention of the manufac-turer from the other items. A short description of the repairs is given

below :

February 1971 Acceptance of order; delivery time 5 months.

September 1971 The OXFORD INSTRUMENTS Cy. (OIC) proposes to agree with a lower guaranteed f i e l d of 9.5T at a reduced p r i c e . The stresses in the superconductor are too high, the radial f i e l d is too high and the applied superconductor not enough s t a b i l i z e d . We judged the magnet "unreliable" at f i e l d s over 9T and preferred to wait another month or two, so that the superconductor could be replaced by a more appropriate

November 1971 F i r s t test of the system in Oxford. Several windings are broken after a quench at 9.8 T and have to be repaired. December 1971 Meeting in London to discuss specifications and warranty.

A central f i e l d strength of 9.6T is agreed upon at a reduced price. The warranty clauses are extended considerably. January 1972 Second test in Oxford. The system meets the modified

speci-fications except for the helium b o i l - o f f rate at 10T. The specified 1 l i t r e per hour can only be reached many hours after a r e f i l l of the helium reservoir.

February 1972 F i r s t test at D e l f t . The magnet quenches at 9.0T after the f i r s t f i e l d reversal. The next run-up is ended by a prema-ture quench at 5.6T. A r e s i s t i v e j o i n t has to be repaired in Oxford.

March 1972 Second test in Delft i s successful, however, the helium b o i l - o f f i s s t i l l too high.

May 1972 The magnet is returned to the manufacturer for inspection after several quenches at r e l a t i v e l y low f i e l d s . Some burn marks are found on the superconductor, nothing e l s e . June 1972 OIC proposes, that the magnet w i l l be rewound by the

INTERMAGNETICS GENERAL CORP. (IGC), subsidiary of the GENERAL ELECTRIC Cy. in the USA. The central f i e l d strength w i l l be again 10T. The time for a complete f i e l d reversal w i l l be 75 minutes.

March Apri 1 June 1973 1973 1973 November 1973 January 1974 April July 1974 1974 September January 1974 1975 June October 1975 1975

Third test in Delft is successful, except for the b o i l - o f f rate, which is 2 1/hr rather than the specified 1 1/hr. The superconductive switch ceases to operate.

A short c i r c u i t to ground causes an unstable operation of the magnet. The short is removed in Delft by a technician of OIC and a new switch i s i n s t a l l e d .

The resistance of the magnet at 10 T i s now 28 uft, while i t should be 5-7 ufl. The steady helium b o i l - o f f rate at 10T i s 2.0 1/hr. This rate can only be reached after 8 hours of operation. The helium reservoir is almost empty then. Fourth test in Delft by technicians of OIC. The high r e s i s -tance of the magnet is f i n a l l y confirmed. IGC w i l l repair the magnet within 6 weeks.

IGC reports the damage of the magnet during the transport to the USA.

IGC reports severe problems with the mechanical design of the magnet. The accumulation of axial stresses under load w i l l buckle the tape and cracks the Nb^Sn. New spacers between the modules are designed and i n s t a l l e d . The cross-over between both c o i l s of the magnet is replaced. The magnet is much improved now and can reach 10.9T.

F i f t h test in Delft is successful, except for the helium b o i l - o f f which i s s t i l l too high.

The superconductive switch ceases to operate above a central f i e l d strength of 9 T. Field reversals are proble-matical. We monitored the voltages across the modules with a twelve channel high speed UV recorder ( f i g . 2 . 4 . ) . It is obvious from f i g . 2.4. that the top-module causes the mal-functioning of the magnet. OIC writes: "I am sorry that there seems to be no end to the problems this magnet i s causing".

OIC and IGC f i n a l l y agree, that the magnet is useless in this condition. The repair w i l l take 6-12 weeks.

The problems with the f i e l d reversals were also found in other s i m i l a r magnets and seem to be fundamental for " s p l i t -pair" magnets. Lots of superconductor have to be replaced

in the unstable regions.

January 1976 "The repair of your magnet was more d i f f i c u l t than we had anticipated and several of the modules have required replacement to achieve the f u l l f i e l d reversal within 75 minutes according to the original s p e c i f i c a t i o n s . Magnet is successfully demonstrated to withstand f u l l f i e l d rever-sals within 75 minutes with no intervening quenches. We acknowledge with appreciation your patience and we are hope-ful that the magnet w i l l now perform satisfactory in the manner intended o r i g i n a l l y " .

March 1976 Sixth test in D e l f t . The magnetic f i e l d shows a time con-stant of about 8 minutes. Several modules are shorted due to interconnections between voltage taps on the modules, made by IGC. The superconductive switch w i l l not close above a central f i e l d strength of 8.9T.

