A theoretical model of avalanche breakdown of air by a Gaussian laser beam and frequency upshift is developed. The laser beam, below the threshold for tunnel ionization, heats the seed electrons to high energy and initiates avalanche ionization of the air. The ensuing plasma density profile that has maximum on axis and falls off radially causes refraction divergence of the beam. The temporal evolution of plasma density causes self-phase modulation of the laser, causing frequency broadening and spectral emission in the visible.
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Verma et al. (2010) studied this question.
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