Nonlinear Landau damping and modulation of electrostatic waves in a nonextensive electron-positron-pair plasma

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Debjani Chatterjee, A P Misra

Abstract

The nonlinear theory of amplitude modulation of electrostatic wave envelopes in a collisionless electron-positron (EP) pair plasma is studied by using a set of Vlasov-Poisson equations in the context of Tsallis' q-nonextensive statistics. In particular, the previous linear theory of Langmuir oscillations in EP plasmas [Saberian and Esfandyari-Kalejahi, Phys. Rev. E 87, 053112 (2013)] is rectified and modified. Applying the multiple scale technique (MST), it is shown that the evolution of electrostatic wave envelopes is governed by a nonlinear Schrödinger (NLS) equation with a nonlocal nonlinear term ∝P∫|ϕ(ξ',τ)|(2)dξ'ϕ/(ξ-ξ') [where P denotes the Cauchy principal value, ϕ is the small-amplitude electrostatic (complex) potential, and ξ and τ are the stretched coordinates in MST], which appears due to the wave-particle resonance. It is found that a subregion 1/3<q≲3/5 of superextensivity (q<1) exists where the carrier-wave frequency can turn over with the group velocity going to zero and then to negative values. The effects of the nonlocal nonlinear term and the nonextensive parameter q are examined on the modulational instability of wave envelopes, as well as on the solitary wave solution of the NLS equation. It is found that th...Continue Reading

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Citations

Jul 18, 2018·Physical Review. E·Thomas Oikonomou, G Baris Bagci
Jul 28, 2020·Frontiers in Behavioral Neuroscience·Ching-Tai ChiangLung-Chang Lin

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