Abstract
Based on the full Zakharov equations, the dispersion relation of the wave-wave interaction by strong Langmuir waves in nonextensive plasma is obtained. The dispersion equation were analyzed with numerical method and the results indicate that both the wave number range and maximum growth rate of the modulational instability by strong Langmuir waves will enhance with the nonextensive parameter q increasing. Moreover, an analytic study of dispersion equations in two special and important cases, the modulation instability induced by transverse perturbations and longitudinal perturbations, is presented. The analysis shows that the growth rate induced by transverse perturbations and that done by longitudinal perturbations are equal when the nonextensive parameter q is the same. Comparison of the calculated modulational instability with the corresponding analytical solutions shows that they are in good agreement. This research provides a clearer physical picture of the modulational instability in nonextensive plasma.
Highlights
The modulational processes result in the formation of strongly coherent structures in a plasma
We examine the problem of the instability of strong Langmuir waves in q-plasma in the Liapunov sense for Eqs. (1) and (2)
(2) From Eq (17) and Eq (19), the growth rate induced by transverse perturbations (θ = 0) is equal to that done by longitudinal perturbations (θ = π/2) when q is the same
Summary
The modulational processes result in the formation of strongly coherent structures (soliton, caviton) in a plasma. −gradωpe, the plasmon concentration increasing leads stronger ponderomotive-force (radiation pressure), which in turn expels more plasma from the diluted region; as a result, the instability like the modulational one occurs. Region.[11] there is little research on modulational instability by strong Langmuir waves in q-plasma. The standard description of Langmuir turbulence is embodied in the Zakharov equations (ZEs) which can nonlinearly couple the Langmuir waves to the ion-acoustic waves.[16] Based on the two-fluid model, the ZEs can be derived by assuming all wave fields are small. ZEs is applicable under Maxwellian distribution in Boltzmann-Gibbs statistics, but might be inadequate for the description of nonextensive systems To solve this problem, many researchers have made relevant investigations. We discuss that the modulational instability by strong Langmuir waves are inferred and numerically study the growth rate of modulational instability in Sect. IV, with a summary and discussion of our main results
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