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A two-dimensional time-dependent laser plasma interaction code is described and used to model the interaction between a 5 psec Nd glass laser pulse of peak power 1013 W and a 35 times ionized tin target. Parameters are chosen so that relativistic self-focusing down to a diameter of the order of the wavelength of the laser light is observed in a distance comparable to the half intensity vacuum beam diameter. At later times strong modification of the plasma density by the nonlinear force is observed. The combination of relativistic self-focusing and axial nonlinear force results in the acceleration of tin ions to a maximum energy of 5 GeV, in agreement with previous approximate calculations.

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We present a new derivation of the time dependent ponderomotive force for an isotropic plasma using the symmetrized stress tensor approach of KOSO er al. (1980), and show that this agrees with the result calculated recently by STATHAM and TER HAAR (1983) using a new fluid-dielectric method.