*3.2. Particle Acceleration*

Following the dissipation of kinetic or magnetic energy, particles are accelerated to high energies. These particles, then, emit the high-energy, non-thermal radiation observed. Modeling this radiation (e.g., as synchrotron emission) provides an indirect evidence for particle acceleration to non-thermal distribution. This was first done in the context of the GRB afterglow [98,99].

The theory of test particle acceleration (i.e., assuming a fixed background) has been well established for many decades [100–105]. In the past 10–15 years, advances in parallel computation, in particular, particle-in-cell (PIC) simulations, have enabled the modeling and studying of this process from first principles [106–109], under various conditions (e.g., magnetization, etc.) [110–113]. There have been several attempts to extend the theory beyond the test particle to include the feedback on the surrounding plasma [114,115]. Alternative theories, such as stochastic turbulence acceleration have also been considered [116].

In recent years, there has been a considerable interest in the theory of magnetized outflows. When the magnetic field is energetically dominant, it may convert its energy to kinetic energy by reconnection of the magnetic field lines, namely, a topological change in the magnetic field structure. Using PIC simulations, many authors have demonstrated that efficient acceleration of particles take place in such reconnection layers [113,117]. Furthermore, the accelerated particles obtain a power law distribution, similar to the expectation from a Fermi-like acceleration [111,113,118–125].
