HEAD-TAIL INSTABILITY IN KEK BOOSTER SYNCHROTRON
T. Kasuga, T. Kawakubo,
H. Someya and M. Suetakes. Takeda,National Laboratory for High Energy Physics·Abstract
A transverse bunched beam instability has been observed
for several years in the KEK booster. The general theory forthe head-tail instability was given by Sacherer.l) The remaining problem of his theory is the estimation of the coupling impedance. It was suppose that the kicker magnet for the fast
beam extraction system was a good candidate for the instability
found in the KEK booster synchrotron. Miyahara analyzed theinstability induced by the kicker magnet with a free string model.2,3) We observed this instability to make sure Miyahara'sexpectation. The head-tail mode was determined and the growthrate of the instability was observed quantitatively using aspectrum analyzer. We found that the growth rate of the instability decreased at a certain timing in the machine cycle.
The decrease of the growth rate is well explained by the reflection of the current induced in the kicker at the end of thefeeding cable.
1 .• Head- Tail Mode

The calculated frequency spectrum for the throbbing pattern of the bunch is shown in Fig.l. Wnen the envelope of theline spectra of A R-signals appearing on the position monitor
is measured, we can determine the head-tail mode number. Weobserved the line spectra with a spectrum analyzer. One of
the results is sho~n in Fig.2. As there is only one peak inthe envelope of the spectra, the head-tail mode m is zero.
We observed the line spectra over the whole machine cycle, but
we could not find any other modes except zero.
2. Growth Rate
We also used the spectrum analyzer to measure the c;r:)wch
rate of the instability. The growth rate can be obtained fro;'l
the time differential of the arnpli tude. The amplitude of acertain line within tl1e line spectra was measured at some timings in the machine cycle. The amplitude change in the machine
cycle is shO\'m in Fig.3. We found the decrease of the growthrate at about lOmsec after injection.
3. Effect of Reflection of Beam-Induced Current at End ofFeeding Cable
As the feeding coaxial cable for the kicker is open-circuited equivalently at the pulse generator side, we can not-305-

neglect the effect of the reflectio n of the beam-indu ced current
at the end of the coaxial cable. The real part of the transverse coupling impedance of the kicker with the open-circ uitedcable isRe Ztot :( 1 - cos w ( Tc.. + T. )/2 ) Re Z
- sin w( 't:c.. + '"Co ) Im Z /2

where Ztot and Z are the coupling impedance s with and without
the open-circ uited coaxial cable respectiv ely, and '!:c. and "Z:oare the travellin g times of the induced current in the cableand in the kicker. The coupling impedance of the kicker ;v.ith
cable is shovv.n in Fig.4. The pattern of the coupling impedanceis oscillato ry. When the peaks of the coupling impedance coincide with the betatron side bands, the growth rate i.s high, andwhen the valleys coincide with them, the growth rate becomes
small. In Fig.4 the betatron side bands at about 10 msec after
injection are shown by line spectra, and in this case the growthrate is very small. This explains the decrease of the growthrate at 10 msec after injection .
Reference sl) F.J. Sacherer: Proc. of 9-th Int. Conf. on High Energy Accelerators, Stanford (1974) 347.
2) Y. Miyahara: IEEE Trans. on Nucl. Sci. NS-26, No.3 (1979).
3) Y. Miyahara: Particle Accelerat ors, 10 (1980) 125.
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