© 1973 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material
for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers
or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
ACCELERATION
OF
POLARIZED
PROTONS
IN
THE
ZERO
GRADIENT
SYNCHROTRON
(ZGS):::
L. G. Ratner
and T. K. Khoe
Argonne
National
Laboratory
Argonne,
Illinois
The motion
particle
is given
Introduction
With the advent
of high currenr
(,6-12 PA) and high
polarization
(7570) proton
sources,
It became
attractive to consider
the acceleration
of polarized
protons
Such a source
has been proto high energy
(12 GeV).
cured
and a second preaccelerator
with a beam transport line to the 50-MeV
linac has been installed.
A
description
of this ;ystem
will
appear
in the conferSince acceleration
of polarized
ence proceedings.
protons
to 50 MeV has been previou;ly
accomplished
we will not go
at the Rutherford
Laboratory
linac,
We will
conceninto this topic in the present
paper.
trate
on explaining
those factors
which
make the ZGS
an excpllant
accelerator
for minimizing
the depolarization
of an accelerating
beam
of polarized
protons.
d:
-=
dt’
As-’
2m
of the
by
spin
sxA>
in the
<B
(1)
1
> = Y
dz
4
B
s
Y
; t’ = proper
In the laboratory
nents at the location
and z (longitudinal)
the form
frame,
the horizontal
compoof the particle
are the x (radial)
components
which
can be written
. .
I:
of Polarized
1.
The ZCS is an essentially
weak
gr,adient
machine.
This assures
us
is smsli
enough so that the ciicct
of
isvvcen the gradjent
and the magnetic
particle
on orbit
can be neglcctccl.
(21
Protons
bB
b2B
BZ:I’)i+L
xyt..
by
-.
E b
x y
For the ZGS it is a good approslmation
osc~ll.at;cn
‘5 s!nl.??r;d?l
the betatr”!?
focussing
zero
that the gradient
interactions
bemoment
oi the
(2 _ ”
R
with
S&,,tit-Jting
curl
B 10,
I?)
.=2$,x
into
(2)
ai;d
neglecting
higher
scricu,
m
WC obt,lir&
i:i Fourii~r
‘It<.
;:Gy> >,,;.5 ij-A--LI <Li ;gl-1: 6 c it i CJii :r n: i:iifI.Tc;it
:~‘,:l;tlis.
Lind foiir .*hort
Thcr~~ :ir<’ f01.1r I on 2 s t rni 4 ht icctions
it:‘1 :;2h: ~.~~~~-tioilr. .i:; WC’ shall
ihow,
th.:: icads to
c,inc~~lldf .ot: term
w17ic.h ~;<a~n rtx6115~ thf :;pin flip
tr.ln:,it:on
I>i-i-)b,tbl!ity.
R
s
,
r;:rilcing
DISC’ of tlx
orricr
,21on:1c
En1:r7y
the
X.
..- ;
A
1
RkT
{,k--i,)
A 1 bk9
((lb.+
iJ i,;
k-0
co
B
of
that
where
terms,
:.
The ~~sluc of the vertical
tune I, is les s than one
LiII <i, a:; me :,hall see, this (,nters4;r; Yo ‘hc transition
Thns,
fhc rcfprobsbllit~;
,x5 ‘I-r:ip
[-constant
‘ii )
Y -;
ililting
probability
[or spir. flipping
1s small.
.LUS~:CC~::
to assume
y = Aron (*,:vO t ro)
I
The ch,inge
in vertical
tunt* a\,
as a function
of
2.
Y
radiIIs
1s less than 0. 01 nt ~11 fields
and indeed has
llecn
made
AS .~mall
as 0. 001.
This
rriults
in a small
nor% near depolsrii;ation.
the
C.~n:misslon.
in
E2B
EB
i‘Je will first
list the features
of the ZGS which
contribute
to reasonably
small
depolarization
effects
and then show how they qcantitativcly
enter into the
rransition
probability
of depolarization.
llndcr
; and
dz
xyt..
: T.~ork ncrior~ed
time
is the average
guide field in the laboratory
frame.
Clearly,
the precession
caused by the vertical
field
does not affect
the axial polarization.
Since the octant
field gradient
is very
small,
the only depolarization
effects
come from
the horizontal
field components
at
the magnet
edges.
