Modulational instability by strong Langmuir waves in q-plasma

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.