BNL 66455
April 19,1999
Editors:
M. Tigner, Cornel1
A. Chao, SLAC
Publisher: World Scientific
Sections written by Thomas Roser, BNL:
-
2.7.1 - Thomas BMT equation
2.2.2 - Spin or Algebra
2.7.3 - Spin Rotators and Siberian Snakes
2.7.4 - Ring with Spin Rotator and Siberian Snakes
2.7.5 Depolarizing Resonances and Spin Flippers
&
7.6.2 Proton Beam Polarimeters
-
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herein to any specific commercial product, process, or
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DISCLAIMER
Portions of this document may be illegible
in electronic image products. Images are
produced from the best available original
document.
Handbook of A c c e l e r a t o r Physics and Engineering
By A. Chao (SLAC) ; M. Tigner (Cornell) World
S c i e n t i f i c , sections(2.7.1-2.7.5
and 7.6,2
.
I
introducing a large number of background beam-
2.7 POLARIZATION
scheme has moved beyond the conceptual stage,
to date.
2.7.1 Thomas-BMT equation
Z Roser; BNL
ion events, No indirect beam-beam compensation
Betatron phase cancelation A single set of
beam-beam resonances may be eliminated by adjusting the phase advance between neighboring
IPS in a storage ring [18]. For example, if t5e
phase advance between two Ips is A& = A& =
2n(p/N q) (p, q, N integers, p odd), then all
beam-beam resonances of order N are canceled.
This scheme, which has not been fried in practice,
relies on the collision points being clustered - not
smoothly distributed around the circumference.
Other resonances, tune shifts, and tune spreads are
left uncompensated.
BNL- 664 5 5
Precession of polarization vector F of a particle
with mass m and charge Z e [l,2,3,4],
+
P‘ is defined in the particle rest ftame, 2 and B
in the laboratory *e.
B’ = 2-1+ Bll, Zil =
(v’. B)v’/v2.
In the ftame rotating with v’ given by the
Lorentz force equation and assume Ell = 0,
= d,xa
dp
-
= fixp’
at
References
YK Batygin, T. Katayama, RTKEN-AF-AC-3,
1997
JE. Augustin et al, p.113, Vol. 2, Proc. 7th Int.
Conf. H. E. Acc. (1969)
G. Arzelia et a$ p.150, Roc. 8th Int. Conf. H. E.
Acc. (1971)
H. Zyngier, AD? Proc. 57 (1979) p.136
YaS. Derbenev, 3rd All Union Conf. on Acc.
(1972); INP 70-72 (1972); SLAC TRANS 151
.
(1973)
E. Keil, Proc. 3rd ICFA Beam Dyn. Wkshp.
(1989); ERN-LEI?-lW89-37 (1989)
Orsay SR Group, EEE Trans. Nucl. Sci. NS-26,
No.3 (1979) 3559
R. Chehab et al, Proc. 1lth Int. Conf. High Energy
Acc. (1980)
VE. Balakin, NA. Solyak, Proc 13th Int. Conf.
High Energy ACC.(1986)
[lo] N Soly&-INP 884,Novosibirsk (1988)
[113 D. Whittum, R. Siemann, PAC 97
1121 Y. Chin, DESY 87-011 (1987)
1131 JB. Rosenzweig et al, hoc. Lake Arrowhead
Wkshp., AD? Press (1989) p.324
1141 R. Talman, unpublished (1976)
[15j E. Tsyganov et al, SSCL-519, (1993); JINR-Eg964, Dubna (1996)
[16] V. Shiltsev, D. Finley, FERMILAB-TM-2008
(1997)
[17J D. Whittum et al, LBL-25759 (1988)
[18] S. Peggs, Proc. Wkshp. on AP Issues for SSC,
UM HE 84-1 (1984) p.58
dv’
dt
9 is the anomalous magnetic moment;
25 is the pqyrom~eticratio (Landau fac-
G =
g=
G
0.00115965
0.00116592
p
1.79285
p
-0.142562
d
3He 4.19144
e
I
3H 7.93689
102
0.440649
90.6220
0523341
13.1522
0.669910
0.680342
0.00330816
0.572843
9.0227940
0.895023
0353779
0.847401
I
One-turn matrix Mo (0):
Mo (e) = M,:
References
[l] B.W.Montague, Phys. Rep. 113 (1984)1
[2] L.H. Thomas,Phil.Mag. 3 (1927)1
[3] V. Bargmann, L. Michel, V.L. Telegdi, PRL 2
(1 959)435
[4] S.Y.Lee, World Scientific (1996)
2.7.2
(11)
where 8 is the starting (and ending) azimuth. The
~
spin tune uw and the spin closed orbit f i (also
called A0 axis or stable spin direction) are
1
(12)
cos (7rvw) = -tr
2 (Mo (e))
Spinor Algebra
2: Rose< BNL
independent of 8
Coordinate frame symbols and indices: (1,2,3)
=(radial outward, longitudinal forward, vertical
up) = (2,-5, 9). Pauli matrices:
a' = (61,a2, a3)
0 1
1 0
1 O)'(
0 -1)]
=[(
(T1q
8
= a2a2 =a3a3 = I
"Spin Rotators" rotate P' without changing G.
