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Intense laser pulses propagating in gases undergoing ionization are subject to a scattering instability due to the dependence of the ionization rate on the laser electric field. The instability is convective, and growth is limited for a pulse of finite extent by propagation out of the unstable region. In the nonlinear regime, where the scattered wave amplitude becomes large, the scattering instability saturates at a level that gives rise to full modulation of both the plasma density and laser pulse amplitude.
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Antonsen et al. (1999) studied this question.
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