The 14th Symposium on Accelerator Science and Technology, Tsukuba, Japan, November 2003

ULTRA HIGH STABILIZATION OF THE MAGNETIC FIELD OFTHE RCNP AVF CYCLOTRON
S. Ninomiya, T. Saito, H. Tamura and K. Sato, RCNP, Ibaraki, Osaka, Japan
Abstract
High-quality beams have been successfully accelerated
in the RCNP cyclotron complex. For such beams, it isfound that stability of a magnetic field of a cyclotron isessential. Now we can keep the constant magnetic fieldwithin the order of 10-6 and high-quality beams are kept
for a long time without any tuning of cyclotron
parameters. In this contribution, the stabilization of themagnetic field of the RCNP AVF cyclotron bytemperature control was reported.

1. INTRODUCTION
The RCNP cyclotron complex consists of a large-sized
ring cyclotron (K=400) and an injector AVF cyclotron(K=140). Beams are used mainly for nuclear physics
research and high-quality beams in momentum spread
have been strongly required. Recently, we have succeededin 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 110 keV
for 420 MeV and 450 MeV 3-herium beams, and 125 keV
and 108 keV for 210 MeV and 400 MeV 4-herium beam,respectively.
For high-quality beams, severe controls of the magnetic
and electric fields to ion beam should be needed.
Therefore, one needs to install good probes. In order tomeasure magnetic fields, two NMR probes withcorrecting coils were installed in the AVF cyclotron[1][2].
These probes were inserted between the magnetic poleand the base plate for the trim coils with different radii ofthe cyclotron, that is, ~50 cm and ~70 cm, respectively.
Now the magnetic field can be measured with theresolution of 10 nT, i.e., ∆B/B can be measured on theorder of 10-8.
It was found that stability of the magnetic fields B of
the injector AVF cyclotron is much important. For
example, for 392 MeV proton beam, when the AVF
magnetic field increased with a rate of ∆B/B ∼ 4x10-6, theenergy spread ∆E/E was observed to increase roughly
twice[2]. At that time, ∆B/B increased with a rate of ∼1.2x10-5 per day without any operation. Clearly, a severe
control of the magnetic fields of the AVF cyclotron is a
key to obtain high-quality beams. At least, ∆B/B needs tobe controlled within the order of 10-6.

2. STABLIZATION OF A MAGNETIC
FIELD
A magnetic field of a cyclotron B is not only a functionof coil current, but also a function of form of iron coreand magnetic permeability. For example, the magnetic

field is very roughly estimated by B = NI / ( L / µ + l /µ0 ), where N is a turn number of the coils, I is coilcurrent, L is length of the magnetic circuit, l is air gap
length, µ is magnetic permeability of an iron core and µ0
is magnetic permeability of the air(or vacuum),respectively.
For a cyclotron operation, current feedback to amagnetic field is usually adopted. In our opinions,however, current feedback is not the most suitable method
to correct a magnetic field of a cyclotron in order toobtain high-quality beams at all times.
Generally speaking, stability of a power supply is quite
good for a cyclotron. For the RCNP AVF cyclotron, thecurrent stability of the main coil is better than 4 x 10-6.
The origin of the drift of the magnetic fields does notcome from current instability in most cases, and therefore,
comes from drifts of other parameters, such as L, l andµ for the above simple model. When these parameters
drift, non-uniform deformation of magnetic fields may
happen and one can not reproduce the magnetic fields bycurrent feedback.
Both form of iron core, such as L and l, and magnetic
permeability, µ, have hidden parameters, i.e., temperature
T. The coefficient of linear expansion for iron and thetemperature coefficients of the magnetic permeability areroughly on the order of 10-5 and 10-4, respectively.
Therefore, generally speaking, both parameters can cause
drifts of the magnetic fields.
For the RCNP AVF cyclotron, main origin of the driftof the magnetic fields was found to come fromdeformation of the iron pole and the return yoke[3]. Inorder to realize that ∆B/B stays within the order of 10-6,
the temperatures of the iron pole and return yoke were
found to be controlled within 0.01 degree[3].

3. A SIMPLE MODEL
In order to realize the temperature of the iron core keep
constant, heat transfer of a cyclotron should be considered.
Figure 1 shows a very simple model for heat transfer.
Let us consider three systems, i.e., coils, an iron core andouter circumstance nearby, where the temperatures ofthese systems are Tc, Tr and To, respectively. Qco, Qro andQcr are heat transfer from the coils to the outercircumstance, from the iron core to the outer circumstance,
and from the coils to the iron core per unit time,respectively. Qcw is heat transfer from the coils to animaginary heat sink through cooling water and P is theelectric 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.

The 14th Symposium on Accelerator Science and Technology, Tsukuba, Japan, November 2003

When Trf - Tri is 1 degree and ∆T is 0.05 degree, theeffective time, teff, is estimated to ∼ 120 hours.

