ORBIT CALCULATIONS OF TARN AND ITS OPERATION CHARACTERISTICS
A. Noda, T. Hori*, T. Hattori, M. Mutou,
T. Katayama and H. Sasaki**Institute for Nuclear Study, University.of Tokyo* On leave from Sumitomo Heavy Industries Co. Ltd.
** National Laboratory for High Energy Physics
Abstract
The closed orbits and beta-functions of TARN for various
fractional momenta around the central one are calculated by thecomputer code SYNCH. The work line for an RF stacking process
is also studied experimentally by an RF knock-out method. A
chromaticity controle system with sextupole magnets is designedand fabricated.
l. Introduction
It is important to choose an optimum operation point toaccumulate ions in the storage ring. Especially in TARN, anRF stacking is applied and the momentum spread of the accumulated
beam is large (-±3% ). From the point of view of avoiding
lower order single particle resonances, it is desirable to
make the chromaticity as small as possible, while some amountof chromaticity is needed to sufmount the transverse coherent
instability by Landau damping. 1
In order to control the workline, the chromaticities in both horizontal and verticaldirections should be variable and a correction magnet systemof sextupoles is to be used for this purpose.
2. Numerical Calculation of Closed Orbits and Beta-functions
The lattice structure of TARN is a separated function FODO
type. 2 l
The arrangement of the magnets is shown in Fig. l.
The linear elements such as drift space, dipole and quadrupole
magnets can be treated by the use of transfer matrices.
In
the present calculation, non linear elements such as sextupole
magnets are linearized in a neighbourhood of the closed orbit. 3 >In TARN, the momenta of injected ions are decelerated by theamount of about 6% and moved to the inner side of the ring.4)
The closed orbits and beta-functions for various fractional
momenta are calculated by the method described above. The
calculated relations between tune values and fractional
momentum is given in Fig. 2 by solid lines.
3. Experimental Study of the Work Line by an RF Knock-out Method
The amplitude of betatron oscillation is increased when an
external RF field is applied in a transverse direction and thefrequency of the field satisfies the following condition,(m = 0, ±l, ±2,
where fis the revolution frequepcy of the ion and c is thefractioftal part of the v-values. S)
By applying a pulsed RFin such timing as shown in Fig. 3(a) and observing the resonant
frequency, at which the beam is kicked out as shown in rig.3(b)-297-the v-value is experimen tally obtained. The result is shown inFig.2 by open circles. The horizonta l chromatic ity is measured
to be smaller than the calculate d value.
4. Correctio n of the Chromatic ity by Sextupole Magnet System
The contribut ion of sextupole magnets to the chromatic ities
dvx
1 J B"
is given byds-. n • s= L'>P )d 0dv.,.

<f6Bp

41!

1- 4TI(X0pf B", ~ • n • i3 z

ds .
two families of sextupole
thatknown
From these equations , it ismagnets are needed, which locate at the positions where Sx, Szandn have different values from each other. Therefore twelve
sextupole magne-ts are used as shown in Fig. 1. 6 )Acknowled gement
The authors would like to present their sincere thanks toDr.
A. Garren who made a valuable collabora tion about chromatic itycorrection system. They are also indebted to Mr. K. Chiba at INS
computer room for his conversio n of the computer code.
Reference s1)
2)
3)
4)
5)
6)

B.
A.
A.
S.
A.
A.

Zotter and F. Sacherer, CERN-77-1 3 (1977) 175.
Noda et al., Proc. of 2nd Sym. On Ace. Sci. &Tech. (1978)83.
Garren and K. Chiba, to be published in INS-NUMA report.
Yamada and T. Katayama, INS-NUMA-12 (1979).
Noda.et al., to be published in INS-NUMA report.
Garren and A. Noda, INS-NUMA-14 (1979).

"- 2.\_•

2.30~0~2.2-2-10I

2-1( '/,)

2.20. . . ..
2.1

2.0-2-1

0

12-f
Fig .1 Arrangeme nt of tl:1emagnets for TAru~.

Fig.2 v-values for various
fractiona l momenta.

Fig.3(a) Upper; Sweep signalof RF frequency forstacking,Lower; the pulsed RF.
(b) Upper; Beam signal
from ES monitor,Lower; the pulsed RF.

-298-( '!.)