Examples of Spin Rotators:
(1)
(2)
3
($4)
($4)=
2.73 Spin Rotators and Siberian Snakes
iT Rosel; BNL
ii)(
=
~ -0103=ia2
1
(cyclic perm.)
tr(ai) = 0, det(ai) = -1
~
1. Wien Filter: Transverse E,, B, with condiE x i 7 - 1B'
tion
-
$
(3)
(iq+iz. (zxc)
Spinor representation of normalized vector F:
I
Y
(4)
Mwien
F = ?pa$
=
2. Solenoid
COS
cp
cp
- ia3 sin -
2
2
Ze(l+G)
mcPY
c p =
Thomas-BMTequation in spinor or unitary representation:
- - M2M1
J ~iids
cp
cp
= cos - - 202 sin (2)
2
2
Example: cp = 90" and p = 1 GeV/c requires J BIIds = 1.88 T-m for protons and
J BIIds = 5.23 T-m for elecuons.
kf&le.oid
-d =p f i x F
dt
3. Dipole:
or
dt
2
solution for constant fi : xis A, 161= w):
(7)
,$ ( t )= M (%4,$ (0) 3 or
(a - P (t))= M ( ~ , w t (a
) - F ( 0 ) ) Mt (fi,wt)
Rotation operation M by angle cp = w t around
axis n
I'
[
cos
Inverse operation:
2
(i) i (Z - ii)sin (g)
n=
A
i
2 sin
0:
-
.
=
4. Full twist helical dipole with
B ( s ) = BO ( s i n y , O , c o s T ) , A
M(fi,cp) = exp - i ( $ - . i z ) -
cp
cp
cos - io3 sin -
(3)
2
2
Example: cp = 90" and /3 x 1 requires J Byds = 2.74 T-m for protons and
J Byds = 2.31 T-m for electrons.
MDipole
(9)
tr ($Ad)
(3)
103
+
>s >
cp
cp
M = cos - i(a2 xa3) sin -
2
ZeG BOX
x = ( 1+-G' r) mc 27r
2
(4)
5. A "Full Siberian Snake" rotates P' by 180"
(9 = n) around an axis in the horizontal
plane with angle Q fkom 2 (Snake axis angle) Ill:
M s n & = -i (a1cos
a2 sin or) (5)
5. Ring with N pairs of full Siberian snakes
with axis angles or; and or; at 0; and g6:
Mo(8) = (-)NexP(-ic3x)
+
N
x = c(or;-a:)
i=l
Note:
(i) MDipoleMSnakeMDipole = MSnake(ii) Type 1 snake: snake axis is longitudinal (or =
CE,($-Q
6EEl (or; - or:).
[l] YaS. Derbenev, A.M. Kondratenko, PA 8 (1978)
and Siberian
Snakes
T.Rose< BNL
MO(8) = exp (-iu3nG~)
(1)
Note: usp= G7.
2. Ring with solenoid (partial type 1 Siberian
snake) at 80 = 0 [11:
cp COS ( X G ~ )
M~(e) = cos -
2
cp sin ((n- 8) G7)
- iul sin 2
cp
- iu2 sin - cos ((n- 8) G7)
2
cp
- iu3 cos sin (nG7)
(2)
2
= cos 5 cos (nGy).
