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

NONLINEAR BEHAVIOR OF BETATRON OSCILLATIONMEASURED WITH A WIDEBAND MAGNETIC BEAM SHAKERTohru Honda, Akira Ueda, Toshiyuki Mitsuhashi, KEK, Tsukuba, Ibaraki 305-0801, Japan
Abstract
A wideband beam shaker using a window-frame ferrite
magnet has been designed and installed at the Photon
Factory storage ring. The characteristic impedance of themagnet and the power-supply system was well adjusted to50 Ohm in a frequency range up to 15 MHz. As a result,we obtain a flat response of the shaker around the low
harmonics of the revolution frequency. The nonlinear
response of betatron oscillation was investigated as afunction of the excitation power. A broad resonanceclosely related to the beam loss phenomenon wasobserved. The resonance shape was changed depending
upon the oscillation amplitude and the direction of thefrequency scan.

betatron oscillation observed by using this beam shaker
system is also described.
Table 1: Parameters of the beam shaker.
Horizontal

Magnetic length
Gap heightGap width
Peak field
Inductance
Capacitor, C1
Capacitor, C2
Core material

Vertical

130 mm
70 mm
140 mm
140 mm
70 mm
1x10-4 T
0.5x10-4 T
2.47 mH
2.45 mH
69 pF
147 pF100 pF220 pF
Ferrite (TDK PE14)

INTRODUCTION
At the Photon Factory (PF) storage ring, we haveseveral types of devices installed for the excitation oftransverse oscillation. An RF knockout (RFKO) systemusing a stripline electrode is mainly used for the tune
measurement and for killing the electrons in thesurrounding bunches at the single-bunch operation [1]. A
high-frequency quadrupole magnet (HFQM) system [2]can make the modulation of betatron tune from bunch tobunch. A fast kicker system is a pulsed deflector for thesingle-bunch beam. It is mainly used for the study of
beam dynamics in conjunction with a phase-spacemonitor [3]. Both the HFQM and the fast kicker are
constituted of window-frame ferrite cores and are excitedin a frequency rage of a few MHz using dedicated highpower supply systems. The stripline electrode is a very
wideband device as is often called the quarter-wave loop.
The center frequency of the stripline was tuned to the RF
frequency of 500 MHz. Hence the kicker function of thestripline near the revolution frequency (1.6 MHz) is low
and no a flat one. The stripline is suitable for killing theelectrons in surrounding bunches and the bunch feedback.
Those functions need a wideband response around the RFfrequency.
The beam shaker system described in this paper has
been matched to 50 Ohm in a bandwidth up to 15 MHz
and has a flat response in this range. Its principal
operation is the excitation of the betatron oscillation near
the low harmonics of revolution frequency. As it is wellcompatible with an all-purpose wideband RF amplifier,the waveform of the input signal can be precisely
controlled in combination with an arbitrary waveformgenerator. In the following sections, we report the design
and the construction of the shaker magnet. A preliminary
experimental result of the nonlinear behavior of theCONSTRUCTION OF THE BEAMSHAKER
The beam shaker has been designed as a window-frame
ferrite-core type magnet with two set of double-turn coil.
One coil is for the horizontal kick and the other for thevertical kick. The coils were made of a copper busbar of 5mm width and 3 mm thickness. In order to suppress across talk between two coils, the width of the busbar waslaid out rather narrow compared with the conventional
design of the window frame magnet such as the injection
kicker.

Figure 1: Photograph of the shaker magnet with theceramic chamber.
Figure 1 shows a photograph of the shaker magnet
installed in the PF ring with the ceramic vacuum chamber.
The shaker was installed in one of the short spaces
between the two quadrupole magnets in the arc section.
The length of the ferrite core is 130 mm. The effective

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

length of the ceramic duct is about 170 mm. The
parameters of the shaker are summarized in table 1.

When the shaker magnet was set with the ceramic ductin the storage ring, the transmission loss was deteriorated
in the lower frequency range. The origin of thisdeterioration was the stray capacitance between the coiland the environmental metallic structure such as thecoating inside of the ceramic duct, the beam duct and thevacuum flanges. The values of capacitors were adjusted tomake transmission loss smaller and to extend the cut-off
frequency larger. The smaller capacitance than thecalculated one was better for the impedance matching,and it also extended the cut-off frequency up to 24 MHz
for the horizontal and 18 MHz for the vertical,
respectively.
0S21 (dB)0-5-10
Horizontal
VerticalHorizontal (without capacitor)
Vertical (without capacitor)-15-20
05

10

15

2025

Frequency (MHz)Figure 4: A result of the adjustment of the transmission
loss after installed in the storage ring.
The current in the coil was measured using a current
transformer (PEASON 2100). Figure 5 shows themagnetic field converted from the measured current as afunction of output power of the arbitrary waveformgenerator. The good linearity is obtained over the power
level of -6 dBm. Beyond this level, output power of theRF amplifier reached to the saturation, we observed alittle deformation of the output waveform.
10Horizontal
VerticalH (x10-4 T)

