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A SAMPLE OF DEPOLARIZATION RESONANCE CORRECTION FROM THE INITIAL COMMISSIONING OF THE POLARIZED BEAM AT THE AGS

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HAL Id: jpa-00224594

https://hal.archives-ouvertes.fr/jpa-00224594

Submitted on 1 Jan 1985

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A SAMPLE OF DEPOLARIZATION RESONANCE CORRECTION FROM THE INITIAL

COMMISSIONING OF THE POLARIZED BEAM AT THE AGS

L. Ratner

To cite this version:

L. Ratner. A SAMPLE OF DEPOLARIZATION RESONANCE CORRECTION FROM THE INI-

TIAL COMMISSIONING OF THE POLARIZED BEAM AT THE AGS. Journal de Physique Collo-

ques, 1985, 46 (C2), pp.C2-625-C2-630. �10.1051/jphyscol:1985276�. �jpa-00224594�

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Colloque C2, supplgment au n02, T o m e 46, fbvrier 1985 page C2-625

A SAMPLE O F D E P O L A R I Z A T I O N RESONANCE CORRECTION FROM T H E I N I T I A L COMMISSIONING OF THE POLARIZED BEAM AT THE AGS+

L.G. Ratner

Alternating Gradient Synchrotron Department, Brookhaven National Laboratory, Associated U n i v e r s i t i e s , Inc., Upton, New York 11973, U. S. A.

REsum6. Nous prssentons une description de la rEponse 1 la correction de plusieurs r6sonances. On observe des comportements diffdrents en- tre les r6sonances de la mCme catsgorie, c'est-2-dire les r6so- nances intrinssques ou d'imperfection. Nous donnons aussi une des- cription rapide des installations et deleur 6tat actuel.

Abstract. A description of the response to correction for several resonances is presented. Different behavior is seen between resonances of the same class, i.e. either intrinsic or imperfection resonances show different behavior within their own genre. A brief description of the facility and present status is also given.

1. Introduction

For orientation purposes, we give a brief description of the polarized beam facility. The whole facility can be functionally divided into two sections: (1) a front end consisting of the polarized ion source, the 20 keV beam transport, the RFQ linear accelerator, the 750 keV beam transport, the 200 MeV linac and 200 MeV polar- imeter and the 200 MeV transfer line to the AGS; (2) the hardware necessary in the AGS to accelerate and maintain the polarization of the injected protons. Fig. 1 is a schematic of the whole faci,lity and, in addition to the front end components, shows the correction dipoles, the pulsed quadrupoles and their power supplies, the internal polarimeter and the high energy polarimeter which make up the AGS modifica- tions necessary to produce a high energy accelerated proton beam.

The ion source produces polarized H- with a peak output to date of 25 PA in a 400 psec FWHM pulse. It is then injected at 20 keV into an RFQ which accelerates the beam to 760keVwithaboutan 8 0 % t r a n s m i s s i o n e f f i c i e n c y . After acceleration to 200MeV in the Linac, the polarization is measured using a pc12 scattering. Polarization to date has been about 70-75%. Beam is then injected into the AGS and accelerated. A peak intensity of 10l0 polarized protons per pulse has been accelerated and a physics run was made at 16.5 GeV/c with a beam polarization of about 40%. The major problem in acceleration is to preserve the beam polarization.

To understand what the problems are in preserving the polarization of an accela- rated beam, let me remind you of what depolarizes the beam.

There are basically two types of depolarizing resonances, oneaso-called "in- trinsic resonance" which is due to the natural periodicity of the accelerator and two, an "imperfection resonance'' which is due to misalignments which lead to closed vertical orbit distortions. These are characterized by

'work performed under the auspices of the U.S. Department of Energy.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985276

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c2-626 JOURNAL DE PHYSIQUE

Gy = kP

*

v i n t r i n s i c

and GY = k i m p e r f e c t i o n

where G = g / 2

-

1 anamolous magnetic moment k = i n t e g e r

P = p e r i o d i c i t y of t h e a c c e l e r a t o r (= 12 i n AGS)

v = v e r t i c a l machine tune (number of b e t a t r o n o s c i l l a t i o n s p e r revolu- t i o n )

Y = r e l a t i v i s t i c energy f a c t o r

k ~ Dipoles i o ?

k.

Pulsed Quodrupoles

A

Fig. 1. AGS F a c i l i t y .

Discussion and d e r i v a t i o n have appeared many times b e f o r e s o we won't say anymore here o t h e r than t h a t t h e i n t r i n s i c resonance can be c o r r e c t e d f o r by a f a s t v e r t i c a l tune s h i f t (V ) and t h e i m p e r f e c t i o n resonance by a r a d i a l magnetic f i e l d a t t h e proper

harmonic.

The f a s t v e r t i c a l tune s h i f t s f o r c r o s s i n g t h e i n t r i n s i c resonances a r e gen- e r a t e d by f e r r i t e quadrupoles with a 2 Usec r i s e time and a 3 msec decay time.

