Particle Acceleration at High-γ\gamma Shock Waves

First-order Fermi acceleration processes at ultrarelativistic shocks are studied with Monte Carlo simulations. The accelerated particle spectra are obtained by integrating the exact particle trajectories in a turbulent magnetic field near the shock, with a few ``realistic'' features of the field structure included. We show that the main acceleration process at oblique shocks is the particle compression at the shock. Formation of energetic spectral tails is possible in a limited energy range for highly perturbed magnetic fields. Cut-offs in the spectra occur at low energies in the resonance range considered. We relate this feature to the structure of the magnetic field downstream of the shock, where field compression produces effectively 2D turbulence in which cross-field diffusion is very small. Because of the field compression downstream, the acceleration process is inefficient also in parallel high-$\gamma$ shocks for larger turbulence amplitudes, and features observed in oblique shocks are recovered. For small-amplitude perturbations, particle spectra are formed in a wide energy range and modifications of the acceleration process due to the existence of long-wave perturbations are observed. The critical turbulence amplitude for efficient acceleration at parallel shocks decreases with shock Lorentz factor. We also study the influence of strong short-wave perturbations downstream of the shock on the particle acceleration processes. The spectral indices obtained do not converge to the ``universal'' value . Our results indicate inefficiency of the first-order Fermi process to generate high-energy cosmic rays at ultrarelativistic shocks with the considered perturbed magnetic field structures.Comment: 4 pages, 2 figures, proceedings of the conference "Astrophysical Sources of High Energy Particles and Radiation" held in Torun, Poland (June 20-24, 2005), to appear in the AIP Proceedings Serie

Spatio-temporal evolution of the nonresonant instability in shock precursors of young supernova remnants

A nonresonant cosmic-ray-current-driven instability may operate in the shock precursors of young supernova remnants and be responsible for magnetic-field amplification, plasma heating and turbulence. Earlier simulations demonstrated magnetic-field amplification, and in kinetic studies a reduction of the relative drift between cosmic rays and thermal plasma was observed as backreaction. However, all published simulations used periodic boundary conditions, which do not account for mass conservation in decelerating flows and only allow the temporal development to be studied. Here we report results of fully kinetic Particle-In-Cell simulations with open boundaries that permit inflow of plasma on one side of the simulation box and outflow at the other end, hence allowing an investigation of both the temporal and the spatial development of the instability. Magnetic-field amplification proceeds as in studies with periodic boundaries and, observed here for the first time, the reduction of relative drifts causes the formation of a shock-like compression structure at which a fraction of the plasma ions are reflected. Turbulent electric field generated by the nonresonant instability inelastically scatters cosmic rays, modifying and anisotropizing their energy distribution. Spatial CR scattering is compatible with Bohm diffusion. Electromagnetic turbulence leads to significant nonadiabatic heating of the background plasma maintaining bulk equipartition between ions and electrons. The highest temperatures are reached at sites of large-amplitude electrostatic fields. Ion spectra show supra-thermal tails resulting from stochastic scattering in the turbulent electric field. Together, these modifications in the plasma flow will affect the properties of the shock and particle acceleration there.Comment: Accepted for publication in MNRAS. 16 pages, 15 figure

Electron Pre-Acceleration at Nonrelativistic High-Mach-Number Perpendicular Shocks

We perform particle-in-cell simulations of perpendicular nonrelativistic collisionless shocks to study electron heating and pre-acceleration for parameters that permit extrapolation to the conditions at young supernova remnants. Our high-resolution large-scale numerical experiments sample a representative portion of the shock surface and demonstrate that the efficiency of electron injection is strongly modulated with the phase of the shock reformation. For plasmas with low and moderate temperature (plasma beta $\beta_{\rm p}=5\cdot 10^{-4}$ and $\beta_{\rm p}=0.5$), we explore the nonlinear shock structure and electron pre-acceleration for various orientations of the large-scale magnetic field with respect to the simulation plane while keeping it at $90^\circ$ to the shock normal. Ion reflection off the shock leads to the formation of magnetic filaments in the shock ramp, resulting from Weibel-type instabilities, and electrostatic Buneman modes in the shock foot. In all cases under study, the latter provides first-stage electron energization through the shock-surfing acceleration (SSA) mechanism. The subsequent energization strongly depends on the field orientation and proceeds through adiabatic or second-order Fermi acceleration processes for configurations with the out-of-plane and in-plane field components, respectively. For strictly out-of-plane field the fraction of supra-thermal electrons is much higher than for other configurations, because only in this case the Buneman modes are fully captured by the 2D simulation grid. Shocks in plasma with moderate $\beta_{\rm p}$ provide more efficient pre-acceleration. The relevance of our results to the physics of fully three-dimensional systems is discussed

Plasma effects on relativistic pair beams from TeV blazars: PIC simulations and analytical predictions

Pair beams produced by very high-energy radiation from TeV blazars emit gamma rays in the GeV band by inverse-Compton scattering of soft photons. The observed GeV-band signal is smaller than that expected from the full electromagnetic cascade. This means that the pair beams must be affected by other physical processes reducing their energy flux. One possible loss mechanism involves beam-plasma instabilities that we consider in the present work. For realistic parameters the pair beams can not be simulated by modern computers. Instead, we use a simple analytical model to find a range of the beam parameters that (i) provides a physical picture similar to that of realistic pair beams and (ii) at the same time can be handled by available computational resources. Afterwards, we performed corresponding 2D PIC simulations. We confirm that the beams experience only small changes in the relevant parameter regime, and other processes such as deflection in magnetic field must be at play.Comment: 11 pages, 19 figures, 1table, accepted for publication in A&

Kinetic simulations of turbulent magnetic-field growth by streaming cosmic rays

Efficient acceleration of cosmic rays (via the mechanism of diffusive shock acceleration) requires turbulent, amplified magnetic fields in the shock's upstream region. We present results of multidimensional particle-in-cell simulations aimed at observing the magnetic field amplification that is expected to arise from the cosmic-ray current ahead of the shock, and the impact on the properties of the upstream interstellar medium. We find that the initial structure and peak strength of the amplified field is somewhat sensitive to the choice of parameters, but that the field growth saturates in a similar manner in all cases: the back-reaction on the cosmic rays leads to modification of their rest-frame distribution and also a net transfer of momentum to the interstellar medium, substantially weakening their relative drift while also implying the development of a modified shock. The upstream medium becomes turbulent, with significant spatial fluctuations in density and velocity, the latter in particular leading to moderate upstream heating; such fluctuations will also have a strong influence on the shock structure.Comment: 8 pages, 6 figures, accepted by Ap