Study of EP instability for a coasting proton beam in circular accelerators

We discuss interactions between a coasting proton beam and electrons. The electrons, which are created near the beam position, are considered in this paper. A coasting proton beam traps the electrons eternally, if there are no perturbations nor diffusion mechanisms. Therefore electrons are accumulated and their density could arrive above a threshold value for the instability, finally: i.e., a coasting proton beam is always unstable. However the instability affects both of the beam and electrons. Electrons may be diffused by the instability, in which the beam still has a small oscillation amplitudes, with the result that the beam amplitude may be kept in the small level, and may be stable in actual operations of accelerators. We study the ep instability with focusing the electron diffusion using a computer simulation method