ULTRA STABLE MAGNETIC FIELD OF THE RCNP CYCLOTRON FOR
HIGH RESOLUTION BEAM OPERATIONS. Ninomiya, T. Saito, H. Tamura, and K. Sato,
Research Center for Nuclear Physics(RCNP), Osaka University, Osaka, Japan,

1 INTRODUCTION
The Research Center for Nuclear Physics (RCNP) inOsaka University has a cyclotron complex, which consistsof a large-sized ring cyclotron (K=400) and an AVF
cyclotron (K=140). The RCNP cyclotron complex iscontinuously operated during a few months even forweekends. Accelerated particles and/or their energies are
typically changed a several times per month for several
kinds of nuclear physics experiments.
One of the strong requirements for beams is highquality beam in momentum spread. Recently, we havesucceeded in producing such high-quality beams. For
example, energy spreads were achieved as 55 keV and 62
keV for 300 MeV and 392 MeV proton beams, 89 keV
and 150 keV for 420 MeV and 450 MeV 3-herium beams,
and 108 keV for 400 MeV 4-herium beam, respectively.
Especially, it should be noted that the ratio of the energy
spread to the beam energy (∆E/E ) is about 1.5x10-4 forproton beams[1].
In past a few years, we have obtained such "ultraprecise" beams, i.e., ∆E/E is less than 4x10-4, in almost
every machine time. In other words, reproducibility ofbeams themselves is quite good, even though cyclotron
parameters need to be slightly changed among
independent beam times. It should be noted that to keep aultra-precise beam as long as possible is also important touse. As described below, long-term stability of such
beams, however, was still a remaining problem.
We considered that temperature control of the iron coreis essential and improved a cooling system of the injector
cyclotron in the RCNP. Recently, we have succeeded toobtain an ultra-precise beam for a long time without any
tunings of cyclotron parameters, which supports oursimple model and criterion for the temperature.

2 FORMER RESULTS
There are a large number of parameters in the RCNP
cyclotron complex. In these parameters, it has been foundto be very important to stabilize the magnetic field for

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Ultra-precise beams have been successfully accelerated
up to 392 MeV/u in the RCNP cyclotron complex. It isfound that stability of a magnetic field is essential. The
temperature of an iron core have been stabilized bycontrolling the temperature of the cooling water for coils.
Now we can keep the constant magnetic field within theorder of 10-6 and ultra-precise beams are kept for a longtime without any tuning of cyclotron parameters.

good operation of a cyclotron. Figure 1 shows a former
record[2] a magnetic field of the AVF cyclotron for 392
MeV proton beam and the observed energy resolution(∆E/E) , which was intermittently measured by theusers, as a function of a relative time t. The magnetic field
is shown as a ratio of a difference from the average field
to the average field (∆B / Bav ).

delt a B/ Bav (x10-6)

Abstract

00

10

20

30

40

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relat ive time(hours )Fig.1 Magnetic Field of the AVF cyclotron (line). Energy
resolution before adjustment(solid circle) and after
adjustment (open circle) of the main coil are also shown.
At t=14, after adjusting some cyclotron parametersincluding the main coil current of the AVF cyclotron, weobtained a good beam of which energy spread goodenough for experiments and started the experiments. Afterthat we found that the magnetic field of the AVF cyclotron
increased. Decreasing the main coil current of the AVF
cyclotron to reproduce the magnetic field, the energy
spread was represented for t < 33. However, for t > 40,
the suitable magnetic field strength observed for ultraprecise beam slightly decreased. It should be noted thatthe energy resolution after adjustments retains about 2 x10-4.
In this machine time, in order to continue to obtainultra-precise beam, occasional measurements on energy
spread of the beam and decreasing the main coil current
were necessary. It is noted that, without any adjustment of
the main coil, the magnetic field may increase with a rateof ∆B / Bav is about 1.2 x 10-5 per day. Even though suchadjustments were carried out only a few times per day, amore stable beam was suitable. Especially, since somenuclear reactions have very small cross sections, someusers strongly require ultra-precise beam for a long time,e.g., 24 hours or more.
As shown in fig.1, the energy spread of the beamstrongly correlated with the magnetic field strength of theAVF cyclotron. Therefore, it is expected that no drift ofCr
k cr + k ro

Trf =(6)k cr Tc + k ro To.
k cr + k ro

(7)

4 RESULTS
From the former result shown in fig.1, it seems that adrift of the magnetic field should be within the order of
10-6. Since the temperature coefficients of the magnetic
permeability and coefficient of linear expansion for ironare roughly on the order of 10-4 and 10-5, respectively, thetemperature of the iron core should be controlled on theorder of 0.01 degree.
1231.8

831.6

431.4

031.2

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31.0

-8-12

Temperat ure(deg.)

3 A SIMPLE MODEL
Figure 2 shows a very simple model for heat transfer ofa cyclotron. Let us consider three systems, i.e., coils, aniron core and outer circumstance nearby, where thetemperatures of these systems are Tc, Tr and To,
respectively. Qco, Qro and Qcr are heat transfer from thecoils to the outer circumstance, from the iron core to theouter circumstance, and from the coils to the iron core perunit time, respectively. Qcw is heat transfer from the coils
to an imaginary heat sink through cooling water and P isthe electric power from the power supply of coils per unit
time. It should be noted that an iron core itself has no heatorigin from electric power.

