Nonlinear Landau damping and modulation of electrostatic waves in a nonextensive electronpositronpair plasma
Abstract
The nonlinear theory of amplitude modulation of electrostatic wave envelopes in a collisionless electronpositron (EP) pair plasma is studied by using a set of VlasovPoisson equations in the context of Tsallis' q nonextensive statistics. In particular, the previous linear theory of Langmuir oscillations in EP plasmas [Saberian and EsfandyariKalejahi, Phys. Rev. E 87, 053112 (2013), 10.1103/PhysRevE.87.053112] 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}d ξ^{'}ϕ /(ξ ξ^{'}) [where P denotes the Cauchy principal value, ϕ is the smallamplitude electrostatic (complex) potential, and ξ and τ are the stretched coordinates in MST], which appears due to the waveparticle resonance. It is found that a subregion 1 /3 <q ≲3 /5 of superextensivity (q <1 ) exists where the carrierwave 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 the modulated wave packet is always unstable (nonlinear Landau damping) due to the nonlocal nonlinearity in the NLS equation. Furthermore, the effect of the nonlinear Landau damping is to slow down the amplitude of the wave envelope, and the corresponding decay rate can be faster the larger is the number of superthermal particles in pair plasmas.
 Publication:

Physical Review E
 Pub Date:
 December 2015
 DOI:
 10.1103/PhysRevE.92.063110
 arXiv:
 arXiv:1508.06903
 Bibcode:
 2015PhRvE..92f3110C
 Keywords:

 52.25.Dg;
 52.27.Ep;
 52.35.Mw;
 52.35.Sb;
 Plasma kinetic equations;
 Electronpositron plasmas;
 Nonlinear phenomena: waves wave propagation and other interactions;
 Solitons;
 BGK modes;
 Physics  Plasma Physics
 EPrint:
 25 pages, 5 figures