RIKEN Accel. Prog. Rep. 50 (2017)

Ⅱ-8. Accelerator

Injection-beam-orbit analysis of AVF cyclotron using 4-dimensional emittanceY. Kotaka, 䠆1 Y. Ohshiro, 䠆1 H. Yamaguchi, 䠆1 N. Imai, 䠆1 Y. Sakemi, 䠆1 T. Nagatomo, 䠆2M. Kase, 䠆2 J. Ohnishi, 䠆2 A. Goto, 䠆2 K. Hatanaka, 䠆3 H. Muto, 䠆4 and S. Shimoura 䠆1For the purpose of increasing the beam intensity of theAVF cyclotron, the improvement of the injection beamintensity is essential because 80% of the beam intensity
produced by ECRIS is lost in this injection line. In order todetermine the reason for this loss and to optimize theinjection beam orbit, the injection beam orbit is analyzed inview of the space charge effect.

The equation of the space charge effect is as follows:4),
where s is the beam axis, (x, y) is the transverse
phase-space coordinate, Ȝ is the number of particles per unit
length, ȕ and Ȗ are Lorentz factors, a and b are the ellipse
axes of the beam, and rp is the classical radius of theparticle.
We solved the equation of the injection beam orbit
including equation (1) and compared the 2-dimensional
emittance measured by EM_I36. The coordinates (u, w) of
EM_I36 are rotated by 45 degree against the coordinates (x,y). The comparisons of (u, u’) and (w, w’) are shown in Fig.
2 and Fig. 3, respectively. The shapes of the calculated
2-dimensional emittances are close to those of the2-dimensional emittances measured by EM_I36. The modelof the space charge effect is thought to be effective.

Fig. 1 Beam injection line of the AVF cyclotron.
Figure 1 shows the beam injection line of the AVFcyclotron. We measured the 4-dimensional emittance by thepepper-pot emittance monitor1) (PEM_IH10) and calculated
the injection beam orbit using the 4-dimensional emittanceas the initial value. We adopted two types of calculation
models for electromagnets. For the calculation in solenoid
coils and quadrupole magnets, we adopted the calculated
magnetic field. On the other hand, we adopted thehard-edge model for a dipole magnet (DMI_23). For theedge focus of DMI23, we used the correction indicated byTRANSPORT.2) These calculation models were tested by a25.4-keV 4He2+ ion beam of 5 eA. The calculated beam
orbit was mostly consistent with the measurement results ofthe beam viewer (I23viewer), profile monitor (PF_I30) and2-dimensional emittance monitor (EM_I36).3)
To evaluate the performance of these models for thehigh-intensity beam, we tested them by a 15.4-keV 4He2+ion beam of 240 eA. The calculated beam orbit was notconsistent. The result was thought to be caused by the spacecharge effect.
There are some models for the space charge effect. In themodel we adopted first, the beam cross section was circular,
and the transverse and longitudinal beam densities wereuniform.3) Next, we adopted an ellipse instead of a circle
because the beam cross section was not always circular.
㸨1Center for Nuclear Study, University of Tokyo
RIKEN Nishina Center
㸨3RCNP, Osaka University
㸨4Center of General Education, Tokyo University of Science, Suwa
㸨2- 146 -
Fig. 2 (left) Image of (u, u’) emittance measured by
EM_I36. (right) Image of the (u, u’) emittance calculated
from the measured 4-dimensional emittance.

Fig. 3 (left) Image of (w, w’) emittance measured by
EM_I36. (right) Image of the (w, w’) emittancecalculated from the measured 4-dimensional emittance.
References
1) T. Hoffmann et al., Proc. 9th BIW, Cambridge, USA (2000), p.
432-439.
2) D. C. Carey et al., FERMILAB-Pub-98/310
3) Y. Kotaka et al., Proc. 13th Annual Meeting of PASJ㸪 Chiba(2016).
4) S. Y. Lee: Accelerator Physics 1st ed. (Singapore, World
Scientific, 1999).