4. IMPROVEMENTThe RCNP cyclotron complex is continuouslyoperated during a few months even for weekends.
Therefore, if the conditions in eqs (3) and (4) are always
satisfied, the temperature of the iron core, Tr, stays
constant after passing the effective time.
Recently, some improvements of the air and watercooling system for the RCNP AVF cyclotron have been
carried out.

Fig. 1: A simple model for heat transfer
In this model,

C c dTc = Pdt − Qcw dt − Qcr dt − Qco dt ,(1)

C r dTr = Qcr dt − Qro dt ,(2)

∆To = 0(3)

∆Tc = 0

(4).

Newton's empirical raw was also assumed to Qcr andQro, i.e.,

Qcr = Qcr (Tr ) = kcr (Tc − Tr )(5)

Qro = Qro (Tr ) = k ro (Tr − To )(6)

where kcr and kro are constant, respectively. Then we get(7)

where Trf and Tri are initial and final temperature of theiron core, respectively, andτ=Crk cr + k ro

Trf =(8)k cr Tc + k ro To.
k cr + k ro

(9).

For the RCNP AVF cyclotron, time constant τ isestimated as ∼ 40 hours[3]. Therefore, it is very difficult
to control the temperature of the iron core rapidly.
The time constant, τ, itself is not a suitable parameter toestimate the effective time, teff, required from the initialtemperature. Assuming that the temperature condition isempirically satisfied when Tr = Trf ± ∆T, the effective timeis estimated asteff = τ ln

Trf − Tri∆T

3130(10).

29degreewhere Cc and Cr are thermal capacity of the coils and theiron core, respectively.
For simplicity, we put strong restrictions, i.e.,

Tr = (Trf − Tri )(1 − exp( −t / τ )) + Tri ,3228272625
24
23456Mont h78Fig. 2: Temperature of the AVF cyclotron room in 2001
(thin line) and 2003 (thick line).
Figure 2 shows the temperatures of the AVF cyclotronroom(i.e., To in eq.(3).) at 2:00 and at 14:00 in every day
as a function of the date. In 2001, the temperatures were
well controlled to 27 degree before the beginning of theJune, except the end period of the April. The reason why
the temperatures decreased in this period is still unknown.
Then the room temperatures increased from the beginningof the June. The room temperatures mainly depended on
atmospheric temperatures and humidity outside. Finally,
the temperatures got to 30 degrees.
The air conditioning systems for the AVF cyclotronroom was reinforced by about 10 percent, by installing anew air conditioner to the old system. The new air
conditioner has a long cooling-medium line(∼60 m), foreffective heat transfer from the radiation control area tooutside. The old air conditioning system was also cleaned
up to ensure arranged heat transfer.
The room temperature in 2003 is also shown in fig. 2,even though some data were missing. The target
temperature was changed to 27.5 degree. The room
temperatures were kept roughly constant until thebeginning of the July. After that, the room temperatureslightly increased. Large deviation at the end of the Julycame from a trouble of the new air conditioner.
In order to realize the condition in eq. (4), a watercooling system of the AVF cyclotron was improved. Inorder to control the water temperature for the main coil
independently, an additional water pump and heatexchanger was installed. A three-way valve was also
newly installed nearby the cooling tower in order toThe 14th Symposium on Accelerator Science and Technology, Tsukuba, Japan, November 2003

cancel out influence on outer disturbance. Finally, watertemperatures both for the main coil and the trim coils canbe controlled by the order of 0.1 degree.

5. RESULTS

1231.8

831.6

4

31.4

031.2

-4

31.0

-8
- 12

Temperat ure(deg.)delt a B/ Bav(x10- 6)

Figure 3 shows the magnetic field of the AVF cyclotronfor 300 MeV proton beam with the temperature of thepole surface and the return-yoke surface as a function of a
relative time t. The return-yoke temperatures have offsetsof 2.3 degree.

30.8
010203040
relat ive t ime(hours)

5060Fig. 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.

1210884604-4
2-8- 12delta E/ E (x10- 4)

delta B/ Bav (x10- 6)

Both the 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.

0010203040

5060

relative time(hours)

Fig. 4: Energy resolution (open circle) and magnetic fieldof the AVF cyclotron (diamond) for 300 MeV proton
beam.
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. The energy
resolution at t=33 was observed as about 3x10-4. As t
increased, the energy resolution became slightly worse.

The energy resolution, however, retained within 4x10-4
during about one-day beam time without any adjustmentsof the cyclotron parameters.
In conclusion, though the conditions in eqs (3) and (4)have not been always satisfied, remarkable improvement
to obtain and to keep high-quality beams was achieved.

REFERENCES[1] M. Kibayashi et al., Proc. of the 12th Symposium on
Accelerator Science and Technology, Wako, 1999,
p.319[2] S. Ninomiya et al., Proc. of the 16th Int. Conf. on
Cyclotrons and their Applications, East Lancing,
2001, p.94
[3] T. Saito et al., in these proceedings