Application of the Green's Function Method to Some Nonlinear Problems of an Electron Storage Ring. Part I. The Green's Function for the Fokker-Planck Equation

摘要

Part I of this work consists of the formal solution of the Fokker-Planck equation in terms of its Green's function and describing the Green's function itself. The Green's function and the description of some of its properties can be found in the Appendices. It discusses the distribution function in the transverse phase space of a particle and it's Fokker-Planck equation for a simple case of a weak focussing machine. The Green's function and solution of this equation are described. Then, this technique is applied to a strong focusing machine and finally there is a discussion of applicability of this method, its limitations and relation to other methods (such as the Hamiltonian method). (ERA citation 08:044560)