• analisi di stabilità
• autofrequenza dello shock
• corrugational instability
• cosmic rays
• instabilità corrugazionale
• onde d'urto
• raggi cosmici
• shock eigenfrequency
• shock waves
• stability analysis

One of the major uncertainties still surrounding particle acceleration around shocks is the level at which this saturates, that is, the fraction of energy that can be transferred from the fluid to non-thermal particles. This saturation level plays a very important role, for instance, in discussions of the origin of cosmic rays as observed at Earth: it has to be rather large (~0.1) to allow SNe to provide the observed flux.

This level can be connected to two phenomena. First, the very uncertain particle injection mechanism at shocks. Second, the feedback of the particles' pressure on the shock structure. Here we study the latter phenomenon. We perform a linear stability analysis for corrugations of a Newtonian shocks with accelerated particles for an arbitrary diffusion coefficient. We study first the dispersion relation for homogeneous media, showing that, besides the conventional pressure waves and entropy vorticity disturbances, two new perturbation modes exist, dominated by the particles' pressure and damped by diffusion.

We then show how to construct a corrugational mode for the shock itself, one, that is, where the shock executes free oscillations (possibly damped or growing) and sheds perturbations away from itself: this global mode requires the new modes, and perturbations in the particles' distribution function are carried by the diffusing particles to the upstream section of the fluid, where the conventional hydrodynamical quantities are perturbed. By using the perturbed Rankine--Hugoniot conditions, we show that this leads to the determination of the corrugational eigenfrequency.

We apply our analysis technique to an exact model for particle accelerations at shocks by Amato and Blasi. The most intriguing feature of their solutions is that the particles' pressure is dominated by the highest energy particles, because their spectra are even more ultraviolet divergent than those in the test-particle limit. This seems interesting for us because it enhances the back-reaction of accelerated particles on the shock.

In this thesis we summarize the fundamental models for particle accelerations, then we discuss some previous studies on shock stability, namely the classical D'yakov's theory and the two-fluid stability analysis by Mond and Drury. Finally we present our theory and we show how to build a global mode with our technique.