Dynamics of shielding of a moving charged particle in a confined electron plasma

Dynamics of shielding of a moving charged particle in a confined plasma, which represents a realistic model of an electron beam in accelerators, is studied. This is a longstanding problem in plasma physics with important applications in accelerator physics. However, only solutions for an infinite unrealistic plasma are available. We developed a novel method to solve this problem, which consists of transformation of the Vlasov-Poisson differential equations to an integral equation for the Laplace image of the electron density perturbation created by an external charge. The integral equation is then solved numerically via the piecewise polynomial collocation method and the fast Fourier transform. We present thorough analysis of the results obtained and their physical interpretation.