Since the particles
have a vertical
betatron
motion,
they will
experience
rotating
horizontal field components
in crossing
the magnet
edges.
These
can contribute
large
depolarizing
effects
if their
angular
frequency
is equal to the precession
frequency.
In Section
I, we describe
the relevant
ZGS parameters
and the corrections
required
to minimize
depolarization.
In Section
II, we describe
the procedure
to be used to measure
the polarization
of the extracted
beam.
.:.
of the
,
Y
g = 5. 58536
to 12 CeV/c
in the ZGS, calculathat there
are ten major
depolarizing
As suggested
by D. Cohen, 5 pulsed
quadresonances.
rupoles
can be used to provide
rapid tune shifts
to
Such a system
has been designed
avoid depolarization.
and constructed
for the Z,GS and is described
in the
b
conference
proceed:Egs.
The
frame
where
show
Section
ZGS as an Accelerator
rest
S.
-
%
f
2
k: 0
217
0 * = j.
-}
{act
that
ar.rl cxp,lndln&
In the laboratory
of the particle
dO
-=
dt
Using
adding
frame,
is given
where
the average
angular
velocity
by the cyclotron
frequency
g(t)
ecBy’
my
==
s
-t*
.
this and going to the particle
rest frame
the Thomas
precession
term,
we obtain
sb +
dt
and
and
A = 6
(up-wk)
at
.
up = ok
m
b
= yA2
x
akLa?rl:
c
k=O
m
bz =$ c bk
k=O
k
t’
The
(3)
and t’ is the proper
frequency
is
From
time.
(l),
the precession
ii
2
111
resonance
y
=
condition
kivyw
t
is Fiven
so that
by ,I, =K
k’
P
bB
--I
Fx
- llyz
Equation
k i ,J
Y
(1’l can be written
.Y
= ib
-i
tb
-
(ak+>)
(5)
show how the values
of these machine
lead to a small
transition
probability.
= !!L
In
‘:
in terns
of rotating
<
~np
*’ 5
fields
the coeificlents
a
) ,“%r.tkt’
b z = (I>- -b-)-Y
.
Y
Eby = EBy
125
Cn
Then
b
=*
%,
0 *
(5
by
The ZGS has four long straight
sections
and four
Since the fields
in the octants
short
straight
sections.
are uniform,
we have only the horizontal
components
of the magnetic
field
at the edges.
The edge angles
are different
for the long and short
straight
sections
and for the short
straight
sections
have a small energy
dependence.
Similarly,
the length
of the short
straight
section
is slightly
energy
dependent.
We characterize
the edge angles
by tLand
“S and the straight
section
i
lengths
by the 1 angles
OL and 6
Let n be a -ector
S’
normal
tc the edge and we then have
>
e<By>
and the
b+
Y “By’
We can now
parameters
e<B
y) y
g vOP - 2
r =-
r is given
sir tuk t’
where
wk = (ktiyt
quantity
i
,i,kt’
“k-;
and bk are
k
determined
from
TI *B
1
.J t ,>2? I<(! do
s En
0
V.~i~ c’ r c
2
: ;
b
!;
k
ii %B
n .,.
:
11
Cl
.’
i ::: I.-O
ilc?
‘3
3.
b
Lt ',, .iiF4>. ,
.$
.
i
_
Let L : the eif?cI!;~~~ Ic,lL<t!l
C!mI k : 5 pi nillltipl~~
of i‘o,lr.
8’ ,3.ntl 1, ,-o.ln+.c’rcl.;cl;The: fii,ld i> / :‘i,!~..I<‘S cloc:P.‘~:c
Since th<, :pin prccc-55i’i
c lockwise,
only- IhC ‘7+
‘!;i;;,s L
ti, rrr .lri.-G .ic ,.lfi ,.-t. ‘Cl>!7 I> trrlil
:n t.-\~c.r-y ]‘ll> rot.itl’?ll
l-he ni.t ;!,:p&r:,&
:><’ .!i-‘.‘$.
‘.‘,. i s I’ .
“k
h
l>k - ;
of tops
inr
i .-:in; < i : h I'r t.h e &.l:i.- -;:i: 11 ne~ll,~nics
I -1,: 11i:i rr, :nc ci:;xr.i i: S) WC can S'JL'i e lor thi, prcl~itb!t:ty
1 I7_.
71.
