Laser-plasma interaction in plasma channel and relativistic particle dynamics

This work is devoted to two important topics in nonlinear laser plasma physics: the excitation of laser wakefields in a pre-formed plasma channel with arbitrary density profile, the stability (Raman Forward Scattering) of channel guided propagation of laser pulse, and the relativistic particle dynamics in the electromagnetic field of ultra-intense laser.; First, we present a unified theory of wake excitation in plasma channels. It is found that the presence of mode continuum causes the collisionless damping of quasi-modes, whose frequency and damping rate can be calculated by analytically continuing the causal Green's function into the lower half of the complex frequency plane. Electromagnetic nature of the plasma wakes in the channel makes their excitation nonlocal, which results in the algebraic decay of the fields with time due to phase-mixing of plasma oscillations with spatially-varying frequencies. For a weakly inhomogeneous channel, an approximated Green's function is constructed and closed form analytical expressions for field evolution are derived. We then derive a general dispersion relation which is capable of describing various electron plasma instabilities for a guided laser pulse in plasma channel, such as Raman Scattering, relativistic modulational instability, self-modulational instability and laser hosing instability. We focus on the Raman Forward Scattering (RFS) for a single-mode plasma channel. The growth rate of the instability is found to be significantly smaller than that in the homogeneous plasma. This reduction, which is appreciable even for sub-relativistic laser intensities and shallow plasma channels, is caused by the radial shear of the plasma frequency and the existence of quasi-modes. The interplay of these two effects produces a peculiar double-humped gain profile.; In the second part of this thesis, we first develop a Hamiltonian theory to describe the averaged motion of charged particle in the electromagnetic field of an ultra-intense laser. The concept of ponderomotive force is generalized into a relativistic ponderomotive Hamiltonian, and its validity region is clarified. We find that when the concept of ponderomotive force is applicable, the electron's averaged motion is independent of the laser polarization at the zero order, and it slightly rotates towards the laser polarization axis at the first order for a linearly polarized pulse. For a circularly polarized pulse, the electron's drift motion contains a first order azimuthal component even when the laser pulse is radially symmetric. We then study the interaction between a circularly polarized radiation and a charged particle in the presence of a static magnetic field. We solve the problem exactly in terms of simple functions when the radiation is approximated as a finite-length plane wave. The condition for an interesting phenomenon called autoresonance is self-evident in our formalism. We find that the averaged particle motion in a realistic laser pulse could contain an inward radial drift, thus provide a possible method for compression of an electron column.