FOKKER-PLANCK THEORY OF TRANSVERSE MODE COUPLING INSTABILITY
Toshio Suzuki · CERN Document Server (European Organization for Nuclear Research) · 1986
The Fokker-Planck equation for transverse collective instabilities is solved by expansion in terms of generalized Laguerre polynomials.The convergence of the expansion is confirmed by computer calculation to be very rapid.Compared with the Vlasov equation treatment, the threshold of transverse mode-coupling instability in PEP, PETRA, and TRISTAN is shown to be somewhat lowered, owing to radiation effects.Dipole oscillations are excited before the eigenfrequencies of two modes (m = 0 and m = -1) meet.It is also shown that when the Vlasov equation is used to study the coupled-bunch instability an approximate stability criterion is that the growth rate should be less than 1/t'~+ Iml/t's' where t'~and t's are radiation damping times for betatron and synchrotron oscillations, respectively, and m is the azimuthal mode number.Higher radial modes are damped more strongly.