An effective theory of laser–plasma-based particle acceleration is presented. Here we treated the plasma as a continuous medium with an index of refraction nm in which a single electron propagates. Because of the simplicity of this model, we did not perform particle-in-cell (PIC) simulations in order to study the properties of the electron acceleration. We studied the properties of the electron motion due to the Lorentz force and the relativistic equations of motion were numerically solved and analyzed. We compared our results with PIC simulations and experimental data.

Brillouin backward scattering is investigated in the interaction of linearly polarized short laser pulse with a homogenous underdense transversely magnetized plasma by taking into account the relativistic and nonlinearity effects up to third order. The plasma is embedded in a uniform magnetic field perpendicular to both of propagation direction and electric vector of the radiation field. Temporal growth rate of instability is calculated by using of the nonlinear wave equation. Results are significantly different in comparison with lower order computations. The growth rate of Brillouin backward instability shows a decrease due to the presence of external magnetic field, while relativistic and higher order nonlinearities due to the external magnetic field, give rise the Brillouin backward scattering instability.

This work is devoted to improving relativistic self-focusing of intense laser beam in underdense unmagnetized plasma. New density profiles are introduced to achieve beam width parameter up to the wavelength of the propagating laser. By investigating variations of the beam width parameter in presence of different density profiles it is found that the beam width parameter is considerably decreased for the introduced density ramp comparing with uniform density and earlier introduced density ramp profiles. By using this new density profile high intensity laser pulses are guided over several Rayleigh lengths with extremely small beam width parameter.

Raman backward scattering is investigated in the interaction of linearly polarized ultra short laser pulse with a homogenous cold underdense magnetized plasma by taking into account the relativistic effect and the effect of nonlinearity up to third order. The plasma is embedded in a uniform magnetic field perpendicular to both of propagation direction and electric vector of the radiation field. Nonlinear wave equation is set up and differential equations, which model the instability, are derived. Using of the Fourier transformation, analytical solutions are obtained for a set of physically relevant initial conditions and the temporal growth rate of instability is calculated. Results are significantly different in comparison with lower order computations. The growth rate of backward Raman scattering shows an increase due to the presence of external magnetic field as well as nonlinear effects.