The envelope soliton for the nonlinear interaction of Langmuir waves with electron acoustic waves in the Earth's inner magnetosphere

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.