The modulational instability of coupled waves

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Abstract
The collinear propagation of an arbitrary number of finite‐amplitude waves is modeled by a system of coupled nonlinear Schrödinger equations; one equation for each complex wave amplitude. In general, the waves are modulationally unstable with a maximal growth rate larger than the modulational growth rate of any wave alone. Moreover, waves that are modulationally stable by themselves can be driven unstable by the nonlinear coupling. The general theory is then applied to the relativistic modulational instability of two laser beams in a beat‐wave accelerator. For parameters typical of a proposed beat‐wave accelerator, this instability can seriously distort the incident laser pulse shapes on the particle‐acceleration time scale, with detrimental consequences for particle acceleration.

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