-, I
.- 7. ! I’ 1;:. ii j ‘;a’; !-e*c!y ,L’:L!-. 1 ,,I:‘. !,-, :,pin
A,
2 IL,I LI
,Li.;i,n
Dt:tt~rmini!l;:
13).
~dircction,
p
L: i.
.F! ;:’ 2 I’:
*,I!!
t
7
y
sn
1
2’
1
2
l-C:;,,
- -L--
2
-$;,,
;;+.y
)
;5.c
ji
11unj
.
A II
LX’< 1’: !lCl 11:,i:
f
,~-“I”
the
i 1, i
Y
.I rLcE!n i I ‘- -:r F ,i
y
3n
218
>
,- .:
I
.,
;<(~,
I,
7~r ;<I,
+ I3
_ y- -Au Zl<
],,
3n
li
%
/;; F
:r
/L 1.))
.>I ::!:t, i cl;;<: TieId ,d ItI I;,>:*’
For i-h,., ZGS, we thin
c,c,t
L
r
->;-’
_+x
sI,d..
^” ” - I
c,q1l,ilion
*
‘Cftij,,
ts”. pi. kOS \,
c,C r:is~tiaJ7
in
.
Chc* ;
This
then
Tbere
is thus a depolarization
of about 270 from
the resonances.
There
is also a small probability
of
spin flip when off of resonance,
and calculations
show
this to be about 4:: during
the acceleration
cycle.
We
additionally
expect
about 3?0 depolarization
between
the
source
and the ZGS and about 170 from the ZGS to the
experimenters.
We anticipate
then a net polarization
of 65% in our extracted
beam of about 109 protons
per
We feel that the effects
of magnet
errors
and/or
pulse.
misalignments
will be smaller
than
the
major
contributions
that we have considered.
gives
2v 2< B r> sir 6L’:ykBLfsin
8S:g:kOS
R
t
sib
Es
ak =
Sk rL
2
2,> <I3
b
=-
ii
From
>
-a?6 LCin kCiLt
R
Eq.
sin F
(5) xc;e tE.us see that
L
:c? ~Ssln kBS
i- sin F
S
r is proport:onal
to v
2
Y’
In the following
table we then show the values
of
the above terms
fcr the ZGS.
In most cases we note
chat the facx <ha:: lh? straight
sections
have different
lengths
leadi
to s=l~llzr
v.Jues
of aI< and b and hence
k
of r and P
1
i’
q-j-2
i
-
-x
4
f
Cl:i>Lc~~r
ML
ii
Extraction
Section
II:
and Measurement
of Polarization
In order
to tune throcgh
the depolarizing
resonances,
we must be able to extract
beam before
and
after
the resonaxe
and tc measure
the amount
of polarization.
When a measurable
depolarization
occurs,
ES51nX0(
sin~,~,inrk~~ -W SLShkOL LO2C
ak
c
b
k
z
l/
=/a,td \ ic
P
bk\
r
Y ,
-6
1
1
29-T
1.785
. 20690
-. 14266
-. 41875
. 33158
. 06424
2.675
. 20690
-. 14623
-. 41875
. 31971
. 06067
-. 03698
. 02369
5. 1
”
4.016
. 14436
. 12186
-. 75603
-. 59388
. 26922
-. 33613
-. 06691
17. 9
Y
4.909
. 14436
. 12567
-. 75603
-. 59050
. 27003
-. 27430
-. 00427
17
0. 24-O
* 03375
-. 09065
-. 94624
. SO6 18
‘. 03; 12
-. 02242
-. 05954
16. 0
. c42
12
7. 140
. 0537 3
-. 09159
-. 9462-L
.a0374
. 037,+i,
-. 019%
-. 05782
14. 2
. c47-
4
-. 04883
+. 01541
1. 1x10
.9
.00023
.0008
. 0:
.00008
16
:3.479
-. 047 34
.oi751
-. 95239
-. 14166
.00017
-. 22338
-. 22321
38.3
. 366
16
‘2. ii 1
-. 647 :4
. OL7?8
-. 9523?
