2017/06/12 by Didier Bénisti, Benisti, Didier
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Dust and Plasma Wave Phenomena #FOS: Physical sciences #Plasma Physics (physics.plasm-ph) #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1706.03545
openalex publication_date 2017/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we provide a general derivation of the nonlinear frequency\nshift, \δ \ω, for a sinusoidal electron plasma wave (EPW) that varies\nslowly enough for the results derived in the companion paper, on the action\ndistribution function, to apply. We first consider the situation when the EPW\nmonotonously grows and then monotonously decays in a homogeneous plasma. In\nthis situation, we show a hysteresis in the wave frequency, which does not\nconverge back to its linear value as the wave decays to small amplitudes. We\nthen address the derivation of \δ \ω for an EPW that keeps growing in\na one-dimensional (1-D) inhomogeneous plasma. We show that, usually, the\nfrequency shift does not only depend on the local EPW amplitude and wavenumber.\nIt also depends on the whole history of the density variations, as experienced\nby the wave. In a multidimensional inhomogeneous plasma, the values assumed by\n\δ \ω are usually different from those derived in 1-D because, due to\nthe transverse electron motion, one must account for the hysteresis in \δ\n\ω in addition to plasma inhomogeneity. Hence, unless the EPW keeps\ngrowing in a homogeneous one-dimensional plasma, one cannot derive \δ\n\ω \a priori as a function of the local wave amplitude and\nwavenumber. Due to the nonlocality in the action distribution function, \δ\n\ω depends on the whole history of the variations of the EPW amplitude and\nplasma density.\n