3. Ring with full Siberian snake with axis angle
a at 00 = 0:
MO(0)
=
+
Note: usp =
- 0)GT)
sin(a! - (n- 8)Gn/)] (3)
--i[01 COS(CY - (T
02
for all 8; 8 = n
ri.cosa$Bsina
=
n; then usp =
References
[l] T.Roser, ROC.
Workshop on Siberian Snakes and
Depolarizing Techniques (1989) p.1442
1. Ideal ring without spin rotators or Siberian
snakes:
Note: cos(nv,)
MO is energy independent for
Note:
References
2*704 Ring With Spin
N
i=l
goo)
(iii) Type 2 snake: snake axis is radial (or = 0")
115
(5)
-+
.720 =
2.7.5
Depolarizing Resonances and Spin
Flippers
I: Roser, BNL
Thomas-BMT equation with azimuthal coordi-
nate 8 as independent variable and the fields expressed in terms of the particle coordinates:
(1
+ G7)g' - p ( 1 +
G)
where p is bending radius. Resonance strength is
111
EK = -f t e x p (-iK8) d6
2n
K = kP =t uy : intrinsic resonance from vertical
betatron motion, P is the super periodicity
K = k : imperfection resonance from vertical
closed orbit distortions.
For isolated resonance: = E K exp (iK8).
In frame rotating around jj with tune K ,
+K = exp ($m3)11,
4. Ring with two full Siberian snakes with axis
angles CY, and ab at Bu and 8b :
Mo (8) = -exp(-iu3x)
(4)
Under adiabatic conditions:
x E - 4- (n- 66 4- &)G7
Note: MO is energy independent for
1
8, = n;then usp= ;
;(ab- cra).
Ob
(2)
-
PY =
104
(G7 - K )
d(G7 - Kl2 + ~
K 2I
(4)
Passage through an isolated resonance, FroissartStora Equation [2]:
-Pfinal
Enitial
with
CY
- 2exp
(-<)
n IEKI
-1
(5)
depolarizingresonances were not too strong in the
weak focusing ZGS; thus it only required careful orbit control and fast betatron tune jumps to
maintain the polarization while crossing the resonances [l].
c
4GY)
= dB
(crossing speed). Fast passage
-+
PfinalM Pinitiai.
-Pinitial 4 spin flip.
Slow passage
-+ Pfinal
M
. Artificial resonance from local oscillating field (w
Linac
= applied frequency, wo = revolution frequency):
BII
=
on Source
\2GQ
SllCOS(Wt)
MeV
Pohrmler
(7)
Spin flip by ramping artificial resonance through
resonance condition with speed CY:
Kend - Kstart
CY=
(8)
2nN
where N is number of turns during ramp. For
more than 99% spin flip:
4)
III a ring with Snakes (vsp =
additional
higher order 'Snake' resonances [3] occur at ener-
gies close to intrinsic resonances of the ring with-
out Snakes when the fractional vertical betatron
tune
2k - 1
AvY =
2(21- 1)
With vertical closed orbit distortions Snake resonances also occur when
References
[l) ED.Courant, R.Ruth, BNL-51270(1980)
[2] M.Froissart, R.Stora, NIM 7 (1960)297
[3] S.Y. Lee, S . Tepikian, PRL 56 (1986)1635
2.7.6
Polarized Proton Beams and Siberian
Snakes
A.D.Krisch, U.Michigan
In 1973, the first polarized proton beam was successfully accelerated in the Argonne ZGS.The
Figure 1: The complex individual depolarizing resonance correction hardware installed in the AGS [21.
In 1984, polarized protons were first accelerated at the Brookhaven AGS. Maintaining the po-
larization was much more difficult, because the
strong-focusing AGS has strong depolarizing resonances. As shown in Rg.1, the AGS required
complex hardware modifications for this difficult
job. Moreover, 45 resonances needed to be corrected individuallyto maintain the polarization up
to 22 GeV. A typical AGS resonance correction
curve is shown in Fig2 [Z]. The polarized beam
tune-up required 7 weeks of dedicated AGS operation. Clearly this individual resonance correction
technique was impractical for a much higher energy, since the number of imperfection resonances
to be crossed is E / (0.52 GeV). Thus, it became
clear [3] that Siberian snakes (41 (Sec.2.7.34)
were needed to accelerate polarized protons above
30 GeV.
Many Siberian snake experiments have been
performed at the 500-MeV IUCF Cooler Ring.
