Nonlinear waves, structure formation and particle acceleration by waves in space physics

The first part of this dissertation is devoted to the theory of nonlinear modulational interaction of lower-hybrid waves with slow background density fluctuations such as ion-acoustic mode and inertial Alfven mode. This type of interaction leads to modulational instability and localization of lower hybrid waves in the plane perpendicular to the magnetic field. The field localizations are correlated with depletions or humps in local plasma density.; Density cavities filled with field fluctuations with frequency of the order of local lower-hybrid frequency are commonly observed in auroral ionosphere of the Earth. These structures are named lower-hybrid solitary structures. In this dissertation, the theory of modulational interaction of lower-hybrid waves with ion-acoustic waves and inertial Alfven waves is studied in the context of auroral ionosphere. The behavior of lower-hybrid waves are investigated in the pre-determined cylindrical background density profile. It is found that the lower-hybrid waves are trapped in density depletions as well as density humps. The wave trajectories show that the wave is best confined in the regions of maximum density gradient. Then the Reynolds' stresses of the lower-hybrid waves are added to the governing equations describing the interaction. The conditions for occurrence of the modulational instability are analyzed. The evolution equations for the envelope lower-hybrid amplitude is obtained for the case when the interacting mode is ion-acoustic as well as inertial Alfven. It is found that the width of an initial modulation in the lower-hybrid wave amplitude contracts by the evolution of modulational instability. This leads to "collapse", or a finite-time blow-up solution.; In the second part of the dissertation, "shock surfing acceleration" is considered as a possible candidate for ion acceleration at quasi-perpendicular collisionless astrophysical shock waves in plasma.; The modification of the acceleration mechanism for relativistic regime is analyzed. It is shown that one of the limitations to shock surfing acceleration ceases at relativistic energies. For sufficiently steep shock fronts, the transition to "relativistic regime" results with acceleration up to ultra-relativistic energies at time scales much shorter than time scales predicted by the widely accepted acceleration mechanism, diffusive shock acceleration. The critical energy for the transition to the relativistic regime is estimated, and conditions for achieving this critical energy are discussed.