ORBIT CALCULATIONS FOR THE IPCR SSC
N. Nakanishi, K. Yamashita, T. Wada, A. Goto, Y. Yano
S. Motonaga, and H. Kamitsubo
The Institute of Physical and Chemical Research
In advance of construction of a SSC at IPCR several computer codes aredeveloped, and orbit dynamics has been investigated. An outline of the orbit'.
calculations for the sse is presented.
A 1/4 scale model magnet, which is composed of two 50° magnets, wasconstructed, and magnetic field distributions at the median plane were measured,at different field strength.!) Since the model magnet, however, is not exactlyof a 1/4 scale in the radial direction, the data have to be not only scaled up
but also exapnded to that of the full scale magnet.
Equilibrium orbits are determined for various particles using the magnetic
field distribution at the corresponding field strength. All of ray tracing
calculations are performed within one sector from a valley centerline to another, because of the four-fold symmetry of magnet structure.
The linear characteristics of the magnet system are calculated on betatronfrequencies, eigen-ellipses, phase plots and so on. An isochronous field is
produced numerically in such a way that a base field is increased graduallyin the radial direction to make the correction for a revolution time. However
the relative distribution in the azimuthal direction is not changed for convenience because of lack of the informations on the field shape of trin~ing
coils. Betatron frequencies are shown in Fig. 1 for typical four examples.
In the calculation for accelerated orbits, informations have to beprepared on the isochronous fields,
geometrical shape of dee structure
1.2l.O
1.4
and acclerating voltage. Since
0.9a linear accelerator is used as
one of injectors, matching conditions between the linac and theSSC should be satisfied. The isochronous field has been obtained
N::l..
in the previous stage. The
field, however, can be corrected to achieve better beam accele0.7
ration. For dee structure a twodee system with delta-shapecavities is designed.2) The
accelerating gap is taken to beconstant (10 em). Dee angle isbasically 20° because of a9.
fundamental harmonic number hThis angle can be changed for0.5
more effective acceleration.
Radial- and frequency- dependence of the accelerating
voltage are introduced based
Betatron frequencies fer tvoicalFig. l
on relative radial distribution
Injection and extrac~lon
four nuclei.
frequencies
variousat
measuredradii are taken to be 82.5 and 375.0 em,Symbols x, &, + and 0
respectively.
using a 1/2 scale model cavity.
represent 0.84 MeV/A u40+, 4.0 MeV/A c6+,
7. 0 MeV /A c6+ and 10.0 :.leV p+, t"espectively.

-295-The minimum voltage along the accelerating gap is taken to be 250 kV.
Properties of an accelerated reference orbit and linear characteristics
of associated orbits are investigated. Injection conditions of an accelerated
reference orbit are determined to minimize the coherent radial oscillation
amplitude. It corresponds to minimization of the phase slip of oscillationof a rotating particle against radio-frequency. Fig. 2 shows phase slip of
4 MeV/A 12c6+ for the first several decade turns. The quality of an accele~
rated beam is evaluated by ray tracing calculations in six-dimensional phasespace. As an example, transformation of phase space pattern projected on the(r,r') plane is shown in Fig. 3 on the above beam up to several hundred MeV.
When a cyclotron is used as one of injectors, extensive studies have tobe performed.
References
1)

2)

N. Kumagai et al: IPCR Cyc1.
Progr. Rep. 12i 10(1978)
H. Nakajima et a1: ibid., p 16

10.0~~.c-5.00.

-10.0

Fig. 2 Phase slip of a particle a~ainst
the radio-frequency. A 4 MeV/A c6 particle
is injected onto its first equiliblium orbit.
Initial injection conditions are not
optimized at all.

Fig. 3 Transformation of a radial phasearea with an initial e~ittance of 2.5,mm mrad. A 4 MeV/A c6 particle isinjected onto its first equiliblium orbit
without any optimizations of acceleration
conditions.

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