The Vlasov equation is simulated by following the characteristics of phase points in phase space. It is shown that by increasing the number of phase points, without enhancing the resolution of phase-space grid, the accuracy of the simulation will be improved. In addition, the phase-point spacing introduces a smaller scale than grid spacing on which fine structures might be more conveniently handled. In order to perform simulation with a large population of phase points, an alternative to the bilinear interpolation scheme is introduced that reduces the number of operations. It is shown that by randomizing initial phase-point velocities, the recurrence effect does not happen. Finally, the standard problem of linear and nonlinear Landau damping will be examined.

A model for describing the physics of both superthermal and trapped electrons is presented. This is important because most of the space and some of the laboratory plasmas contain a population of superthermal particles. Due to the superthermal electrons, a high-energy tail appears in the electron distribution function that is conveniently modeled by the κ distribution function. The distribution function of trapped particles is modeled based on the simulation result of the Vlasov-Poisson system of equations. An analytical expression for the electron density is obtained. The ion-acoustic solitons are studied in this framework.

The possibility of the nonlinear decay of a localized perturbation into the ionacoustic solitons is studied. This corresponds to the formation of several electrons-holes in the phase space. The plasma is assumed to contain a population of super-thermal electrons and therefore the κ distribution is used to model the high energy tail in the electron distribution function. The formalism is derived near the ion plasma frequency. In this range of frequency, the ion dynamics is considerable and the ion-acoustic solitons are the stationary solutions of the governing equations. It is shown that a slowly varying dynamics of the order of ion motions causes an initial Gaussian hole to be disintegrated into a number of electron-holes. The non-stationary process of the hole formation is adiabatic. The hole velocities, which are of the order of the ionacoustic velocity, are slightly different. The set of ion-acoustic solitons forms neighboring (neighboring in phase space) holes. The influence of both trapped and super-thermal electrons on this process is studied.

Effects of superthermal and trapped electrons on the oblique propagation of linear and nonlinear ion-acoustic waves in an electron-ion plasma in the presence of a uniform external magnetic field are investigated. In order to model the superthermal electrons, a Lorentzian (kappa) velocity distribution function has been employed. The ions are cold and their dynamics are studied by hydrodynamic equations. First, the linear dispersion relation of the fast and slow modes are obtained. It is shown that the superthermal electrons cause the both modes to propagate with smaller phase velocities. Then, modified Korteweg–de Vries equations describing the propagation of nonlinear slow and fast ion-acoustic waves are derived. It is shown that the presence of superthermal and trapped electrons has great influence on the nature of magnetized ion-acoustic solitons. The dependency of soliton attributes to the parameters associated with the superthermality and trapping mechanism will be shown.