Theory and Simulations of Nonlinear and Inelastic Processes in Relativistic Laser Plasma Interactions

The major aim of this thesis is the study of tunneling ionization, binary collision in relativistic laser-plasma interactions and the Weibel and two-stream instabilities in the context of Fast Ignition (FI) scheme of Inertial Confinement Fusion (ICF). While laser-induced charged particle acceleration in the GeV-range has recently been paced up, three dimensional particle-in-cell (3D PIC) simulation of the laser acceleration of high quality, high energy beam of electrons has been demonstrated using ionization of high-Z material within the framework of this thesis. Simultaneous effect of plasma collisions and beam temperature on the Weibel and two-stream instabilities in Fast Ignition scenario has been studied for the first time in-detail using 3D collisional particle-in-cell (PIC) simulations. Furthermore, the other major goal was the development of a new particle-in-cell-hydrodynamic hybrid simulation code, which can virtually deal with arbitrary densities. Three dimensional particle-in-cell (3D-PIC) simulations of the electron acceleration in vacuum with radially polarized ultra-intense laser beams have been performed. It is shown that single-cycle laser pulses efficiently accelerate a single attosecond electron bunch to GeV energies. When multi-cycle laser pulses are used, one has to employ ionization of high-Z materials to inject electrons into the accelerating phase at the laser pulse maximum. In this case, a train of highly collimated attosecond electron bunches with a quasi-monoenergetic spectra is produced. It is shown that the radially polarized laser pulses are superior to the Gaussian pulses both in the maximum energy gain and in the quality of the produced electron beams. Additionally, hot electron and x-ray production from high-contrast laser irradiated polystyrene-spheres studied in an experiment have been reconfirmed using 3D-PIC simulations. A sphere-size scan of the x-ray yield and the observation of a peak in both the x-ray production and temperature at a sphere diameter of 0.26 micron, indicates that these results are consistent with the Mie enhancements of the laser field at the sphere surface and multipass stochastic heating of the hot electrons in the oscillating laser field. Further, the electron acceleration by sub-10-fs laser pulses of focused intensity of $\sim 10^{16}$ W/cm$^2$ from solid target surface has been studied. The electrons have a narrow angular distribution and their observed energies exceed from the usual ponderomotive acceleration energies. It is shown that this boost in electron energies is not due to collective plasma effects, but comes mainly from the laser field due to a repeated acceleration of the electrons in the vacuum after scattering in the solid. A computationally efficient model of the Weibel instability of a relativistic electron beam in a plasma is developed. It is shown that the Weibel instability of a warm electron beam could not be suppressed in the presence of finite collision frequency in the background plasma. This finite collisionality of the plasma excites negative energy wave, which in turn drives the Weibel instability in a warm plasma. The model describes this negative energy wave for the beam plasma system. Moreover, the coupled Weibel and two-stream instabilities in a 3D model have been studied to show that relatively high beam temperature can not suppress the instability. Detailed 2D and 3D PIC simulations on the transport of a relativistic electron beam have been carried out to show this effect. A new one-dimensional full electromagnetic relativistic hybrid plasma model has been presented. The full kinetic particle-in cell (PIC) and hydrodynamic model have been combined in the single hybrid plasma code H-VLPL (Hybrid Virtual Laser Plasma Laboratory). The semi-implicit algorithm allows to simulate plasmas of arbitrary densities via automatic reduction of the highest plasma frequencies down to the numerically stable range. At the same time, the model keeps the correct spatial scales like the plasma skin depth. We discuss the numerically efficient implementation of this model. Further, we carefully benchmarked the hybrid model validity by applying it to a series of physical examples. The new mathematical method allows to overcome the typical time step restrictions of explicit PIC codes.