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Nonlinear propagation of a randomized laser beam through an expanding plasma.

We present simulations of the interaction of a random phase plate laser beam with an underdense, expanding plasma for conditions typical of recent LULI experiments. We use a new code that describes the paraxial propagation of the laser, accounting for the nonlinear evolution of the plasma in an isothermal fluid description with weakly collisional electrons. The transmitted light, in excellent agreement with experiment, is shown to be strongly redshifted as a result of self-phase modulation due to self-focusing.