For t h e i m p e r f e c t i o n resonances we g e n e r a t e a harmonic c o r r e c t i o n a t t h e ap- p r o p r i a t e energy u s i n g 96 d i p o l e magnets. Searches a r e t h e n made around t h e reson- ances and t h e r e l a t i v e p o l a r i z a t i o n of t h e beam i s measured by an i n t e r n a l polar- i m e t e r a s a f u n c t i o n of t h e c o r r e c t i o n amplitude o r timing. The resonance cor- r e c t i o n c u r v e s Fig. 4 t o 8 and 10 t h a t w i l l be shown a r e i n a r b i t r a r y u n i t s f o r p o l a r i z a t i o n . The a b s o l u t e v a l u e of t h e p o l a r i z a t i o n was measured a t 16.5 GeV/c d u r i n g t h e physics run with a double-arm s p e c t r o m e t e r looking a t PP e l a s t i c s c a t t e r -

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ing and gave the 40% value quoted earlier and this is the polarization value seen in Fig. 9.

Fig. 2 shows the calculated energy and strength of both the imperfection and intrinsic resonances that we expected to correct in the AGS. As can be seen, we expected to correct only about a half dozen imperfection and four intrinsic reson- ances below 16.5 GeV/c. However, the real world was a little different and we had to correct some thirty imperfection resonances as well as the four intrinisic ones.

y G

=

k IMPERFECTION I y G

=

kP 2 v y INTRINSIC x

x 9g0/0 SPIN FLIP

CORRECTIONS

5 10 15 20 25

PROTON MOMENTUM ( G e V / c )

F i g . 2 . Fredicted AGS resonances

Fig. 3 shows some typical corrections in tune-energy space for an intrinsic resonance. The resonance line is crossed in less than one turn ( " 2 psec) and the tune

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remains a fixed distance from the resonance as the correction pulse decays at a rate comparable to the change of energy during the normal acceleration cycle

(1.2

-

2.9 msec depending on the

-

I I I I ~ I strength of the correction 0.125

-

24:85 2 5 : ~ 0 25115 0.30 tune units).

7

Fig. 3. Typical corrections in tune-energy space.

2. Examples of Resonance Jumping and Correction

The description of what occurs when we try to correct for resonances can best be seen in the following examples of passing through both imperfection and intrinsic resonances.

In tuning through GY = 0

+

vy, an intrinsic resonance, one sets a reasonable amplitude and then varies the time at which the quadrupole is energized. In this particular case we set the quads to produce a tune shift of 0.2 units. We then

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s t a r t e d t o s e a r c h i n t i m e n e a r t h e c a l c u l a t e d p o s i t i o n of t h e resonance. The a b c i s s a i n Fig. 2 is t h e number of "Gauss c l o c k counts" ( a magnetic f i e l d g e n e r a t e d number) which is p r o p o r t i o n a l t o t h e momentum of t h e a c c e l e r a t e d beam. We s e e i n

t h i s r e s u l t a n t curve a s p i n f l i p r e g i o n a t 8400 Gcc and t h e r e g i o n where we have s u c c e s s f u l l y jumped t h e resonance a t 8635 Gcc. The bump a t 8250 Gcc i s s t i l l n o t u n d e r s t o o d , but t h e f l i p and c o r r e c t i o n p a t t e r n i s e x a c t l y what one e x p e c t s from a resonance. The o r d i n a t e i s a measure of t h e r e l a t i v e p o l a r i z a t i o n a s measured w i t h t h e i n t e r n a l p o l a r i m e t e r . The l o c a t i o n of t h e resonance was i n e x c e l l e n t agreement w i t h t h e p r e d i c t e d number of Gauss c l o c k c o u n t s .

RESONANCE

G A U S S CLOCK C O U N T S

7800 8200 8600 9000

~ ~ S E C *

Fig. 4. I n t r i n s i c GY=O+Vy Resonance C o r r e c t i o n .

2 7 6 0 0 27800 2 8 0 0 0 2 8 2 0 0 GAUSS CLOCK COUNTS Fig. 5. I n t r i n s i c GY=36-9

Resonance C o r r e c t i o n . The GY = 36

-

v (Fig. 3) h a s a much w i d e r s e m i - c o r r e c t i o n b e f o r e t h e s p i n f l i p and l o o k s q u a l i t a t i ) 3 e l y d i f f e r e n t

.

These d i f f e r e n c e s are probably n o t due t o t h e n a t u r e of t h e resonance but r a t h e r t o some anomoly i n t h e c o r r e c t i o n p u l s e . The odd be- h a v i o r o c c u r s b e f o r e t h e main c o r r e c t i o n p u l s e and i s , t h e r e f o r e , e a r l i e r i n time.

T h i s means t h a t t h e f i r s t i n t e r a c t i o n of t h e c o r r e c t i o n p u l s e and t h e resonance t a k e s p l a c e when t h e t r a i l i n g edge of t h e p u l s e r e a c h e s t h e resonance. Some o s c i l - l a t o r y b e h a v i o r n e a r t h e end of t h e decay p u l s e could account f o r t h e s e d i f - f e r e n c e s

.

