Numerically-analytical method for research of transporting and focusing of thin beams in the electrodynamic structures

The problem of formation of high-current beams of charged particles demands the solution of self-consistent nonlinear electrodynamic problems. The computing complexities increase, if there are the following factors: strong nonlinear effects, unstable modes, and virtual cathode. The development of numerical-analytical methods for the solution of such problems is difficult. To overcome this the method of small parameter decomposition arising in the multiscaling of physical quantities is presented in the paper.