Possibility of Polarized Proton Acceleration- in KEK PS
S. Hiramatsu and K. Muto
National Laboratory fo High Energy Physics(K~K)

There are some estimations for the depolarization)resonance of polarized
proton beam during the acceleration in KEK 12 GeV PS. 1
However, these give
only qualitative results. Thus we calculated the depolarization by the intrinsic spin resonance (due to betatron oscillation) and the resonance due tothe closed orbit distortion (COD), quantitatively.
It is well known that the depolarization resonance occurs at yG ~v + n = 0for the intrinsic resonance and yG + n = 0 for the resonance due to COD~ wherey is the relativistic factor, v the wave number of vertical betatron oscillation, G = g/2-1 the anormalou~ gyromagnetic ratio, and n is an integer. In
KEK PS there are 11 intrinsic resonances and 22 resonances due to COD. The )polarization after passing through the n-th intrinsic resonance is given as 2Pf=P.[2exp(-a )-1]ln'(1)

where Pi is the initial polarization and an is given bya(2)nwhere E is the resonance strength and w0 is the angular frequency of revolution.n Eq.(l) represents that the spin flips for a >0.693.
Fig. 1 shows the depolarizations ~P/P.= 2[1-exp~-a-)] at intrinsic resonances, in which the polarizations are aveFaged over th~ beam emittance. The
total depolarization is 99.9: % during the acceleration 'from 500 MeV to 12 GeV
in the usual operation of KEK PS (-i>::: ·o). To accelerate the polarized proton,
we must choose the adequate value ot a by choosing 0 (v-jumping method).
For the case that 0 ::: +yG to increase ll: , we call "sl5w passage". On the other
hand if lv l>>yG tozdecrease a , we callf "fast passage". These methods areschematically shown in Fig. 2.n Applying the slow passage to the strong resonances and the fast passage to the weak resonances, we obtain the results ofdepolarizations as shown in Fig. 3, in which the total depolarization is lessthan 19.3 %. In order to apply the v-jumping method successfully, 4 or 8
quadrupole magnets must be installed additively in PS. The operations of those
fields are very critical and difficult but we think that is possible.
Fig. 4 shows the ~epolarizations arising from the resonances due to:CuD.
In this calculation we' use the statistical expectation values)of the harmonic
amplitudes of COD under the assumption of <zCOD>= 0.5 mm. 3
This resultshows that the depolarization is less than sever~Ts% for the resonances due to
COD except for 4 resonances at T = 4.8, 6.9, 9.0 and 11.1 GeV. It is possible
to avoid these depolarizations by increasing the harmonic amplitude of COD
near the betatron wave number to about 3 mm, in this case the spin flips atthese resonances. In order to control COD in such manner, it is necessary toimprove the correction magnet system for COD which consists of 28 dipoles.
References
1) T. K. Khoe, KEK-73-8, 1973
H. Sasaki, Proc. U.S.-Japan Semi. on H.E.A.S., 1973
A. Ando and E. Takasaki, KEK-ACCEL.-78-4, 1978
S. Suwa, 3rd Int. Symp. on H.E.Phys., ANL, 1978
M. Kobayashi, KEK~79-9, 1979-299-2)

3)

M. Froissart et al., Nucl. Instr. and Method 7 (1760) 297
E. Grorud et al., GOC-GERMA 75-48/TP-28, 1975L. C. Teng, Proc. AIP Conf. 43 (1978) 248
T. Suzuki, CERN/ISR/TH-77/64~1977

2.0APp(a)1.5 -spinflip

f

1.0!

spin
non flip

0.5 I-2Fig. 1

46I,II8(b)1012T(GeV)

Depolarizations by the intrinsic
spin resonances. 6P/P=O means nondepolarization, 6P/P=l complete
depolarization and 6P/P=2 complete spin flip in which depolarization does not occur.

2.0r.dPFig •. 22 ..0APpp

1.5 -1.5

1.0

1.0

0.5 -0.50.00

Schematics of v-jumping
methods. (a) Slow passage.
(b) Fast passage.

24681012T (GeV)

Fig. 3 Depolarizations in which v-jumping
method is applied.

o.o0Fig, 424

Expected depolarizations
by the spin resonances due

to COD. <zCOD>rms=0.5 mm
is assumed.

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