The snake was a 2 T-msuperconducting solenoid
installed in a 6-m straight section, as shown in
105
Dr. T. Roser
AGS Dept
Broohaven National Lab
Upton, NY 11973-5000
May 16,1998
Dear Dr. Roser,
Enclosed you will find type set proofs of your article for the Handbook of Accelerator
Physics and Engineering for your correction before final editing and publication. Even
though time is very short, it is being sent to you by post so that you can see, with good
resolution, how it will appear in the book.
While the type setting process is largely automated, some needed format changes and
equations require human intervention, thereby creating opportunity for errors. For this
reason it is extremely important for you to check every aspect PARTICULARLY
EQUATIONS AND REFERENCES.
Please mark the corrections clearly and fax them back to me at 607 254 4552 as soon as
possible. If you are unable to do it immediately, please note that it will be very difficult to
include any corrections received after July 15 so if we have not heard from you by then we
will assume that you have no corrections to submit.
Your expert and patient participation in this enterprise is very deeply appreciated indeed and
we hope that you will have your copy of the finished book in hand early in 1999.
I
?
(max for 90" scattering):
All =
(7
+ cos2 8') sin28'
(3 + cos2 8/12
7
I
9
(22)
The polarized electron targets in Moller polarimeters typically consist of thin ferromagnetic
foils exposed to a 100 gauss external magnetic
field oriented with a given angle to the foil axis.
A 8.3% maximum polarization of the target electrons (2 external out of 26 electrons per iron atom)
has been achieved. The target polarization is measured to 1.5 - 2.0% precision (1.7% at SLAC).
The full beam polarization vector is determined by varying the foil orientation relative to
the beam.
The analyzing power of Mraller polarimeters
need corrections due to orbital motion of inner
shell target electrons [141 (momenta comparable
-
to e* rest mass).
Fig3 shows the SLAC E-154 Mdler Polarimeter [U, 161
Bend Plane
Moller
. . Target
,
[2] DB. Gustavson et al,NIM 165 (1979) 177.
[3] F.W. Lipps, HA. Toelhoek, Physica, XX (1954)
85 and 395
[4] HA. Toelhoek, Rev. Mod. Phys. 28 (1956) 277
[5] 0. Klein, Y. Nishina, Z . Phys. 52 (1929) 853
[6] U.Fano, J. Opt.SOC.Am., 39 (1949) 859
171 M. Woods, Proc. Workshop on High Energy Polarimeters, NIKHEF (1996)
[8] A. Most, Proc. Workshop on High Energy Polarimeters, NIKHEF (1996); PhD Thesis (1996)
[9] M. Placidi, R. Rossmanith, NIM A274 (1989) 79
[103 B .Dehning, Dissertation der Facultiit fijr Physik
(1995)
[I 13 L. Arnaudon et al, Z . Phys. C66 (1995) 45
[12] K. Abe et al, PRL 78 (1997) 2075
[13] C. Maller ,Ann. Phys. (Leipzig) 14 (1932) 532;
J. Arrington et al, NIM A3 11 (1992) 39
[14] L.G. Levchuk, NTM A345 (1994) 496
[15] HR. Band, AIP Proc. 343 (1994) p245
[161 H.R. Band et al, SLAC-PUB-7370 (1997)
7.63 Proton Beam Polarimeters
T Roser; BNL
Beam polarization is typically measured using a
nuclear reaction in a plane that is perpendicular to
the polarization direction. The polarization P and
its statistical error A P (for P A << 1)are calculated as:
Mask,
vv
Secondary Mask
Scattering Plane
A: Analyzing power of nuclear scatteringor reaction
NL(NR):Number of particles observed to the left
(right) of the beam.
If the beam polarization is alternated between
(along the stable spin direction n) and - (opposite to the stable spin direction n) the polarization
can be measured with much less sensitivity to systematic errors:
+
See Tab. 1.
