The possibility of beat wave current drive in tokamaks is considered in this thesis in steady state 2D geometry. The problem is considered by including in the analysis the 2D toroidal inhomogeneity effect and the effect of finite spatial width of the pump microwave pulses on the beat wave excitation. Both a Langmuir beat wave as well as an obliquely propagating upper-hybrid cyclotron beat wave are considered in this study. The three wave coupled system of equations in a magnetized plasma has been derived and solved numerically for this purpose. It has been found that Langmuir type beat wave excited by two almost antiparallel pump microwaves is more efficient for action transfer than a cyclotron beat wave. It has also been found that for the same input parameters, right hand polarized pumps are more efficient than left hand polarized pump microwaves for depositing power in the beat wave. The second part of the thesis considers the relativistic excitation mechanism of a large amplitude plasma wake field by a single ultra-short laser pulse. This type of large amplitude wake field has been proposed for particle acceleration to very high energies for future generation of accelerators. The problem has been modeled self consistently in ID geometry and the relevant coupled system of equations have been solved numerically. It has been found that the shape of the laser pulse profile and the ratio of the ambient plasma frequency to the incident laser frequency play an important role for the excitation of the wake-field and the stability of the laser pulse profile.