Relativistic self-focusing of ultraintense laser pulses in inhomogeneous underdense plasmas

We investigate the propagation of high-intensity short laser pulses in a plasma. A two-parameter perturbation expansion is used to consistently treat the nonlinear mass variation and ponderomotive contribution to self-focusing, including plasma inhomogeneity. An analytical expression for the critical power is given and it is found that it greatly depends on the plasma inhomogeneity. A tailoring of the preformed plasma is suggested in order to obtain a strong reduction of the critical power. The temporal evolution of the pulse and plasma dynamics are also considered.