Weak-strong simulation of beam-photoelectron instability in a positron storage ring

Growth of the photoelectron instability has been discussed by using a wake force occurred by electron cloud. Concept of the conventional wake force is available for the force which satisfies linearity and superposition for the coherent amplitude of bunches. Weak-strong simulation method for beam-photoelectron interactions is proposed to study the nonlinear wake effect. In the method, photoelectrons are expressed by macro-particles and the beam by a series of rigid Gaussian bunch. We can investigate by the method not only nonlinear wake effect but also instability for a bunch train and an arbitrary bunch filling