-. 94080
. 00064
-. 20203
-. 20135,
21. 5
. 312
.?0
10.710
-. 1:071I
.00055
-. 77 326
. 98740
. 13866
.019$9
-. 11867
23. 3
.2;5
20
ll.hO3
-. 13921
.00055
-. 77 326
. ?E740
. 13666
.OlSa6
-* 12020
22.7
* 255
21
-
12. 342
=i,
--
-
-.vc can
:i-?c’ Irom
ihc
table,
transItion
the
WC -,vill tilrn on the pulsed
cl;:x!r:lpoles
;u.;t Fe<o:e ,rd
move the pulse in time until xce minimize
t’hc dcpolarization.
This a-ill be done ox “Tront-;>orcX
fl;lrtops
.et
just before
re.>on:z,lci,
;Ir,d jzst after.
D e5 n-l XL11 be er.:tracted
usin,; an energy
loss txryet
and with ..low spill.
It has beer, predicted
theo:rticc,.Ily
by WolCc:l*:c;n7
:z,nd
i /,
_.-. ..:...
ql,o,lrl~ C~:npl.;r’TIl+l?!;i
ir. ‘7 -iiril,li
-J-C---i~,,,,i.~-~i‘,.~l~~.,’
LL1<7
i
L
depolzr:za:icn
do<: 5 not oc:‘~r
in .:.nv ,:r.i i”.~ 10: :i t.:r:,e t
proxr;dc-d tbc :;c,-.‘;teri:i!r
~n;le
is 5 1-‘;~11. 7.;:,.:,iyt: I>;, liil
these “lroct-porch”
rl.ittops
will
nI:so 1;~. II:-,:t’:-, 1 I->- io1
thr high cne rgy physics
tspzrin?,:nts
~.ir;sz
r-;i:;i’ will
bi done <AS n function
31 cnc rcy ‘ram
lb >I;t 3. 0 G*?S’!,:
to 12. 0 Gc’4’/ c.
prob-
is rea:sonibl;-m;,ll
up to *; = 7. 1. In order
to
IVC’ :::u.;t St111 I.F.dilce tkL5 cl,-.po5,- ; cc 1~~~lleT c;ler;>ie>,
IrryiZGet’ -*Al_.
-,?Jhinir twc qu,:drupoles,
spaced
ll;O” apart,
..‘:ilit>-
i :~ch ,v;;th .I 73-111
; ,P c,, .n :‘cr
<i
tit.11
effisctivc
the ~oll~~:,.:~~
chance:,
-1
_ .7.,::e
.?Ci !lcl\-?
1.
_____
tl:n::
q ;;xl:-.:p
‘3 ‘-_
6’1,
j1,-:
,liT
le@h
q
2500
;11v3 a gradient
G-i!i/lri,
we
can
,-::d tr;.ins-tqLs,n
nrnhzhil
::ul.-+ci
7.;:ill .i !Cl-_ *: ri:,i
,ii‘.,-
iti~i:.
!:l!;le
3
do,
i
7;
‘1
/ 4 II
___~
5,
.”
-7
-:
ij:l;
-;
. \)\I-i,?
-” 0
s
. dO27
ra 0
k
. ilO
I- 0
i
-
, 0’117
.0:102
12
, 0 0 1i
. 0 00 2
1:;
. ‘1017
. 00 3
1 i-
. 11011
.001
30
. IO009
.003
-----p
0009
T 1ble 11
1
0
1.1
1.1;
of
asl-.:eve
fl~rttop.
)
I
--
TC mch.:ure
the- pc)lnr.;;.it:
:,11 0: tC> ‘ ,tr.xct<,d
beam,
V.TF are .~ss~mbling
ii ?air oi dcubl~. nri:: sptactrcjil:l-trrs
whiciwill
I?w:-x;ure the el-*itic
proton-:jroton
acattrring
of the polnr; r,ibd hc‘am iron1 .I liqliiti
h>-dra::cn
target
(Yig.
1). \Yc w-ill measure
the left-right
.isymmetro
(A) b?twcen
thr two .~p~ctrr,i~~,~t~~r.s 3nd II,~~’ ti-.,,
p-p asymmetry
parameter
(f\l,p) m~~;~sl;r~~d in oth<,r t~:~:?eYim:~ r.ts I:? ;:,i;-c: thr l>?;ni p,i.,LLLL~Lsll
G).
