Ⅱ-8. Accelerator

RIKEN Accel. Prog. Rep. 51 (2018)

Improvement of injection beam-orbit analysis of AVF cyclotron
Y. Kotaka,∗1 Y. Ohshiro,∗1 H. Yamaguchi,∗1 N. Imai,∗1 Y. Sakemi,∗1 T. Nagatomo,∗2 M. Kase,∗2 J. Ohnishi,∗2A. Goto,∗2 K. Hatanaka,∗3 H. Muto,∗4 and S. Shimoura∗1In order to increase the beam intensity of the AVF
cyclotron, the injection beam transport system must beimproved. As the ﬁrst step of this improvement, wehave developed a calculation method of the beam orbit
down to the center of the AVF cyclotron from the ion
source by using the 4-dimenssional emittance measured
with a pepper-pot emittance monitor1) (PEM IH10), as
shown in Fig. 1. One feature of our calculation method
was the use of the 3D magnetic ﬁeld calculated with acalculation code to take into account the fringe ﬁelds ofelectromagnets. The other was to implement a spacecharge eﬀect.2–4)
As reported previously, the beam-orbit calculation
with such magnetic-ﬁeld distributions of solenoid coils
and quadrupole magnets was successful.2) Therefore, we
also renewed the model of the dipole magnet DMI23
shown in Fig. 1 from the hard-edge model of a dipole
magnet with a fringing ﬁeld and pole-face rotations5) to3D magnetic-ﬁeld distributions. The result did not differ from that of the previous model. However, this hashelped us to ﬁnd a practical beam energy by calculating the beam orbit with the 3D dipole magnetic ﬁeld
including the fringing ﬁeld.
In order to improve the calculation of the space charge
eﬀect, we formulated a multistep-ellipse model insteadof a single-ellipse model. In the single-ellipse model, theshape and beam-intensity distribution of the beam crosssection are approximated by an ellipse and by a uniform distribution, respectively. However, the real beamintensity distribution is not uniform.3) Therefore, we increased the number of ellipses that keep the center andgive each ellipse the amount of beam elements that exist
within it.
To construct the equation of motion (EOM),4) a standard ellipse must be deﬁned by the combination of
the average, standard deviation, and correlation of thebeam-intensity distribution. Multistep ellipses are madeby evenly dividing the ellipse, the radius of which is 6times larger than the radius of the standard ellipse, into
30 ellipses.
First, the EOM including the space charge eﬀect forthe beam element in the innermost ellipse is constructed.
Then, the EOM for the beam element located between
the second and ﬁrst innermost ellipse is constructed fromthe second ellipse. For the outer ellipses, the EOM isconstructed accordingly. The beam elements beyond theoutermost ellipse are neglected.
The result of the multistep-ellipse model is shown in∗1
∗2∗3
∗4

Center for Nuclear Study, University of Tokyo
RIKEN Nishina CenterRCNP, Osaka University
Center of General Education, Tokyo University of Science,
Suwa

Fig. 1. Injection beam line of the AVF cyclotron.

Fig. 2. (Left) Beam-intensity distribution measured withI23viewer. (Middle) Beam-intensity distribution calculated by the single-ellipse model. (Right) Beam-intensity
distribution calculated by the multistep-ellipse model.
The ion beam is 4 He2 + at 15.4 keV and 250 eµA.

Fig. 2. Ion beam measured is 4 He2 + at 15.4 keV and250 eµA. The left of Fig. 2 shows a beam-intensity distribution measured by I23viewer, which is a beam viewer
and is shown in Fig. 1. The middle of Fig. 2 shows abeam-intensity distribution calculated using the singleellipse model. The radius of the single ellipse is 1.8 times
larger than the radius of the standard ellipse. The rightof Fig. 2 shows a beam-intensity distribution calculatedusing the multistep-ellipse model. It can be seen that themultistep-ellipse model reproduces the measured distribution better than the single-ellipse model.6) The reasonfor this is thought to be that each beam distribution of
the cross section on the beam axis is close to the realdistribution.
By these improvements, the shapes of the beam deduced from the calculated beam orbit have become close
to the measured ones. In addition, we plan to ﬁnd amethod to evaluate these diﬀerences of shapes quantitatively. However, the calculated central position andbeam angle were not always the same as in the measurement. This is a problem to be improved in the future.
References1) T. Hoﬀmann et al., AIP Conf. Proc. 546, 432 (2000).
2) Y. Kotaka et al., Proc. 13th Annual Meeting of PASJ,(Chiba, 2016), pp. 1072–1075.
3) Y. Kotaka et al., RIKEN Accel. Prog. Rep. 50, 146(2017).
4) S. Y. Lee, Accelerator Physics 1st ed. (Singapore, World
Scientiﬁc, 1999), p. 62.
5) D. C. Carey et al., FERMILAB-Pub-98/310 (1998),p. 131.
6) Y. Kotaka et al., Proc. 14th Annual Meeting of PASJ,(Sapporo, 2017), pp. 1118–1122.

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