Study of non-linear effects of a resonant cavity on the longitudinal dynamics of a coasting particle beam

A computational method has been developed to simulate the longitudinal motion of a relativistic beam of charged particles circulating in a strong focusing synchrotron or storage ring. Unlike most analytical approaches the simulation is not restricted to small perturbations and thus the growth of instabilities can be followed into the non-linear region. The investigations show that, as a result of an instability, the final energy spread of an initially unbunched beam interacting with a resonant cavity is larger than the value at threshold and tends to a limit which depends on both the initial energy spread and on the spread at threshold. Although the cavity has a high impedance only at the revolution frequency of the beam, the particle distributions contain Fourier components at multiples of the revolution frequency.