Figure 3: The SLAC M0ller Polarimeter.
"drvL+ + NR+
+N;
+ N;
References
[l] W. Haeberli et al, NIM 163 (1979) 403
[2] H. Spinka et al, NIM 21 1 (1983) 239
References
[3] S.Kat0 et al, NIM 169 (1980) 589
[4] M. W. McNaughton et al, NIM A241 (1985)435
[5] DL. Adams et al, Phys. Lett. B264 (1991)462
[l] VN. Baier and V.A. Khoze, Sov. J. Nucl. Phys. 9
(1969)238
178
Table 1: Typical nuclear reactions used for proton beam polarimeters.
Energy
< 0.1 GeV
0.1.. .1 GeV
1.. .20 GeV
>2OGeV
Reaction
p+” C - ) p +12 C
p+’” C + p + X
p + p +p + p
p+p+p+p
ZI+12 C + T+(-)
+X
7.7 CONTROLS A N D TIMING
K. Rehlich, DESY
Change in computer hardware and software is
Kinematic region
6 x 50’
6 x 15”
t = -0.15 (GeV/c)2
t = -0.0001 (GeV/c)2
vt
0.5GeV/c:x~ x 0.5
Anal. power
A = 0.8. . -0.9
A x 0.2. ..0.6
A 0.7GeV/c
PT,ah
A x 0.04
A x 0.15
Client programs often need information from
a group of devices or need to operate on such a
group. A middle layer server should provide such
collective reports and controls. Likewise, the mid-
Architecture As shown in Fig.1, the overall architectureconsists of three layers of computers. A
dle layer should supply frequently requested data
of all its front-end computers in a single block
transfer. Proxy services may also be added since
the middle layer servers can be faster than the
front-end computers. But, a direct access to frontends (and not just for debugging purposes) is still
necessary. In general, the middle layer implements higher services and improves the performance of the system.
Data bases, file servers, simulation servers
and other kind of servers without direct device
connections should be placed in the middle layer
also. Subsystems of the machine use their own
subnet with front-end computers. The front-ends
are distriiuted and close to the devices of the machine. Some hardware is directly connected to the
device servers, other equipment use field busses
to connect the front-end electronics to the device
servers. Fieldbus electronics introduce a further
level of computers in the system. Programmable
end layer with device servers and UO and a middle layer with powerful group servers. The upper
layer is the interface to the operators. These upper
services should be available to the consoles in the
control room, the experts working at the machine
and the specialists in their offices. All of them
should be able to use the same programs. Only the
level of det‘ails presented should be different, but
nonetheless available to all levels of users. Modifications of device data must be protected with
access rights.
Since a lot of users and client programs access
a lot of data from the front-end and the middle
layer, a fast network is necessary to decouple the
display stations. A net switch that routes packets from the clients to their servers provides the
important bandwidth.
are examples of such stand-alone processors.
All group servers and most fi-ont-end servers
are equipped with disk drives. The other device
servers mount their N e systems from the corresponding group server. If a front-end has to
run stand-alone in case of a network problem, it
should have a direct connected disk or must have
the program and data files in memory. Archiving
of all data fiom the equipment can consume a high
portion of the network bandwidth if the storage is
not in a local disk.
Front-end computer Most of the device input
and output channels connect via VME modules
or fieldbus electronics to the device servers. The
VME system is designed for a reliable industrial
electronic environment. Almost any computer,
analog or digital input/output module and field-
rapid on the scale of accelerator construction
schedules. Nevertheless software development
must begin early to be ready in time. Most of
the investment in a control system goes into the
software and front-end electronics. For front end
components the use of industrial standards is now
quite safe as systems such as VME have shown a
long lifetime.
Softwaredevelopment should be based on the
new industrial methods. Object oriented tools
have proven to be very powerN for control system design. In addition to object orientation, implementation on more than one platform leads
to better design and helps to prepare for the inevitable evolution of computer systems during the
project lifetime. Below we discuss the general architectureof a system and argu for a clear modular
design of hardware and software together.
top level with display or client programs, a fi-ont-
Logic Controller (PLC) and “intelligent” devices
179