T 1 1 1 1 1 1 r

t i m e ( s e c o n d s ) •+

J I I I I I I L

0 1 2 3 4 5 6 7

Fig, 2.4. Voltages across the modules of the magnet during temporarily unstable operation, monitored with a twelve channel high speed UV recorder. Field strength is 2.75T, field increase rate 1.74mTs~.1

June 1976 The superconductive switch is replaced once more. The resistance of the magnet is s t i l l too high and strongly f i e l d dependent ( f i g . 2 . 3 . ) . The helium b o i l - o f f remains therefore higher than s p e c i f i e d . The f i n a l homogeneity is 0.23% over the source volume.

More than 100 letters have been exchanged between us and: The OXFORD INSTRUMENTS Cy., the INTERMAGNETICS GENERAL CORP., the NETHERLANDS GOVERNMENT PURCHASING OFFICE, the Dutch customs, the Financial Department of the Uni-v e r s i t y , transport firms, etc. e t c . , a l l after the acceptance of the order in February 1971, in order to get the magnet ready for nuclear physics experiments. The warranty of the system was comprehensively described at the i n -stance of the NETHERLANDS GOVERNMENT PURCHASING OFFICE. The repairs had no financial consequenses for us. OIC and IGC on the contrary spent a lot to solve the problems concerning our magnet, which problems proved to be fun-damental for " s p l i t - p a i r " magnets.

The discussions and negotiations with both firms were always conducted in a kind and pleasant atmosphere. We were always convinced, that OIC and IGC did everything in their power to solve the matter. We wanted our magnet system probably just some years too early.

After a l l these troubles we ruined the thin-walled stainless steel inner section of the cryostat because of a small mistake, while we were flushing the helium reservoir with helium gas prior to cooling down. The magnet was sawn out of the imploded vessel. A new helium reservoir and magnet support system were made, using a l l the reusable parts of the old one, by technicians of the workshop of the Physics Department. The g-factor measurements started in November 1976.

2.4. Some aspects of the mechanical design of the magnet support system and the table for the radiation detectors.

The 10T superconducting magnet system was introduced to obtain more accurate g-factors of s h o r t - l i v e d nuclear states. If the l i f e t i m e t is shorter than - 1 0 "9 s e c , one is restricted to the Integral Rotation method

(65Fr). The angular s h i f t AO of the directional correlation function due to a magnetic f i e l d B i s :

•9MNBT

The required accuracy of AG i s 5--10"1* radians for a desired accuracy of a

one-hundredth of a nuclear magneton in the magnetic dipole moment at a given f i e l d strength of 10T and a l i f e t i m e x of ~10"1 0sec. Such small s h i f t s

are just detectable with a mechanically and e l e c t r o n i c a l l y very stable experimental set-up, provided that the s t a t i s t i c a l error can be made small enough. The positions of the detectors.

tolérance of 1 ' : section

I

defined in chapter 4, are with a

II III i t i o n angle 1 00° 00' 2 15° 00' 3 29° 59' 4 44° 58' 5 60° 00' 1 120° 07' 2 135° 07' 3 150° 06' 4 165° 03' 5 180° 04' 1 240° 06' 2 255° 04' 3 270° 03' 4 285° 03' 5 300° 00'

Formula (2.1) can also be written as : 4+"A„ 9UW = 12"A„ ti_ BT (2.2)

in which q is the relative difference of the ratio of coincident counting rates at 135° and 225° due to a magnetic f i e l d B and " A 2 " is the experi-mental directional correlation c o e f f i c i e n t without corrections for the geo-metrical attenuation and source perturbations (chapter 4). Changes in the detection e f f i c i e n c y , for instance due to changes in the source-to-detector geometry, are reflected in this q. Hoewever, in the relative method we used, these changes are automatically corrected for. Nevertheless the corrections should be small. The design is such ( f i g . 2 . 1 , 2.5 and 2.6), that the re-sulting corrections in the nuclear magnetic dipole moment are smaller than 0.01 u^. This means, that the systematic errors due to the mechanical design

are negligibly small after the corrections are made.

In designing the system we made the following separation: in one part we considered the source-to-detector geometry disregarding the presence of the magnet, and in the second part we considered the r i g i d i t y of the magnet support system.

The changes in the source-to-detector geometry are determined by the movements of the detectors, since the source position is f i x e d . There are no forces acting upon the source support construction. The source is mounted on a small x . y . z - or r.o>.z-table for fine adjustments ( f i g . 2 . 5 . ) . The tempera-ture in the laboratory was s t a b i l i z e d to ± 1° C, which is good enough for the whole construction to meet the mechanical design requirements.