τ=delt a B/ Bav(x10- 6)

the magnetic field may become long-term stable operationof an ultra-precise beam.
A magnetic field in a cyclotron is not only a function of
coil current, but also a function of form (length, width andso on) of iron core and magnetic permeability. As thecurrent stability of the main coil for the AVF cyclotron isgood enough( better than 4 x 10-6), the form of iron core
and/or magnetic permeability should change, which havea hidden parameter, temperature T.

30.8
010

20
30
40
relative time(hours )5060

Fig 3. Magnetic field of the AVF cyclotron(center),temperature of the pole surface(upper) and temperature of
the return-yoke surface(lower). The return yoke
temperature has an offset of 2.3 degree.
It is again noted that, in order to realize the ex. (5), thebelow simple conditions should be satisfied,Fig. 2: A simple model for heat transfer
In this model,

C c dTc = Pdt − Qcw dt − Qcr dt − Qco dt ,C r dTr = Qcr dt − Qro dt ,

(1)
(2)

where Cc and Cr are thermal capacity of the coils and theiron core, respectively.
For simplicity, we put strong restrictions, that is, bothTc and To keep constant. Neuton's empirical raw was also
assumed to Qcr and Qro, i.e.,

Qcr = Qcr (Tr ) = k cr (Tc − Tr )Qro = Qro (Tr ) = k ro (Tr − To )

(3)
(4)

where kcr and kro are constant, respectively. Then we get

Tr = (Trf − Tri )(1 − exp( −t / τ )) + Tri ,(5)

where Trf and Tri are initial and final temperature of theiron core, respectively, and∆To = 0
∆Tc = 0(8)
(9).

We improved a cooling system of the AVF cyclotron
and achieved exs. (8) and (9) in some machine times.
Figure 3 shows the magnetic field of the AVF cyclotronfor 300 MeV proton with the temperature of the polesurface and the return-yoke surface as a function of a
relative time t. The return-yoke temperature has an offset
of 2.3 degree.
Both temperatures stayed within ±0.06 degree over 60
hours. The magnetic field kept the level within ±2.5x10-6
during this period. In this period, any cyclotron
parameters, including the main coil current, was notadjusted. Therefore, it is concluded that controlling
temperature realizes a stable magnetic field, as expected.
Figure 4 shows the observed energy resolution (∆E/E)
at that time, as a function of a relative time t. The
magnetic field is also shown in fig.4 again. As a reference,
the former results already shown in fig.1 are also shown.

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lack of the ability of the air conditioning system for theAVF cyclotron room.
In the spring of 2002, we improved the air conditioning
system, power of which became stronger by about 10 %.
The room temperature in 2002 is also shown in fig. 5.
Though we could keep the temperature constant before
the mid-July, it increased by 1.5 degree in summer. In
other words, eq. (8) was not satisfied especially insummer.

0010203040
relative time(hours )50

32313060Fig. 4:Energy resolution (square) and Magnetic Field of
the AVF cyclotron (diamond) for 300 MeV proton beam.
The former results for 392 MeV proton beam are alsoshown.
The energy resolution at t=33 was observed as about
3x10-4. As t increased, the energy resolution becameslightly worse. However, comparing the former energy
resolution for 392 MeV proton, time dependence wasvery small. During t=47-51, 102 keV of the energy spread
was observed without any checking measurements.
Totally, the energy resolution retained within 4x10-4
during about one-day beam time without any adjustmentsof the cyclotron parameters.
We would like to emphasize that a feedback control of
the coil current is not an adequate method for magnetic
field of a cyclotron. Generally we consider that a main
reason why the magnetic field moves in a cyclotron is tochange the temperature of an iron core. A feedback
control of the coil current may not cancel out the thermal
effect on the total iron core. For example, effects of nonuniform deformation of magnet pole and return yoke,
which causes discrepancy from isochronism at any radii,
can not adjust by main coil current.
Measuring time constant τ of the AVF cyclotron in theRCNP, we got the order of τ is about a few tens of hours.
Therefore, if the temperature changes very much, it cannot come back to the adequate temperature soon. It isimportant that Tri (and Tr) keep constant near Trf to avoid
the effect of such long time constant.

°Cdelt a B/ Bav (x10- 6)122928272625242345678MonthFig.5 Temperature of the AVF cyclotron room in 2001
(open circle) and 2002 (solid circle).
Electric power for the main coil changes as theaccelerated particles and/or their energies changes.
Therefore the temperature of the cooling water needs tobe controlled to satisfy the condition in eq. (9). However,
we have not obtained sufficiently results and techniques,
and, therefore, the temperature of the coil, Tc, slightly
changed in every beam time. Since the differences of Tc
for successive beam times depended on the difference ofthe main coil currents, we got negligible changing of Tc
sometimes. At that time, a ultra-precise beam for a longtime has been easily obtained.
In conclusion, for a long-term operation of the ultraprecise beam, the whole temperature distribution of thecyclotron needs to be kept at all times to keep themagnetic field within the order of 10-6 for the AVF
cyclotron in the RCNP. In near future, improvement
methods in keeping the temperature well for an eachexisting cyclotron will be studied, which may lead to acriterion to design a new cyclotron.

5 FURTHER PERSPECTIVE

6 REFERENCES

Unfortunately, Conditions (8) and (9) was not
actualized all time. Figure 5 shows temperatures of theAVF cyclotron room as a function of the date, which
represented to To in eq.(8). In 2001, the temperature wasroughly constant before the start of June. After that theroom temperature increased by 2-3 degrees, because of[1] H. Saito et. al., In this workshop[2] S. Ninomiya et. al., Proc. of the 16th Conf. on Cycl.
and their App., East Lansing, USA, p.110, 2001.