Based on self-consistent modelling of the radio-frequency sheath parameters, such as the ion and electron densities and the ion velocity, the dust particle charging process in an RF sheath is investigated by employing the kappa $(\kappa )$ distribution for the electrons. It is shown that the charge number of the dust particle decreases near the sheath–wall interface while it shows the opposite tendency near the plasma-sheath edge, as the $\kappa$ value is decreased. The fluctuation of the dust particle charge modified by the $\kappa$ value depends on the dust particle radius. With an increases in the $\kappa$ value, the fluctuation of the dust particle charge has a slight increase for a small dust particle, and it shows a significant increase for a large dust particle. In addition, as the $\kappa$ value is decreased, the charge number of the dust particle obtained from the time-averaged plasma parameters deviates from the results obtained from the instantaneous plasma parameters. Moreover, a smaller deviation can be found for a large dust particle under the same $\kappa$ value conditions.

The modulation instability of a circularly polarized laser pulse in a magnetized non-Maxwellian plasma is investigated. Based on a relativistic fluid model, the nonlinear interaction of an intense circularly polarized laser beam with a non-Maxwellian magnetized plasma is described. Nonlinear dispersion relation and growth rate of the instability for left- and right-hand polarizations are derived. The effect of temperature, external magnetic field, value of Kappa and state of polarization on the growth rate are analyzed. It is shown that the growth rate increases with increase in the magnetic field for the right-hand polarization and inversely it decreases for the left-hand one. Also it is observed that existence of super-thermal particles causes the decrease in the growth.