The movements of the detectors are caused by:

Fig. 2.5. Cross-section of detector table with source support system (diameter 1.26 m).

Fig. 2.6. Top view of detector table with detectors (diameter 1.26 m).

- bending of the table by the weight of the detectors, when they are moved from one position to another. The weight of one detector i s approximately 100 kg mainly due to the heavy magnetic shielding (section 2 . 5 . ) . The vertical displacement has to be less than ± 0.1 mm because of "shadow" effects due to the size of the source and the limited apertures of the radiation ports in the magnet. The detector table i s , after adjustment of the length of the 6 legs, " f l a t " within ± 0.1 mm.

- attractive forces between the magnet and the magnetic shieldings of the detectors, when the magnet i s energized. These forces are determined from an experiment on a small model. The forces were limited to 1000 N per detector by placing the magnetic shieldings 90 mm r a d i a l l y outwards from the cryostat. This required longer l i g h t guides between the s c i n t i l l a t i o n crystals and the photomultipliers. The largest contribution to the radial

Fig. 2. 7. The upper photograph shows the magnet and the magnet support system. The support system consists of a mechanical support, two copper gas-cooled high-current leads for the magnet, four gold-plated radia-tion shields, leads for the magneto-resistance probe, for the supercon-ductive switch heater and for the diagnostic voltage taps on the mag-net, and a liquid nitrogen can for pre-cooling of the magnet.

The lower photograph shows the lower part of the cryostat in which the magnet is fitted. The shieldings of the photomultipliers for the stray fields of the magnet are visible at the left and the right side. The machined part of the cryostat between the detectors is the thin aluminium radiation window in the outer vessel of the cryostat.

movements originates from a deformation of the table due to a moment, exerted on the central a x i s . The bending angle of the surface in the centre of the table can be calculated with formulae given by Roark et a l . (59Ro, p. 363). The design of the table is such, that the radial displacement of the detectors (less than 0.1 mm) is within the design philosophy. Moreover in the f i n a l design the magnet was centered through the bottom of the cryo-stat ( f i g . 2.1.) on the rotation axis of the detectors ( f i g . 2 . 5 . and 2.6). This construction v i r t u a l l y eliminates a moment exerted on the detector table.

An additional weight of about 25 kg had to be placed on the detectors to keep the detectors fixed on the t a b l e , when the magnet was f u l l y energized.

The movements of the magnet have to be kept small to avoid "shadow" effects due to the sizes of the source and the detectors and the limited aper-tures of the radiation ports. The s c i n t i l l a t i o n crystals were placed about 7 mm r a d i a l l y outwards from the cryostat. The s o l i d angle from the source to the detector is then in practice limited by the diameter of the s c i n t i l l a t i o n crystal (3 inch) and not by the "heavy"-alloy spacer blocks and c o i l cheeks, which define the radiation ports ( f i g . 2.1.).

Axial displacements of the magnet are caused by a varying temperature p r o f i l e inside the cryostat with a varying contents of l i q u i d helium and nitrogen. They are smaller than ± 0.1 mm. The axial displacement of the magnet is 3.9 mm, when the system is cooled down from room temperature to 4.2K.

Radial displacements, caused by the attractive force between the magnet and the detectors, are kept smaller than 0.2 mm by a set of spacers of a l u -minium and fabric reinforced phenolic resin ( f i g . 2 . 1 . ) . The difference in the contraction of the magnet and the cryostat is used to f i x the magnet in the cryostat. The forces on the magnet are transferred to the bottom of the cryostat, which is centered on the rotation axis of the detectors.

2.5. Design of shieldings for photomultipliers against strong magnetic f i e l d s .

Introduction

Detectors and electronic devices have to be very stable in g-factor measurements, since the changes in count rate, that have to be detected in such time consuming experiments, are small, even when strong magnetic f i e l d s are applied. The photomultipliers of the s c i n t i l l a t i o n detectors that we employed are, however, very sensitive to magnetic f i e l d s . For instance, in a

g-factor measurement on 1 7 7H f a f i e l d with a strength of the earth magnetic

f i e l d acting on the photomultipliers changed the count-rate in the selected energy windows about 2%, while a f i e l d of 10T on the Hf nuclei was required to change the count rate about 1%. The stray f i e l d of the magnet at the p o s i -tion of the photomultipliers is about 0.3T when the magnet produces a central f i e l d of 10T. The photomultipliers give no output at a l l when placed in such a f i e l d . We aimed at a reduction of the stray f i e l d by a factor of 1 06. The

