HIGHER-ORDER MODES OF KEK-PF CAVITY
AND BEAM INSTABILITIESY. Yamazaki, K. Takata and S. Tokumoto
National Laboratory for High Energy Physics

It is well known that the bunched beam instabilities can be driven bycavity-like objects. The possible beam instabilities for the KEK-PF electron
storage ring were discussed in detail by Takata;) It was expected that theslowly varying parts of the cavity and ring impedances are small enough tostore the designed beam current 500 mA for the multi-bunch operation. However,serious instabilities of the coupled bunch oscillations may arise from therapidly varying part of the cavity impedance associated with the higher-ordermode resonances. Here, the number of bunches is 312 and the accelerating
frequency is 499.99 MHz. Thus the higher-order modes in the accelerating
cavity were studied by using the model cavity. (see Ref. 2).
Resonant modes possible in an axially symmetric cavity are designated byTMO, TEO and HEMV (V ~ 1). The TMO modes can cause the longitudinal beam
instabilities;• 4)which are studied in terms of the shunt impedances. TheHEMl modes are associated with the transverse beam instabilities~• 6 ) The
transverse coupling impedance defined by 5 )Z.L = lim j

Ll->0Illhas been widely used in studies of the transverse bunched beam instabilities.
The deflecting mode is excited by the beam current I displaced from theequilibriumorbit by an infinitesimal amount Ll. Then ez~...·Ill is a transverse
momentum impulse received by a relativistic electron traversing the cavity of
the length d.
The resonant frequencies and shunt impedances of the TMO modes can becalculated by the computer program SUPERFISH. However, no computer program
is available to calculate the parameters of the HEMl modes. Thus the experiment is crucial for the transverse beam instabilities.
Fifteen resonances were observed up to 1,300 MHz, and mode assignments
were made for all of the resonances. Field distributions were measured for
the TMO and HEMl modes with a technique developed by Maier and Slater?> Themeasured data were used to determine the shunt impedances for the TMO modes
and the transverse coupling impedances RL/Q for the HEMl modes. The procedure
is detailed in Ref. 8. The results are listed in Table I. The present
experimental results for the TMO modes were in excellent agreement with theSUPERFISH calculation.
The growth-rates of the longitudinal and transverse coupled bunch oscillations were estimated from the present experimental results and the formulas
developed in Refs. 3-6. The estimated growth-rates for almost all observed
resonances were faster than the radiation damping rates (sometimes 1,500 times-227-

faster).

Thus it is necessary to develop a device to avoid the instabili ties.

Two openings are prepared in the cavity to damp the higher-or der mode
resonance s (see the figure in Ref. 2). Coupling loops and antennas weretested in the model cavity. A half-wave length shorting plunger was attachedto the coupling loop to stop the fundament al (accelerat ing) mode. The external
Q-values of the damping couplers are listed in Table I. The damping couplers
had practical ly no effect on the fundament al mode.
The growth-ra tes of the beam instabili ties with the damping couplers arecompared with the radiation damping rates in the last column of Table I. I~
is expected that the Landau damping will be factor two or three faster than
the radiation damping. Thus the higher-or der modes were well damped tostabilize the beam except for the 1,300 MHz resonance . Another opening will
be necessary at the position where the electric or magnetic field of the
1,300 MHz resonance is very strong.
1)
2)
3)
4)
5)
6)
7)
8)

K. Takata, Nucl. Instr. Meth. (to be published ), KEK Preprint 80-1
(1980).
Y. Yamazaki and K. Takata, present Proceedin gs.
C. Pellegrin i and M. Sands, PEP Report PEP-258 (1977).
K. Takata, KEK Report KEK-79-6 (1979).
F.J. Sacherer, Proc. 9th Jn • Conf. on High Energy Accelerat ors, Stanford,1974, p.347.
R.D. Kohaupt, DESY Report Hl-74/2.
L.C. Maier, Jr. and J.C. Slater, J. Appl. Phys. 23 (1952) 68.
Y. Yamazaki, K. Takata and S. Tokumoto, KEK Report (to be published ).

Table I

Propertie s of observed TMO- and HEMl-mode resonance s in the KEKPF cavity.

ModeandParity

Frequency

External
Q of
Damping
Couplers

Unloaded(MHz)Rsh/Q (D)orR;)Q W/m)

TMO+
TMOTMO+TMO+

499.5
758.41052.2
1299.9222
810.1912.0

44,00037,00038,00097,0002 X 10 7
60
570
2,600

HEMlHEMl+
HEMlHEMl+
HEHl-

689.0
829.3
1070.81137.91245.0< 22

45,00056,00040,00045,00095,00050190207(35)666 (31)6(3)< 34Q-228-

so290
890

Growth-Ra tes ofInstabili ties
Divided byRadiation
Damping Rates

20.1
30
<.0.1
230.1
<2