A : P il
1’1’
nt
4
.ooi
219
KFCll <‘n?rgy
is men:;urrd
I’P
WC WJl ,lS;i’ J ‘;i.<l:tering
,IIIXli. ‘:Jhcro
and large.
As Cdr, I>(‘ nc<‘n in F’:g.
2,
appreciable
polarizations
gies up to 17. 5 GeV.
exist
at all
measured
Quadrupole
197 3 Particle
cisco,
Cal.,
ener-
We should point
out another
interesting
possibility.
The source
can also produce
polarized
deuterons.
These can also be accel.erated
and extracted.
The
The
deuterons
can then be passed
through
a stripper.
proton
could then go through
the polarimeter
while
the
whose
energy
is well determined,
polarized
neutrons,
would then provide
a monoenergetic
polarized
neutron
beam tar high energy
experimentation.
At the present
time,
there
are four
periments
and three proposals
or letters
These
experiments
use these facilities.
vestigating
the following
topics:
approved
of intent
propose
7
could
3.
Measurement
of inclusive
cross
charged
and neutral
final
states.
F.
exto
in-
Study
4.
actions.
of resonance
Study
5.
cesses.
of parity
production
violations
Stuciy of interactions
6.
1 Z-it bubble
chamber.
Polarization
7.
both
in PP and PN
inter-
of polarized
in proton
neutron
scattering
protons
elastic
U. Kruse,
Phvs.
Rev.
Rev.
;5,
1664
(1949).
J. Marshall,
L.
2,
250 (1255).
Marshall,
%
L- POLARlZED
PROTON BEAM
Fig.
for
in proton
Solmitz,
Phys.
r ,/*;/*,/N-’
Hz
TN?CET .-___..
i \
p
R -\\\
\\‘*.b
of /i’s produced
lead to high
sections
JVolfenstein,
8E. Heiberg,
1.
Measurement
of total and differential
elastic
cross
sections
with the initial
spin states
parallel
and
This
uses the polarized
beam and a poantiparallel.
larized
target.
Measurement
of the polarization
2.
by a polarized
proton
beam
This
intensity
polarized
hyperon
beams.
L.
System
for Preventing
Depolarization,
Acceleration
Conference,
San FranMarch
5-7,
1973.
High Energy
Polarimeter
Showing
Right
and Left Arms
of Spectrometer
for
Detecting
Asymmetry
in Elastic
Scattering
of Polarized
Protons
1
proin the
scattering.
1
i
I
0
Acknowledgements
We would like to thank E. D. Courant,
Teng,
NAL,
and A. D. Krisch,
University
for valuable
discussion
and comments.
Reference
1
;\UCLC~:I~C! .\uciear
[ANACi,
Auckland,
7
5
0
3
Associates
Nccessories
New Ztssland.
Co.
E. Parker,
J. Xladsen,
N. Sesol,
R. Stocklcy,
R. Timm,
Argonne
National
Laboratory,
Zero
Gradient
Synchrotron
(ZGS) High Energy
Polarized
197 3 Part:Proton
l3pa1-n Pra~rnm-Ir.jector
System,
,-lc Accc 1~r,ltor
Conference,
San Francisco,
Cal. t
March
:, -7, 1’!7 3.
‘G. 14. Stafford,
Cratlciock,
Nucl.
1
SNL,
L. C.
of Michigan,
D.
Cohen,
J.
M.
Inst.
R.c~r. sci.
“Acccl~:ratlon
1. b:ha2,
7r.c
i?:,port
,L<.,, ’ I:>+rr.,T!
Accelerator
I.aborat’~ry,
.i. Bywater,
L. R-atnr r,
Dickson,
D. C. Salter,
Meth.
15, l-C6 (1?62).
Inst.
x,
M.
K.
161 (1962).
0; Polarized
Protons
In thr
TF:?:- IO, Ar~onn:?
N2’;ionaI
Dtvibion.
T. Khoe,
R. Lsri,
C. F’otts,
.,1rxonnr~ P;.lt:onal
I,aboratory,
Fig.
ih’. Pr,l(>::,
A Pul~c,d
220
2
Polarization
Proton-Proton
iL<easuremen:s
Scattering
in Elastic