Vll-3

CHROMATICITY CORRECTION IN KEK MAIN RING
KEK Mai-n Ring Uagnet Group (presented by Ao Ando)
National Laboratory for High Energy Physics
Two families of sixteen sextupole magnets are used to control the chromaticity, i.e., the dependence of the tune on momentum. They are consistedof those near focusing quadrupoles; SF' and those near defocusing quadrupotes; SD. They are separately powered to control horizontyl chromaticity(~H = 3vH/3p) and vertical one (~v = 3vv/3p) independently;
Chromaticity for some correcting pattern are shown in Fig.l.
correcting current and strength of sextupoles respect to Fig.l.

Fig.2 shows

Chromaticity was determined from measuring kicked coherent betatronoscillations in few hundred revolutions for various momentum shift which wascaused by giving offset bias to r.f. feedback. In correction pattern III,measurements were not performed later more than 300 msec after acceleration
start, but it is expected from the relation between pattern II and pattern III
that chromaticity must be almost zero for those time.
The correcting sextupole current are determined from the matrix equation,

where M11

= 4nip JsF XeqSHds and other terms are like this.

Dominant terms of ~~ and ~ 0 are due to the variation of the focussing strengthof quadrupoles, and sextupZler field (B") in the guiding field. The former
is about -8.2 and -7.8 for v "'7.1 , ve"' 6.2, and the latter is about 6.3 B"/Band -5.9 B"/B, respect to~orizontalvand vertical. Dominant part of B" ateinjection por~ is induced with the finite permeability of the vacuum cha~er.
With respect to eddy current, the maximum contribution to B"/B is about-0.33/m 2 per one bending magnet and its effect is negligibel aft~r 100 msec
from acceleration start (see real line in Fig.l(a)). Sextupoler field in bending magnets after 200 msec from accelerytion start is larger by about 70 %than the results of field measurements~
Octupoler tune shift is caused by sextupoles;) and shown in Fig. 3 .. Agreements between the measurement and calculation are good enough. Moreover, thedeviati~ns of beta (SH an~S) and momentum dispersion function (X) are also
caused~Fig.4 shows resultX of calculations.· Deviations of SH aii~ X aresmall but that of S is respectively large. In this time these shift ~addeviation are not c~red but they must be corrected.
References
1)
2)

A. Ando et al., Proc. 5th Int. Conf. on Magnet Technology, Frascati (1975).
T. Kasuga et al., ibid.
1353)
4)

A. Schoch, CERN 57-21.
E.D. Courant and H.S. Snyder, Anal. of Physics, l (1958), 1.

-J

L--~~~~.~~~--~.~~~.-.-,-L--~.7.~~.~~~.~~~.-.~~7·:~,ne.tT·rFig.l(a) horizontal and (b) vertical chromaticity from the injection
porch t9 flat top start. Closed circle and real line: Pattern I,
triangle and broken line: particle II, open circle and dotted-line:
Pattern III.

.....A-tolsp-!CO.,.

Fig.2

Correcting current and strength of (a) SF, and (b)(a.){Q)'Vvf • •. . ... ."'.-"!' ... ..
•6s0 (= 0 in pattern I0•0•

Ill • • •u:

••'/.

(b)

xv.- ..t aF l-.:-M r•:...t ·f X~>
J'L

Fig.3

(a) tune shift vs. momentum shift at the injection porch.

Closedcircle is measurements, open circle is analytical calcualtion, andcross is results of particle tracking.

(b), (c) and (d) are deviation of Xeq' SHand Sv' respectively
calculated analytically.

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