Vlasov simulation of modulational instability and Langmuir collapse

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Abstract
Vlasov simulations are developed to study the one-dimensional modulational instability and Langmuir collapse in a plasma driven by an external field. Both electrons and ions in the plasma are described by the Vlasov equations. The external driving field energy density is ∼10−3 times the initial electron thermal energy density. The plasma has a mass ratio of mi/me=1836, and a temperature ratio of Ti/Te=0.1 or 1.0, where mi, me, Ti, and Te are the ion mass, electron mass, ion temperature, and electron temperature. The modulational instability is saturated by the formation of Langmuir cavitons which later collapse and burn out due to the strong wave–particle interactions. The particle heating during a single Langmuir collapse is small under this weak driving field. The accelerated electron and ion jet-like streams in phase space as well as the nucleation of cavitons are observed during the evolution. Zakharov equations with the same parameters and similar initial conditions are also simulated, and the results are compared with those of the Vlasov simulations. The two models agree with each other quantitatively up to the first collapse following the saturation of exponential growth; dynamic differences appear after the first collapse.