The 11th Symposium on Accelerator Science and Technology, Harima Science Garden City, 1997

Eddy Field Measurement Using a Peaking-Strip
Yasumori KANAI, Toshikazu ADACHI*, Manabu FUJIOKA** and Yoshiharu MORI*
Department of Physics, Tohoku University,
Aramaki-Aoba, Aoba-ku, Sendai 980-77 JAPAN*KEK High energy accelerator research organization
accelerator division
1-1 Oho,Tsukuba-shi Ibaraki-ken,305 JAPAN**Cyclotron and Radioisotope Center, Tohoku University
Aramaki-Aoba, Aoba-ku, Sendai 980-77 JAPANAbstract
An eddy field in a bending magnet wasmeasured along the longitudinal direction, when themagnet was excited by a sinusoidal current with arepetition of 49.73Hz. The measurement wasperformed by using a peaking strip[l]. It was foundthat eddy field generated iln the edge plate made bystainless steel became larger as the position becamecloser to the magnet edge.

A test magnet[2] for the B-factory wasexcited with the repetition of 49.73Hz using LC
resonant circuit. Fig.l shows a schematic view of thetest magnet. The field measurement was performed
along the longitudinal direction(y-axis) on the medianplane.

1. Introduction
In Japan, the JHF(JAPAN HADRONFACILITY) plan are being progressed. The JHF
accelerator complex comprises the 200MeV linac, the3GeV booster synchrotron and the 50GeVsynchrotron.
The 3 Ge V booster synchrotron is a rapidcycling synchrotron with a repetition of 25 Hz. In thefuture, the repetition will be increased up to 50Hz, inorder to obtain a beam power over lMW. Although, insuch a rapid-cycling synchrotron, the vacuum chamberused in the magnet is made of ceramics to avoid thefield disturbance due to an eddy current, the eddy
current is also induced in the magnet, which may
disturb the magnet field. Especially, in a dipolemagnet, a sextu-pole component of the eddy field must
be considered in order to accelerate a high-intensity
beam without beam loss.
Field measurement in a dipole magnet has
been performed for the purpose of estimations of the
field disturbance due to an eddy field. In this paper,
the results obtained so far are described.

Fig.l. Schematic view of the test magnet.

Since the magnet is excited by a sinusoidal
current, magnetic flux density(B) is given byB=Bosinmt.

(1)

Since an eddy current depends on B. the eddy field isgiven by(2)2. Field Measurement-386-

The lith Symposium on Accelerator Science and Technology, Harima Science Garden City, 1997

Then, total magnetic field (B101) is obtaind as

Btot = B+ Beddy = ~ Bo2 + B12 sin(mt+8),

tan8 =~Bo'(3)

in order to confirm the coincidence of two peaking
timings. As shown in Fig.3, two peaks coincide witheach other. Here,a little difference is seen between twosignal tails due to a difference of inducance of a pick-up
coil for each peaking-strip.
1-------·'1'---- ------1

where a is the phase difference between the main
dipole field and the eddy field. Therefore, theamplitude of the eddy field can be obtained by
and amplitude ofmeasuring the phase difference (the main dipole field (B 0).
Phase· difference was measured by two
peaking strips, each of which generates a voltage pulse
by detecting a zero-crossing timing of a dynamic field.
A phase gap was measured between the signal ofpeaking strips and zero cross timing. But it was verysmall. The amplitude of the main field was measured
by a seach-coil method[3].

a).
" ... ' ...... .
.

· •· lOOmVtdiv ·.

.

.

.

· · : · 1 P: s/div- · · : · · · ·Fig.3. Signals of two peaking-strips which were placedat the center of the magnet.

3. Experimental Results
Fig.2 shows a block diagram of themeasuring system. Here, peaking stripl was fixed at
the center of the magnet. Peaking strip2 and the seachcoil were moved along the longitudinal direction.
Signals of two peaking-strips were sent to anosilloscope, and phase difference was measured. A
signal of the seach-coil was integrated for the interval
between instants givinig the minimum and maximum
field, so that the amplitude of the main field wasobtained. The time interval for integration wasdetermined by a signal of the back-leg winding.

The phase difference becomes larger as theposition of the peaking-strip2 goes far away from themagnet center. Fig.4 shows typical phase difference
where the peaking-strip2 was set at the end of themagnet core. In this case, the time difference is 29.2 p.
s. Since the operation frequency is 49.76Hz, the phasedifference amounts to 0.00913rad.
The aL~plitude of the main dipole field at thispoint was measured by the seach-coil. Therefore, thenormalized amplitude of the eddy field(Beddy) is
obtained in terms of the following formula:(4)
In this case, the normalized amplitude is 0.00364.
Fig.5 shows the position dependence of thenormalized amplitude of the eddy field, together withthe magnet cross-section cut by the y-z plane at x=O.
POWER SUPPLYzero cross detector

Fig.2. Block diagram of the measuring system.
The eddy field was measured along thelongitudinal direction on the median plane. At first,two peaking-strips were set at the center of the magnet,-387-

The lith Symposium on Accelerator Science and Technology, Harima Science Garden City, 1997

end plate made by stainless steel.
4. Conclusion
An eddy field in a bending magnet wasmeasured along the longitudinal direction on themedian plane, when the magnet was excited by asinusoidal current with a repetition of 49.76Hz. The
field disturbance due to the eddy field was found to belarge around the magnet end part, and amounts to
0.4% of the main dipole field at the magnet center.
The transverse distribution of the eddy field
is necessary in order to estimate an effect of the eddy
field to a circulating beam in a synchrotron. Inaddition, a 3-dimensional simulation code for a
dynamic field is also being prepared in order tocompare the experimental result with the simulation.
When the simulation code is confirmed, it gives a
guiding principle in design of a magnet for a rapidcycling synchrotron.

1-+~·--~--~--~~--~--~~--~~--~

Fig.4. The typical phase difference of peaking strips

Acknowledgment
The authors would like to say thanks to Mr. H.
Someya, Dr. M. Yoshii, Dr. A. Takagi and Dr. F. Q.
Zhang for their advice during this work. We must also
acknowledge Prof. K. Endo for lending their test
magnet and power supply.

stainless steel

References"" J[1] S. Yamaguchi et al, INS REPORT,
INS_TH_18(1957)[2] W. Zhou and K.Endo, KEK REPORT 93-3(1993)[3] M. Kumada, et al., KEK REPORT, KEK-7730(1978)

0.005
"0-.;

-i~0.004

0.003't]"'i0.002alN~

g0.001o~~~~~~~~~~~~~~~~

0. 5

0. 55

o. 6

0. 65

0. 7

0. 75

0. 8

0. 85

position(m)Fig.5. Position dependence of the eddy field.
As shown, the eddy field becomes larger as
the position becomes closer to the end plate ofstainless steel. This result implies that the eddy current
induced by the main field can not be ignored aroud the-388-