Landau damping of wave envelopes in a nonextensive electron-positron plasma

The nonlinear theory of amplitude modulation of electrostatic wave envelopes in a collisionless pair plasma is studied by using a set of Vlasov-Poisson equations in the context of Tsallis' q-nonextensive statistics. Applying the multiple scale technique (MST), it is shown that the evolution of electrostatic wave envelopes is governed by a nonlinear Schroedinger (NLS) equation with a nonlocal nonlinear term 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 (MI) 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 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. (author)