remaining small changes in the count rate are further reduced with peak s t a b i -l i z e r s (section 2 . 6 . ) , and can be neg-lected then. The outer diameter of the shieldings in our f i r s t design was so large, that parts of the shieldings and the cryostat of the superconductive magnet had to share the same space. Moreover, the shieldings were so heavy that a very heavy (and expensive) support system was required to keep the bending of the support small enough, when the detectors were moved around the magnet. We had to reduce the size and the weight of the shieldings, retaining the reduction factor of 106 and

keeping the inner diameter 94 mm for the housings of our 3" 0 Nal(Tl) s c i n -t i l l a -t i o n de-tec-tors. The described procedure for minimizing -the size or -the weight of c y l i n d r i c a l shieldings is applicable to shieldings with different sizes and shielding factors.

The magnetic f i e l d inside a c y l i n d r i c a l shielding can be considered to be the sum of a f i e l d penetrating the i n t e r i o r through the open ends of the cylinder and a f i e l d leaking through the cylinder w a l l .

Fields penetrating through the open ends.

We r e s t r i c t ourselves to s t a t i c homogeneous f i e l d s , for which we can define a potential F that s a t i s f i e s the Laplace equation:

Theory.

AF = •=• 0; H = - grad F (2.3)

In this f i e l d H we place an open cylinder with inner radius , wall thickness d and length L and with a r e l a t i v e permeability p. We f i n d , after separation of the variables, inside the cylinder (z > 0) under the conditions:

u » 1, L » R. and d >> :

F(r,tj>,z) = Jt |(cr)cos(b<)))exp(-cz) * const. (2.4)

or

Hr =-J^(cr).cos(b<)))exp(-cz) - const.

= +Jb(cr) .b.sin(b<j))exp(-cz) - const. (2.5)

Hz =+Jj3(cr) .cos(bij)) .c.exp(-cz) » const.

where i s the Bessel function of the f i r s t kind and of order b. We consider two configurations:

- the external f i e l d l i e s along the z - a x i s , which i s the axis of the cylinder (longitudinal f i e l d ) ,

the external f i e l d i s perpendicular to the zaxis (in the positive r d i r e c -tion for <fj = 0) (transverse f i e l d ) .

We further normalize a l l l i n e a i r measures to R^.

In the case of a longitudinal f i e l d the f i e l d strength does not depend on cfj, thus b = 0. The boundary conditions for thick (d » 1) and long (L » 1) cylinders are, under the assumption of u - » » rather simple:

Hz(r=l)=0 •> JQ(c)=0; c=2.405; 5.520; 8.654; . . . (2.6)

We take c = 2.40 since the other solutions give fast decreasing f i e l d s , which hardly contribute. Another boundary condition i s found from an extrapolation of the measured internal f i e l d on the z - a x i s :

H /r = 0 ) = const. * c = 0.92/L.H , (2.7)

z\z=0 or z=L/ e x t

This l a t t e r value i s an approximation, which takes the demagnetizing effect of the cylinder into account (67Ma). We find 0<z<L, since J0( c r ) = - c J ^ c r ) :

Tj = 0.92/L J , (2.4-r) [ e x p ( - 2 . 4 » z ) + e x p ( - 2 . 4 - ( L - z ) ) ] (2.8)

ext 1

H

jr^~ = 0.92/L J (2.4-r) [exp(-2.4-z) +exp(-2.4-(L-z))] (2.9) ext

The approximation of d >> 1 and u - « is usually not v a l i d . This w i l l result in a less steep exponential decrease of the f i e l d inside the cylinder (67Ma). The f i e l d strength is maximal on the z - a x i s . For r=0 we find under the

assumptions u » 1 and L » 1 :

Hi n t (r = 0> Hz (r =° )

- 4 r = - n = 0.92/E ,[exp(-2.2*z) + exp( -2.2*(L-z))] (2.10) ext ext

Formulas for the shielding of longitudinal magnetic f i e l d s with t h i n , closely spaced, concentric cylinders of high permeability material have recently been published by Gubser et a l . (79Gu).

