During researches on Tokamaks, it was clear that the ohmic heating used in them was not sufficient to obtain the temperatures needed for initiation of a self-sustaining thermonuclear reaction. Therefore a search was begun for methods of heating which could supplement ohmic heating. One of them is radio frequency (RF) wave heating. In this thesis, it has been shown thatinteractions between waves and particles can lead to either wave damping or wave instability depending on the shape of the velocity distribution of the particles and magnitude of the waves. This fact is based on Landau problem which has been deduced from imaginary part of the wave frequency during propagation. Beside, cold plasma wave in a background magnetic field has been described and main modes in such waves have been discussed not only mathematically but also physically. A certain additional subtle and practical aspects of wave propagation in an inhomogeneous plasma has been discussed. We also have shown that how the energy content of a wave is related to its dispersion relation. The particle-in-cell (PIC) computational method allows the statistical representation of general distribution functions in phase space. It has been shown that how nonlinearities occur after the existence of a perturbed electrostatic wave. Non-extensive statistical mechanics (NSM) has been developed as auseful tool to describe the complex systems whose properties cannot be exactlydescribed by Boltzmann–Gi (B-G) statistical mechanics. It is thought tobe a useful generalization of B-G statistics and to be appropriate for the statisticaldescription of the long-range interaction systems such as Plasmas. The generalized dispersion equation and Landau coefficient for longitudinal oscillationin an unmagnetized, collisionless and isotropic plasma with non-extensiveq-distribution like statistics is derived and compared with conventional distribution. Surprisingly it has been shown that how the damping rate depends on wave number of oscillations. A characteristic wave number is deduced as a criterion for comparing the damping in the two statistics. Key words Wave-plasma interaction, RF heating, Landau damping, inhomogeneities, nonlinearity, Particle-In-Cell (PIC) computational method, Boltzmann–Gi (B-G) statistics,q-distribution.