A block diagram of the power supply for the shaker isshown in figure 2. The input signal from the arbitrary
waveform generator is amplified by a 100-W RF
amplifier of 30-MHz bandwidth. The RF amplifier has afixed gain of 50 dB. The current after passing through theshaker is terminated by a 50-Ohm dummy load. The same
driving systems are prepared for the both coils of theshaker.
In order to match the impedance of the magnet in awide frequency range, we applied a simple filter design
theory known as the constant-K design for the circuitdesigning. A 5th-ordrer low pass filter was made by theinductance L and the shunt capacitors at the both ends
(C1) and the center (C2) of the coil as shown in the figure
2. We determined the values of both C1 and C2 by
calculation to match the impedance by using themeasured values of inductances of coils. The cut-off
frequency was also estimated by the calculation. A
comparison of the transmission loss (S21) of the shaker
with and without the capacitors is shown in figure 3.
When the capacitor was applied, the cut-off frequency
was extended to 17 MHz for the horizontal and 14 MHz
for the vertical, respectively. These values agreed wellwith the estimated values.

S21 (dB)

Figure 2: Block diagram of the beam shaker system.

10.1-5-10

0.01-40

Horizontal
VerticalHorizontal (without capacitor)
Vertical (without capacitor)-15

510-30-25-20-15-10-50Input power (dBm)

-20
0-35

1520

Frequency (MHz)Figure 3: Measurement of the transmission loss, S21,
without the ceramic chamber.

Figure 5: Magnetic field as a function of the output powerof the arbitrary waveform generator at a frequency of 1MHz.
Hence the vertical gap is a half of the horizontal gap,
the vertical field strength is twice as much as thehorizontal one. At the installation point of the beam

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

shaker, the square root of the b -function in the horizontal
direction is about one half of that in the vertical direction,
so the effective kick angles in the both directions arealmost same for the same input power.

EXPERIMENTAL
By using the shaker, we measure the betatron tune shift
as a function of amplitude of the betatron oscillation. The
principal parameters of the PF ring during themeasurement were as follows: E = 2.5 GeV, frf = 500.1
MHz, fr = 1.602 MHz, nx = 9.60, n y = 4.28 and ns = 0.013.
Where E is the electron energy, fr the revolution
frequency, n x and n y are the horizontal and verticalbetatron tunes, respectively, and n s the synchrotron tune.
The vertical fractional betatron frequency was 441 kHz
and the synchrotron frequency 21 kHz. The beam current
was about 400 mA, and the octupole field was applied forsuppression of the transverse instability. The amplitude of
the oscillation was observed at an upper side-band of thefrf in the signal from a button electrode. The result of thebetatron tune shift is shown in figure 6. The abscissa isthe observed amplitude of the betatron oscillation. The
both data for the vertical and horizontal tune shift areplotted together in the figure 6. The amount of tune shift
has a similar tendency in the both directions.

same in the shape, and the distinctive broad resonanceshape did not appear in the downward scan. When thefrequency scan reached to the broad resonance, the beamloss or the drop of the beam lifetime was observed. In
other hand, no beam loss was observed in the downward
scan even using a maximum input. We have not yet
understand how such broad resonance continues in theupward scan, and why it is related to the beam loss. We
are planning to investigate the instantaneous transverseand longitudinal beam profile during the resonance.

Figure 7: The resonance spectrum for the upward
frequency. The input power was -20 dBm for the left and-3 dBm for the right.

4Tune shift (kHz)

3.5

Horizontal
Vertical32.5
2

Figure 8: The resonance spectrum for the downward
frequency scan. The input power was -20 dBm for the leftand -3 dBm for the right.

1.5
10.5
0-75

SUMMARY-70-65-60-55-50-45-40-35

Amplitude (dB)Figure 6: Tune shift as a function of the amplitude ofbetatron oscillation.
For the vertical direction, we observed a change ofresonance shape in the spectrum when the input power
was increased as shown in figure 7. The left spectrum inthe figure 7 shows a sharp resonance at the center and thisspectrum is usually observed at the lower input power.
Also in the left spectrum, the small peak was observed at
the frequency that is about 20 kHz above the betatronpeak. It corresponds to the synchrotron sideband. At thehigher input power, the resonance peak was started at thesame frequency as in the lower power and it continued
until fb+20 kHz as shown in the right spectrum. This
broad resonance shape was only appeared in the upward
frequency scan. Two results of spectrum taken by adownward frequency scan using the same input levels areshown in figure 8. Two spectra in figure 8 are almost

A wideband beam shaker using a magnet with a ferrite
core was newly constructed and installed in the Photon
Factory storage ring. As the impedance could be wellmatched in the wide frequency range, it was suitable forthe precisely controlled beam excitation around the low
harmonics of the revolution frequency. The preliminary
experimental results showed that it was useful for theinvestigation of nonlinear behaviour of the betatronoscillation.

REFERENCES[1] T. Obina et. al., “A new purification method for single
bunch operation at the Photon Factory storage ring”,
PAC’99, New York, March 1999, p 2310.
[2] S. Sakanaka et. al., “Excitation of a transverse
quadrupole-mode oscillation of the electron bunchusing a high-frequency quadrupole magnet”, PAC’01,Chicago, June 2001, p 393.
[3] T. Miyajima et. al., “Experimental measurements ofthird-order resonance islands at the Photon Factorystorage ring”, PAC’01, Chicago, June 2001, p 1729.