In the case of a transverse f i e l d , we obtain b=l for symmetry reasons. Since the permeability i s i n f i n i t e , no f i e l d w i l l pass the cylinder w a l l . The only f i e l d , that is found inside the cylinder is the f i e l d , penetrating through the open ends of the cylinder. Boundary conditions for long cylinders (L » 1) are then: Hz (r=l) = 0 independent of o) and z -» J1(c)=0 c = 3.832; 7.016; 10.173; r=0s ( 2 -1 1) 0=0 z=C" Hf U = 0 ) = y * const. ^ 0.33 * He x t •> const. = -0.66 * H ^ . c "1

We take c = 3.83, since the other solutions give fast decreasing f i e l d s , which hardly contribute. The value for i s found from an extrapolation of the measured f i e l d in the cylinder on the z-axis for <j> = 0. Mager (67Ma) found, that the measured value of H (r=cf>=z=0) (0.20-0.25) * H , . We find

I i ^ 6 X L then, substituting J^(cr) = c JQ( c r ) - — J ^ ( c r ) :

He x t [3 g3 - J1(3.83r)-Jo(3.83r)]cos(().exp(-3.83z)^0.66 Tt-2- = - J i (3.83r)siri()).exp(-3.83z)"0.172 (2.12) ext 1 Hz r r ^ - = - J , (3.83r)cost().exp(-3.83z)-''0.66 He x t 1

The largest component of H i s Hz (r=0.48; (|>=0 or IT) - - or +0.38exp(-3.83z).

In the calculations we shall further use Hr(r = $ = 0) = 0.33exp(-3.83z) as

a measure of the internal f i e l d strength.

The approximation of u - m is usually not v a l i d . This w i l l result in a less

steep exponential decrease of the f i e l d inside the cylinder. Mager (67Ma) found, assuming u >> 1 and L >> 1:

H. H

J T1^ = rr^- = 0.33*exp(-3.18z) (2.13)

ext ext Fields leaking through the cylinder wall

We confine ourselves to s t a t i c homogeneous magnetic f i e l d s , perpendicular to the cylinder axis ( z - a x i s ) . We shall further assume that the solutions do not depend on z (L=°°). We can again introduce a scalar potential F, that s a t i s f i e s the two dimensional Laplace equation: AF = 0. We f i r s t consider a single cylinder with inner radius , outer radius Ry and r e l a t i v e

permeability p.

The external f i e l d (r > Ry) is (H= -grad F):

The f i e l d in the cylinder wall i s given by:

Hr = )c o s^

(2.14)

(2.15) % = " c y l ^1 + 7 ^si n *

The f i e l d inside the cylinder i s , since the f i e l d has to remain f i n i t e at r=0

Hr = Hi n t coscO and = H .n t sin^ (2.16)

We can define a shielding factor S as the ratio of the f i e l d strength inside the cylinder and the f i e l d strength in the same volume before the cylinder was put in the f i e l d , since both f i e l d s are homogeneous. This external f i e l d , before the cylinder was introduced, is of course the same as the solution of the external f i e l d in (2.14) for r = <*» and thus:

H.

S = -ppLDI (2.17) ext

At the surfaces of the cylinders we have the boundary conditions:

is continuous,

H (2-18)

<j) is continuous.

This delivers four equations for Hg x t, H -j , K j ^ , a and @.

We can thus express the f i e l d strength in the cylinder wall and inside the cylinder in the external f i e l d strength Hg x t with y, and Ru as parameters.

In the cylinder wall we f i n d :

H f—f^, S H R? ((P + 1) - (y - 1) ^ ) cos^ , S H , R? (2.19) or for p >> 1: R2 Hr = 1S He x t t1 - 4 ) ^ R2 H^ = 1 S He x t t1 + 4 ) s1 n *

Inside the cylinder we find by d e f i n i t i o n of S:

H = S H , cosn _{r ext} 1 H, = S H , sin* i> ext r (2.20) (2.21)

For S we f i n d : or for p >> 1: r 2 r1 4p ^ 2>\ u 1 R? I"1 u 1 (2.22) (2.23)

When d = R -R. is much smaller than R. (R. - R = R) _u

1 1 v 1 u '

S = 1 + yd I

2R

and for & » 1:

S = 2R

(2.24)

(2.25)

The same procedure is applicable to 2, 3 or more concentric cylinders. The resulting formulas are extremely simple as long as the r e l a t i v e permeability of the cylinders is much larger than 1. This condition i s usually f u l f i l l e d . Let us consider n cylinders (the outer cylinder is taken cylinder 1) each with a permeability much larger than one and l e t us define S . and S . a s : c , j a,j (1 R? . Ru , j (2.26) S a,J 1 Ru,j+1 R? .

For the f i e l d strengths in the wall of cylinder k we obtain then:

1 Hr , k =i\ Hext t1 — ) c o s^ V k = 2 Sk He x t ( 1 r i ,k. (2.27) sintj) with Sk j=T,k Sc , j * Ä.=1 Jk-1 Sa,i 38

The f i e l d strength within the inner cylinder is again: H = S H , coscb _{r ext} y H = S H , sind) _{d> ext} T (2.28) wi t h : s = s = . o s . *H , n S „ n 3=1,n c , j £= 1, n-1 a,I

Only the shielding factor S can be considered as a ratio of f i e l d strengths, since only the original external f i e l d and the f i n a l internal f i e l d are homogeneous; a l l other "shielding factors" are introduced for convenience only. The m u l t i p l i c a t i v e character of the shielding factor suggests that shiel dings can be made lighter by replacing one cylinder by some thinner ones. Let us consider n cylinders with thickness dn (relative to the radius

R) and (n-1) a i r gaps, also dn wide.

