A laser beam propagating along the density gradient in a laser‐produced plasma is unstable to a transverse density perturbation. When ambient density scale length is comparable to growth length, spatial growth is faster than the exponential. For a linear density profile the amplitude of the filament varies with z as an Airy’s function, whereas for an exponential profile it goes as a Bessel function of imaginary order and argument. In both cases the growth rate increases with the transverse wave vector of the perturbation.

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