Abstract
The evolution of adiabatic waves with autoresonant trapped particles is described within the Lagrangian model developed in Paper I, under the assumption that the action distribution of these particles is conserved, and, in particular, that their number within each wavelength is a fixed independent parameter of the problem. One-dimensional nonlinear Langmuir waves with deeply trapped electrons are addressed as a paradigmatic example. For a stationary wave, tunneling into overcritical plasma is explained from the standpoint of the action conservation theorem. For a nonstationary wave, qualitatively different regimes are realized depending on the initial parameter S, which is the ratio of the energy flux carried by trapped particles to that carried by passing particles. At S < 1/2, a wave is stable and exhibits group velocity splitting. At S > 1/2, the trapped-particle modulational instability (TPMI) develops, in contrast with the existing theories of the TPMI yet in agreement with the general sideband instability theory. Remarkably, these effects are not captured by the nonlinear Schrödinger equation, which is traditionally considered as a universal model of wave self-action but misses the trapped-particle oscillation-center inertia.
Highlights
Within the geometrical-optics (GO) approximation, adiabatic nonlinear waves in collisionless plasma are described conveniently within the average-Lagrangian formalism originally proposed by Whitham [1, 2]
For a stationary wave, tunneling into overcritical plasma [17,18,19] is explained from the standpoint of the action conservation theorem (ACT)
Qualitatively different regimes are realized depending on the initial parameter S, which is the ratio of the energy flux carried by trapped particles to that carried by passing particles
Summary
Within the geometrical-optics (GO) approximation, adiabatic nonlinear waves in collisionless plasma are described conveniently within the average-Lagrangian formalism originally proposed by Whitham [1, 2]. (Only δ-shaped distributions of trapped particles are allowed at a → 0.) Second, as flows from Paper I, L can contain terms which are independent of a [so they cannot be inferred from Eq (1)] and yet depend on ω and k, affecting the wave dynamics. At S > 1/2, the trapped-particle modulational instability (TPMI) develops, in contrast with the existing theories of the TPMI [9,10,11] yet in agreement with the general sideband instability (SI) theory [20] These effects are not captured by the nonlinear Schrodinger equation (NLSE), which is traditionally considered as a universal model of wave self-action [6] but misses the inertial of the trapped-particle oscillation centers (OC).
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