The c a s e f o r t h e i m p e r f e c t i o n r e s o n a n c e s i s d i f f e r e n t and t h e y indeed show v a r i e d p r o p e r t i e s . The c o r r e c t i o n t e c h n i q u e f o r t h e i m p e r f e c t i o n resonance curve shown i n Fig. 6 i s a l i t t l e more complex. S i n c e t h e v e r t i c a l o r b i t d i s t o r t i o n of harmonic number k is d r i v e n by h o r i z o n t a l i m p e r f e c t i o n f i e l d s of harmonic k , we c o r r e c t t h e s e GY = k resonances by c a n c e l l i n g t h e k t h component of t h e h o r i z o n t a l i m p e r f e c t i o n f i e l d . We c o r r e c t by p u l s i n g t h e 96 d i p o l e s w i t h t h e a p p r o p r i a t e amplitude and phase t o minimize d e p o l a r i z a t i o n . We f i r s t had done t h e c o s cor- r e c t i o n w i t h an a r b i t r a r y s i n e c o r r e c t i o n and t h e n we s e t t h e cos a t i t s peak of -5 and d i d t h e s i n c o r r e c t i o n . S i n c e t h e s e a r e o r t h o g o n a l , o u r c o r r e c t i o n v e c t o r s h o u l d have t h e c o r r e c t amplitude and phase. Notice t h a t t h e r e s o n a n c e i s 6 u n i t s FWHM. For c o n t r a s t , Fig. 7 shows a resonance c o r r e c t i o n w i t h almost 120 u n i t s FWHM f o r GY = 19.

Another t y p e of resonance c o r r e c t i o n i s s e e n i n Fig. 8 f o r G Y = 30. On one s i d e we see a f l a t l e v e l v a l u e of p o l a r i z a t i o n f o r 60 u n i t s of c o r r e c t i o n , b u t on t h e o t h e r p o l a r i t y we s e e a r e l a t i v e l y weak but d e f i n i n t e d e p o l a r i z a t i o n . For t h i s resonance z e r o c o r r e c t i o n was a p p r o p r i a t e .

The v a r i a t i o n s we s e e i n t h e s e i m p e r f e c t i o n resonances a r e f u n c t i o n s of t h e i r st'rength and were expected. However, thougb we a n t i c i p a t e d t h a t t h e r e might be some

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new behavior s i m i l a r t o what had been s e e n a t S a t u r n e , we were s u r p r i s e d by t h e s t r e n g t h of t h e r e s p o n s e t h a t we s e e i n Fig. 9. GY = 27 i s an i m p e r f e c t i o n reson- ance, but a t t e m p t s t o c o r r e c t w i t h t h e 2 7 t h harmonic f a i l e d . Indeed, t h e d r i v i n g f o r c e h e r e i s due t o t h e " i n t r i n s i c " b e t a t r o n o s c i l l a t i o n s i n t h e a c c e l e r a t o r . To s e e t h i s we n o t e t h a t t h e b a s i c t u n e of t h e machine i s 8.75 which is v e r y c l o s e t o 9 and f u r t h e r we n o t e t h a t t h e 27th i m p e r f e c t i o n i s t h e n v e r y c l o s e t o t h e v e r y s t r o n g i n t r i n s i c GY = 36 -V

.

A s s e e n i n Fig. 9 t h e c o r r e c t i o n r e q u i r e d was t h e 9 t h har- monic and t h i s f u l l y Y r e s t o r e d t h e p o l a r i z a t i o n . Other r e s o n a n c e s where t h e d i f - f e r e n c e were c l o s e t o 8.75 such a s d i f f e r e n c e s of 7, 8, and 1 0 a s w e l l as 9 were i n f l u e n t i a l i n c o r r e c t i n g d e p o l a r i z a t i o n , a l t h o u g h t h e y were not always t h e major component (e.g. GY = 26 = 36-10, GY = 29 = 36-7 Fig. 10).

F i g 6. S i n e and c o s i n e harmonic c o r r e c t i o n s f o r G Y = 9 i m p e r f e c t i o n resonance. Narrow and s t r o n g .

16 GeV/c P O L . O/O 2 0

4 0

Gy

= 19 I M P E R F E C T I O N

R E S O N A N C E 9.90 GeV/c A R B I T R A R Y

U N I T S

-

C O S C O R R E C T I O N -60 -40 -20 0 20 40 60

Fig. 7. GY = 19 c o r r e c t i o n . Wide and weaker.

Fig. 8. GY = 30. Zero cor- r e c t i o n needed.

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Fig. 9. GY = 27 corrected with 9th harmonic.

Acknowledgments

16 GeV/c P O L . O/O

Fig. 10. GY = 29 corrected with 7th harmonic.

The work described here was made possible by the dedicated effort of very many talented people at Brookhaven, as well as the important contributions by Argonne National Laboratory and the Universities of Michigan, Rice, and Yale.

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