“…In general, a complete description of collective processes in intense charged particle beams is provided by the nonlinear Vlasov-Maxwell equations [1] for the self-consistent evolution of the beam distribution function, f b (x, p, t), and the self-generated electric and magnetic fields, E(x, t) and B(x, t). While considerable progress has been made in analytical and numerical simulation studies of intense beam propagation [6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,…”