Self-consistent Analysis of Three-dimensional Uniformly Charged Ellipsoid withZero Emittance

摘要

A self-consistent treatment of a three-dimensional ellipsoid with negligibleemittance in time-dependent external field is performed. Envelope equations describing the evolution of an ellipsoid boundary are discussed. For a complete model it is required that the initial particle momenta be a linear function of the coordinates. Numerical example and verification of the problem by a 3-dimensional particle-in-cell simulations are given.