The linear and the non-linear behaviors of the ion temperature gradient (ITG) mode in a plasma with regularized κ-distributed electrons are investigated using the fluid model. The dispersion relation of the ITG mode obtained on the basis of the local approximation shows that the growth rate of the ITG mode decreases with the increase in the spectral index κ and the exponential cut-off parameter α. It indicates that the presence of the superthermal electron leads to destabilization of the ITG mode, especially in the low κ ( κ < 1.5) region. In addition, the existence and the nature of the soliton structure driven by the ITG are studied using the pseudopotential technology. The soliton amplitude increases with the increase in the exponential cut-off parameter α and the spectral index κ, whereas the width of the soliton varies inversely. The present results will help to understand the low-frequency electrostatic wave and nonlinear structure in space and experimental plasmas with non-thermal electrons.
The nonlinear coupling of Langmuir waves with electron-acoustic waves is investigated using the kinetic theory, where the hot electron component is modeled by the kappa distribution with an exponential cutoff at high energy tail, i.e., the cutoff kappa distribution. The one dimensional structure of envelope Langmuir solitons is analyzed by the numerical calculation with parameters typical of the Earth's inner magnetosphere. In the case of hot electrons with a cutoff kappa distribution, envelope Langmuir solitons have larger width and slower speed than that in the case of hot electrons with a Maxwellian distribution. The envelop Langmuir soliton with density depletion obtained in the Earth's inner magnetosphere propagates at a speed lower than the electron-acoustic velocity. At a given amplitude of electrostatic field, the envelope Langmuir soltions have a speed comparable with the ones of electron-acoustic wave solitons, but a wider scale in the case of hot electrons with a cutoff kappa distribution.
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