Magnetospheres of many astrophysical objects can be accurately described by the low-inertia (or "force-free") limit of MHD. We present a new numerical method for the solution of equations of force-free relativistic MHD based on the finite-difference time-domain approach, with a prescription for handling the spontaneous formation of current sheets. We use this method to study the time-dependent evolution of pulsar magnetospheres in both aligned and oblique magnetic geometries. For the aligned rotator, we confirm the general properties of the timeindependent solution of Contopoulos et al. For the oblique rotator, we present the three-dimensiional structure of the magnetosphere and compute, for the first time, the spin-down power of pulsars as a function of the inclination of the magnetic axis. We find that the pulsar spin-down luminosity is , wherem is the stellar dipole moment, is the rotation frequency, and a is the magnetic inclination angle. We also Q * discuss the effects of current sheet resistivity and reconnection on the structure and evolution of the magnetosphere.

In magnetized astrophysical outflows, the dissipation of field energy into particle energy via magnetic reconnection is often invoked to explain the observed non-thermal signatures. By means of two-and three-dimensional particle-in-cell simulations, we investigate anti-parallel reconnection in magnetically-dominated electron-positron plasmas. Our simulations extend to unprecedentedly long temporal and spatial scales, so we can capture the asymptotic state of the system beyond the initial transients, and without any artificial limitation by the boundary conditions. At late times, the reconnection layer is organized into a chain of large magnetic islands connected by thin X-lines. The plasmoid instability further fragments each X-line into a series of smaller islands, separated by X-points. At the X-points, the particles become unmagnetized and they get accelerated along the reconnection electric field. We provide definitive evidence that the late-time particle spectrum integrated over the whole reconnection region is a power-law, whose slope is harder than −2 for magnetizations σ 10. Efficient particle acceleration to non-thermal energies is a generic by-product of the long-term evolution of relativistic reconnection in both two and three dimensions. In three dimensions, the drift-kink mode corrugates the reconnection layer at early times, but the long-term evolution is controlled by the plasmoid instability, that facilitates efficient particle acceleration, in analogy to the two-dimensional physics. Our findings have important implications for the generation of hard photon spectra in pulsar winds and relativistic astrophysical jets.

We use 2D and 3D hybrid (kinetic ions -fluid electrons) simulations to investigate particle acceleration and magnetic field amplification at non-relativistic astrophysical shocks. We show that diffusive shock acceleration operates for quasi-parallel configurations (i.e., when the background magnetic field is almost aligned with the shock normal) and, for large sonic and Alfvénic Mach numbers, produces universal power-law spectra ∝ p −4 , where p is the particle momentum. The maximum energy of accelerated ions increases with time, and it is only limited by finite box size and run time. Acceleration is mainly efficient for parallel and quasi-parallel strong shocks, where 10-20% of the bulk kinetic energy can be converted to energetic particles, and becomes ineffective for quasi-perpendicular shocks. Also, the generation of magnetic turbulence correlates with efficient ion acceleration, and vanishes for quasi-perpendicular configurations. At very oblique shocks, ions can be accelerated via shock drift acceleration, but they only gain a factor of a few in momentum, and their maximum energy does not increase with time. These findings are consistent with the degree of polarization and the morphology of the radio and X-ray synchrotron emission observed, for instance, in the remnant of SN 1006. We also discuss the transition from thermal to non-thermal particles in the ion spectrum (supra-thermal region), and we identify two dynamical signatures peculiar of efficient particle acceleration, namely the formation of an upstream precursor and the alteration of standard shock jump conditions.

We present evidence that relativistic shocks propagating in unmagnetized plasmas can self-consistently accelerate particles. We use long-term two-dimensional particle-in-cell simulations to study the well-developed shock structure in unmagnetized pair plasma. The particle spectrum downstream of such a shock consists of two components: a relativistic Maxwellian, with a characteristic temperature set by the upstream kinetic energy of the flow, and a high-energy tail, extending to energies 1100 times that of the thermal peak. This high-energy tail is best fitted as a power law in energy with index Ϫ2.4 ‫ע‬ 0.1, modified by an exponential cutoff. The cutoff moves to higher energies with time of the simulation, leaving a larger power-law range. The number of particles in the tail is ∼1% of the downstream population, and they carry ∼10% of the kinetic energy in the downstream region. Investigating the trajectories of particles in the tail, we find that the energy gains occur as particles bounce between the upstream and downstream regions in the magnetic fields generated by the Weibel instability. We compare this mechanism to the first-order Fermi acceleration and set a lower limit on the efficiency of the shock acceleration process.