Non-linear Langmuir waves are examined in the context of the heat-wave accelerator. With a background of immobile ions the waves in one dimension are subject to the relativistic non-linearity of Rosenbluth and Liu (Phys. Rev. Lett vol.29, p.701 1972). In two or three dimensions, other electron nonlinearities occur which involve electric and magnetic fields. The quasi-linear equations for these nonlinearities are developed and solved numerically in a geometry representative of laser-driven beat waves.
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Bell et al. (1988) studied this question.
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