We have successfully developed the two-dimensional quasi-static particle simulation code MLPIC2D, which is an effective numerical tool to be used to describe the long-time plasma behavior under the action of an ultra high intensity short pulse laser. Simple physical modeling, numerical realization and code framework are discussed in detail. Three nonlinear phenomena of laser-plasma interaction:1) production of laser wake-fields, 2)relativistic focusing for short laser pulses, 3)quasi-static magnetic fields, are correctly simulated and analysed.
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