We w i l l assume d « 1 and R equal for a l l cylinders. We further assume A

u >> 1 and -Vy- >> 1. The "shielding factors" S n and S . can then be

p 2 3 cyl a i r

approximated by:

Jc y l yd °air 2d

S , = - l and S . = 4 - (2-2 9)

The weight of a shielding consisting of n+1 cylinders of equal thickness dn +^

and n a i r gaps of equal width dn +^ r e l a t i v e to the weight of a shielding

with the same shielding factor but consisting of n cylinders of equal thickness dn and (n-1) a i r gaps of equal width i s defined as R"+^.

We f i n d : i n n v n/

' . I T "1 (2.31)

d _{n \ n-i}

\y

As long as R ^1 < 1 i t is possible to reduce the weight of the shielding and

to retain i t s shielding factor by taking more cylinders. Let this shielding factor be:

2

Relation (2.30), (2.31) and (2.32) give with R"+ 1= 1:

» n '

(2n+i)(an-i) ₄ US2

(2.33)

These relations are useful for the inner cylinders of a composite shielding. The f i e l d strength i s low then and the permeability rather constant.

Saturation plays no role. Results of formula (2.33) are drawn in figure 2.9.

s h i e l d i n g f a c t o r S •

Figure 2.9. The number of concentric cylinders n that minimizes the weight of a magnetic shielding for a transverse field at a given r e l a -tive permeability p^ for all the cylinders and a desired

shielding factor S. The thickness of the cylinders is found from formula (2.34). This figure can only be used for cylinders in weak fields for which \ip is almost constant.

The optimal thickness of the cylinders and the width of the a i r gaps i s in case of n cylinders:

d = (H±l _n

v n - e u

(2.34)

In strong f i e l d s however, our f i r s t concern i s to keep u » 1. A useful material for the outer cylinders, which determine the weight of the shielding almost completely, should have a high saturation induction in the f i r s t place.

Final design

We have chosen for a shielding consisting of three cylinders: - an outer cylinder of ARMCO MAGNETIC INGOT IRON, a material with a high

saturation induction,

- an intermediate cylinder of HYMU 80, a material with a high permeability at an intermediate induction,

- an inner cylinder of VACOPERM 100, a material with a high permeability at a low induction.

Table 2.1. Constituents and manufacturers of investigated shielding materials

ARMCO MAGNETIC INGOT IRON

A n a l y s i s o f r e s i d u a l c o n t a m i n a t i o n s : C = 0 . 0 3 % Mn = 0 . 0 8 % P = 0 . 0 2 % S = 0 . 0 3 % Si = t r a c e s

ARMCO STEEL CORPORATION M i d d l e t o w n , O h i o ( U . S . A . ) AMEI IRON A n a l y s i s o f r e s i d u a l c o n t a m i n a t i o n s : C

-

HYMU 80 THE CARPENTER STEEL COMPANY, R e a d i n g , P e n n s y l v a n i a ( U . S . A . ) C o m p o s i t i o n : 8 0 % N i , 20%Fe VACOPERM 100 C o m p o s i t i o n : 70 - 80%Ni 30 - 20%Fe N E T I C , CONETIC C o m p o s i t i o n : u n k n o w n . VACUUMSCHMELZE GMBH Hanau (Germany) MAGNETIC SHIELD D I V I S I O N , PERFECTION MICA COMPANY C h i c a g o , I l l i n o i s ( U . S . A . ]

We measured B-H loops of several materials (table 2 . 1 , f i g . 2.10 and 2.11) to obtain r e a l i s t i c r e l a t i v e permeabilities as a function of the f i e l d strength These loops change considerably after welding and machining of the material, even when the material is properly annealed afterwards. This i s p a r t i c u l a r l y important at low f i e l d strengths. We were not sure that we could anneal the inner cylinder according to the description of the manufacturer and we decided to order these inner cylinders with a specified permeability from the manufac-turer. The other cylinders were made in the workshop of the Physics Depeartment

Fig. 2.10. B-H loops for high-induction materais and CONETIC. t B(T) HYMU 8 0 > ) 0.5-J^/*^ HYMU 80 2) -10 1 -5 1 // 5 10 1 i 1 1 1 1 T — 1 1 J H(Am_ 1) •+

