Axiomatic approach to wave-particle interactions and its applications to waves with trapped particles

Physics

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A general axiomatic approach is developed that yields ponderomotive Lagrangians for wave-particle collisionless interactions deductively and, often, without even referring to the Maxwell-Vlasov system [PRL 107 (2011) 035005; Phys. Plasmas 12 (2012) 012102, 102103, 102104]. From those, nonlinear dispersion relations and dynamic equations are derived, and, as a spin-off, the long-standing controversies are resolved pertaining to photon properties in dielectric medium. Langmuir waves with trapped electrons are studied as a paradigmatic example. For the case of deeply trapped electrons in particular, action conservation predicts different regimes depending on the energy flux S carried by trapped particles. For example, the trapped-particle modulational instability (TPMI) can develop just due to large S, in contrast with the existing theories. Remarkably, this effect is not captured by the nonlinear Schrödinger equation, which is traditionally considered as a universal model of wave self-action.

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