In order to solve the system of nonlinear partial differential equations that describes the 3D ion and electron dynamics in a plasma wakefield excited by a sharp laser pulse, we propose a difference scheme and an iteration algorithm realizing this scheme. It is important to note that in this paper we do not assume that the problem is axially symmetric, which leads to complication of equations and to increase of dimension. The results of numerical modeling show a distinction among wakefields excited by laser pulses of circular and elliptic cross sections. The work was partially supported by the Russian Foundation for Basic Research (05-01-00511).

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