-0.5-Fig. 2.11. B-H loops for high \iP

material HYMU,80. 1) specified for bars and rods. 2) measured on a torus (see text),

We measured the B-H loops on small t o r i . The dimensions of such tori are standardized to an inner diameter of 1 inch and an outer diameter of 1| inch. In the case of HYMU 80 we used a torus with an inner diameter of 100 mm and an outer diameter of 109.5 mm. This torus was made by bending a s t r i p and welding the ends together. The original material was supplied in the weld. This torus was annealed for about 6 hours at 1100°C in a dissociated ammonia atmosphere. This procedure was chosen because an identical procedure was required to make cylinders out of the s t r i p s , which were generously granted by the manufacturer.

We s i m p l i f i e d the calculations by taking the permeability everywhere in a cylinder equal to the permeability in one representative point. This point is for the outer and intermediate cylinder the point (r = R^, a) = — w h e r e the induction is maximal. The permeability as a function of the f i e l d strength is approximated by a number of straight l i n e s . For the inner cylinder we took the permeability to be constant, which is a good approximation as long as the f i e l d strength is very low. Using the exact formulas (which are

only given here in approximated form in (2.27)) and requiring a minimum weight we found for a total shielding factor of 1 0 "6:

outer cylinder R.=61.55(mm) Rll=100.5(mm) Bm =1.60(T) y = 522

intermediate cylinder 50.19 54.72 3.67*10_ 1 103750

The approximated "shielding factors" of (2.26) give, using these dimensions and permeabilities: S = 1.22 * 1 0- 6. The agreement is good, which j u s t i f i e s the

use of formula (2.27) which is based on these approximated "shielding factors" in future calculations. For the inner cylinder we find that the f i e l d strength is low indeed, as we had assumed in the calculations. The calculated thickness of the inner cylinder is already smaller than the optimum thickness (according to (2.34) dQ p t=0.94mm).

We changed the dimensions in our f i n a l design a l i t t l e ( f i g . 2.13) in order to be able to use standard sizes and thicknesses. The shielding factor became then, assuming the permeabilities unchanged, S = 0.8 * 1 0 "6.

Fig. 2.13. Final design of shielding against strong transverse magnetic fields (dimensions in mm).

The weight of the shielding depends further only on i t s length. The length is determined by the f i e l d s penetrating the i n t e r i o r of the shielding through i t s open ends. Using formula (2.13) and requiring a "reduction factor" of 1 0- 6 for these f i e l d s too, we find z > 4.OR. = 188 mm.

i

The intermediate and inner cylinder can be taken shorter, since the shielding factor of this combination is "only" about 10"1*. The inner radius at the open

ends should be as small as possible, resulting in the construction of f i g . 2 . 1 3 . The cylinders are separated by brass rings. The welds in the intermediate and inner cylinder are put in the $ = 0 d i r e c t i o n , where the induction is r e l a t i v e l y low.

We f i n a l l y decided to use the shielding at some distance from the magnet in a stray f i e l d of 0.1T instead of 0.3T and measured the internal f i e l d . We found at the point (r = 0, z = 0), that H.jnt/H t= 0 - 2 5 i n a9r e e m e n t w i t n

Mager (67Ma). We also found, that the f i e l d strength on the axis is very well represented by formula (2.13), except that we found an exponential decay coef-f i c i e n t ocoef-f 3.76, which is very close to the theoretical value ocoef-f 3.83, instead of 3.18, which was found by Mager for single cylinders with r e l a t i v e l y thin w a l l s . We were not able to measure the shielding factor in the centre of the shielding, since we could not measure inductions of less than 1 uT. Moreover, the external f i e l d is a dipole f i e l d rather than a homogeneous f i e l d , which was assumed in our calculations. The remaining f i e l d strength in the relevant central part of the shielding i s , however, lower than the 1 uT, where we aimed at. The weight of one shielding i s 85 kg.

2.6. The design of a peak s t a b i l i z e r .

The changes in count rate, that have to be determined in g-factor meas-urements, are very small. Even very small s h i f t s in the peak position have a considerable e f f e c t , when single-channel-analysers and scalers are used. We decided to aquire the data in the form of two-dimensional gamma spectra and to analyse these spectra later o f f - l i n e . Shifts in the peak positions are then of less importance. Nevertheless we designed and b u i l t p e a k - s t a b i l i z i n g systems to keep these s h i f t s small.

