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

Non-relativistic perpendicular shocks modeling young supernova remnants: nonstationary dynamics and particle acceleration at forward and reverse shocks

For parameters that are applicable to the conditions at young supernova remnants, we present results of 2D3V particle-in-cell simulations of a non-relativistic plasma shock with a large-scale perpendicular magnetic field inclined at 45-deg angle to the simulation plane to approximate 3D physics. We developed an improved clean setup that uses the collision of two plasma slabs with different density and velocity, leading to the development of two distinctive shocks and a contact discontinuity. The shock formation is mediated by Weibel-type filamentation instabilities that generate magnetic turbulence. Cyclic reformation is observed in both shocks with similar period, for which we note global variations on account of shock rippling and local variations arising from turbulent current filaments. The shock rippling occurs on spatial and temporal scales given by gyro-motions of shock-reflected ions. The drift motion of electrons and ions is not a gradient drift, but commensurates with E x B drift. We observe a stable suprathermal tail in the ion spectra, but no electron acceleration because the amplitude of Buneman modes in the shock foot is insufficient for trapping relativistic electrons. We see no evidence of turbulent reconnection. A comparison with other 2D simulation results suggests that the plasma beta and the ion-to-electron mass ratio are not decisive for efficient electron acceleration, but pre-acceleration efficacy might be reduced with respect to the 2D results once three-dimensional effects are fully accounted for. Other microphysical factors may also be at play to limit the amplitude of Buneman waves or prevent return of electrons to the foot region.Comment: Astrophysical Journal, in press, some figures with low resolutio

Kinetic simulations of nonrelativistic perpendicular shocks of young supernova remnants. I. Electron shock-surfing acceleration

Electron injection at high Mach-number nonrelativistic perpendicular shocks is studied here for parameters that are applicable to young SNR shocks. Using high-resolution large-scale two-dimensional fully kinetic particle-in-cell (PIC) simulations and tracing individual particles we in detail analyze the shock surfing acceleration (SSA) of electrons at the leading edge of the shock foot. The central question is to what degree the process can be captured in 2D3V simulations. We find that the energy gain in SSA always arises from the electrostatic field of a Buneman wave. Electron energization is more efficient in the out-of-plane orientation of the large-scale magnetic field because both the phase speed and the amplitude of the waves are higher than for the in-plane scenario. Also, a larger number of electrons is trapped by the waves compared to the in-plane configuration. We conclude that significant modifications of the simulation parameters are needed to reach the same level of SSA efficiency as in simulations with out-of-plane magnetic field or 3D simulations

Could Cosmic Rays Affect Instabilities in the Transition Layer of Nonrelativistic Collisionless Shocks?

There is an observational correlation between astrophysical shocks and non-thermal particle distributions extending to high energies. As a first step toward investigating the possible feedback of these particles on the shock at the microscopic level, we perform particle-in-cell (PIC) simulations of a simplified environment consisting of uniform, interpenetrating plasmas, both with and without an additional population of cosmic rays. We vary the relative density of the counterstreaming plasmas, the strength of a homogeneous parallel magnetic field, and the energy density in cosmic rays. We compare the early development of the unstable spectrum for selected configurations without cosmic rays to the growth rates predicted from linear theory, for assurance that the system is well represented by the PIC technique. Within the parameter space explored, we do not detect an unambiguous signature of any cosmic-ray-induced effects on the microscopic instabilities that govern the formation of a shock. We demonstrate that an overly coarse distribution of energetic particles can artificially alter the statistical noise that produces the perturbative seeds of instabilities, and that such effects can be mitigated by increasing the density of computational particles.Comment: 22 pages, 5 figures, published in Ap

Cosmic-Ray Acceleration at Ultrarelativistic Shock Waves: Effects of Downstream Short-Wave Turbulence

The present paper is the last of a series studying the first-order Fermi acceleration processes at relativistic shock waves with the method of Monte Carlo simulations applied to shocks propagating in realistically modeled turbulent magnetic fields. The model of the background magnetic field structure of Niemiec & Ostrowski (2004, 2006) has been augmented here by a large-amplitude short-wave downstream component, imitating that generated by plasma instabilities at the shock front. Following Niemiec & Ostrowski (2006), we have considered ultrarelativistic shocks with the mean magnetic field oriented both oblique and parallel to the shock normal. For both cases simulations have been performed for different choices of magnetic field perturbations, represented by various wave power spectra within a wide wavevector range. The results show that the introduction of the short-wave component downstream of the shock is not sufficient to produce power-law particle spectra with the "universal" spectral index 4.2. On the contrary, concave spectra with cutoffs are preferentially formed, the curvature and cutoff energy being dependent on the properties of turbulence. Our results suggest that the electromagnetic emission observed from astrophysical sites with relativistic jets, e.g. AGN and GRBs, is likely generated by particles accelerated in processes other than the widely invoked first-order Fermi mechanism.Comment: 9 pages, 8 figures, submitted to Ap

Electron Acceleration at Rippled Low-Mach-number Shocks in High-beta Collisionless Cosmic Plasmas

Using large-scale fully-kinetic two-dimensional particle-in-cell simulations, we investigate the effects of shock rippling on electron acceleration at low-Mach-number shocks propagating in high-$\beta$ plasmas, in application to merger shocks in galaxy clusters. We find that the electron acceleration rate increases considerably when the rippling modes appear. The main acceleration mechanism is stochastic shock-drift acceleration, in which electrons are confined at the shock by pitch-angle scattering off turbulence and gain energy from the motional electric field. The presence of multi-scale magnetic turbulence at the shock transition and the region immediately behind the main shock overshoot is essential for electron energization. Wide-energy non-thermal electron distributions are formed both upstream and downstream of the shock. The maximum energy of the electrons is sufficient for their injection into diffusive shock acceleration. We show for the first time that the downstream electron spectrum has a~power-law form with index $p\approx 2.5$, in agreement with observations.Comment: 15 pages, 14 figures, to be published in Ap