The design is based on a comparison of the pulse-height with a reference D.C. voltage. When a deviation (and what this means w i l l be explained later) is detected, the s t a b i l i z e r changes the amplification-factor of the main-amplifier ( f i g . 2.14), which is part of the system, to restore the equality of pulse-height and D.C. l e v e l .

r e g u l a t i o n v o l t a g ef

s t a b i l i z e d s i g n a l

Fig. 2.14. Block-diagram of peak-stabilizing system.

RGMA - r e g u l a t e d - g a i n m a i n - a m p l i f i e r UCA - ' u p p e r1- c h a n n e l a n a l y s e r o u t p u t

C a n b e r r a 1413 ( m o d i f i e d ) LCA - ' 1 ower ' - c ha n n e l a n a l y s e r o u t p u t TDCA - t i m i n g - d o u b l e - c h a n n e l a n a l y s e r SCA - s i n g l e - c h a n n e l a n a l y s e r o u t p u t MDAC - ' m e m o r y ' a n d d i g i t a l - t o - a n a l o g c o n v e r t e r

We have assumed, that only s h i f t s in the a m p l i f i c a t i o n - f a c t o r could occur and that there were no base-line s h i f t s (the base-line is already restored in the main-amplifier). The change in the gain can e.g. be caused by a change in the temperature of the photomultiplier or by a change in an external magnetic f i e l d , acting on the photomultiplier.

We decided against a p e a k - s t a b i l i z a t i o n by means of a regulation of the high-voltage on the photomultiplier, because this should also have affected the time-definition of the anode signals. Our choice implies, that we had to modify the mainamplifier. We included a f i e l d e f f e c t transistor in the f i n e -gain control in the f i r s t stage of the amplifier ( f i g . 2.15). The -gain of the

Fig.2.15. Upper part: original saheme of the first stage of the main-amplifier

Lower part: modified saheme with external gain control.

f i r s t stage of the main amplifier is now (table 2.2) approximately: „ 3010 a.500+226+R

909 R (2.35)

where a i s the fraction of the finegain potentiometer and R is the r e s i s t -ance of the f i e l d - e f f e c t t r a n s i s t o r . The gain was measured as a function of the regulation voltage ^reg f °r a = 0.89. The reduced gain G/GQ and the

reduced f u l l - w i d t h at half maximum FWHM/FWHMQ of the 662 keV peak of 1 3 7C s

were determined. The peak at 59.5 keV of 2 k lA m was used as a low-energy

reference point.

Table 2.2 Gain of the first stage as a function of vYeg or R and a,. (v) r e g R(f2) o f =0 a=0 5 a=l 0 - 1 .0 175 7 6 12 3 17 0 - 0 . 5 102 10 6 18 8 _{26 9} 0 75 13 3 24 3 35 4 +0.5 60 15 8 29 6 43 4 + 1 .0 52 17 7 33 6 49 5 46

The resistance of the f i e l d - e f f e c t transistor for small signals should have the form (70Da):

R '1

C

2

3

Ve"g -

The data from table 2.2 f i t nicely to: 73.38

R =

1.378/ 2 . 0 6 2 + V , - 1 _reg The reduced gain can be written as:

(2.36)

(2.37)

uo a=0.i

which i s , when (2.37) i s used:

0.101 + 67.45 (2.38) o a=0.89 1.267/ 2.062+V -0.819 _reg (2.39) 1.6. 1 . 4 - _{t - a l c u l a t e d ^ - - * *} 1 . 2 -^ -^ d f5^ ^ m e a s u r e d r e d u c e d FWHM _{1 . 0 ,} 0 . 8 . 0 . 6 -tr^^—reduced g a i n 0 . 4 -I 1 1 1 vr eC ( V ) > • • i i i

Some points, calculated with this formula, are drawn in f i g . 2.16 as t r i a n g l e s . The measured and calculated reduced gain agree f a i r l y w e l l .

Fig. 2.16. The reduced gain G/GQ and the

reduced full-width at half maximum FWHM/FWHM0 as a

function of V

The other two units of the system, the TDCA and the MDAC, are separated for practical reasons. The TDCA is e s s e n t i a l l y a timing-single-channel analyser, in which the "channel" is s p l i t in an "upper-channel" and a "lower-channel" of about equal width. The single-channel analyser function i s retained. Special attention was paid to the s t a b i l i t y of the DC-reference l e v e l s , because the s t a b i l i t y of these references is completely reflected in the s t a b i l i t y of the peak-position. At the time of the design, some years ago, only timing-single-channel analysers with a l e v e l - s t a b i l i t y e s s e n t i a l l y the same as the s t a b i l i t y of the +12V NIM-power supply were commercially available. The temperature dependence was 3mV/°C. We aimed at an overall s t a b i l i t y of