Simulations of ion acceleration at nonrelativistic shocks. II. Magnetic field amplification
Abstract
We use large hybrid simulations to study ion acceleration and generation of magnetic turbulence due to the streaming of particles that are selfconsistently accelerated at nonrelativistic shocks. When acceleration is efficient, we find that the upstream magnetic field is significantly amplified. The total amplification factor is larger than 10 for shocks with Alfvénic Mach number M = 100, and scales with the square root of M. The spectral energy density of excited magnetic turbulence is determined by the energy distribution of accelerated particles, and for moderately strong shocks (M ≲ 30) agrees well with the prediction of resonant streaming instability, in the framework of quasilinear theory of diffusive shock acceleration. For M ≳ 30, instead, Bell's nonresonant hybrid (NRH) instability is predicted and found to grow faster than resonant instability. NRH modes are excited far upstream by escaping particles, and initially grow without disrupting the current, their typical wavelengths being much shorter than the current ions' gyroradii. Then, in the nonlinear stage, most unstable modes migrate to larger and larger wavelengths, eventually becoming resonant in wavelength with the driving ions, which start diffuse. Ahead of strong shocks we distinguish two regions, separated by the freeescape boundary: the far upstream, wheremore »
 Authors:
 Department of Astrophysical Sciences, Princeton University, 4 Ivy Lane, Princeton, NJ 08544 (United States)
 Publication Date:
 OSTI Identifier:
 22370482
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Astrophysical Journal; Journal Volume: 794; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ACCELERATION; ALFVEN WAVES; AMPLIFICATION; ENERGY DENSITY; ENERGY SPECTRA; INSTABILITY; IONS; MACH NUMBER; MAGNETIC FIELDS; NONLINEAR PROBLEMS; QUASILINEAR PROBLEMS; RELATIVISTIC RANGE; SHOCK WAVES; SIMULATION; SUPERNOVA REMNANTS; TURBULENCE; WAVELENGTHS
Citation Formats
Caprioli, D., and Spitkovsky, A., Email: caprioli@astro.princeton.edu. Simulations of ion acceleration at nonrelativistic shocks. II. Magnetic field amplification. United States: N. p., 2014.
Web. doi:10.1088/0004637X/794/1/46.
Caprioli, D., & Spitkovsky, A., Email: caprioli@astro.princeton.edu. Simulations of ion acceleration at nonrelativistic shocks. II. Magnetic field amplification. United States. doi:10.1088/0004637X/794/1/46.
Caprioli, D., and Spitkovsky, A., Email: caprioli@astro.princeton.edu. Fri .
"Simulations of ion acceleration at nonrelativistic shocks. II. Magnetic field amplification". United States.
doi:10.1088/0004637X/794/1/46.
@article{osti_22370482,
title = {Simulations of ion acceleration at nonrelativistic shocks. II. Magnetic field amplification},
author = {Caprioli, D. and Spitkovsky, A., Email: caprioli@astro.princeton.edu},
abstractNote = {We use large hybrid simulations to study ion acceleration and generation of magnetic turbulence due to the streaming of particles that are selfconsistently accelerated at nonrelativistic shocks. When acceleration is efficient, we find that the upstream magnetic field is significantly amplified. The total amplification factor is larger than 10 for shocks with Alfvénic Mach number M = 100, and scales with the square root of M. The spectral energy density of excited magnetic turbulence is determined by the energy distribution of accelerated particles, and for moderately strong shocks (M ≲ 30) agrees well with the prediction of resonant streaming instability, in the framework of quasilinear theory of diffusive shock acceleration. For M ≳ 30, instead, Bell's nonresonant hybrid (NRH) instability is predicted and found to grow faster than resonant instability. NRH modes are excited far upstream by escaping particles, and initially grow without disrupting the current, their typical wavelengths being much shorter than the current ions' gyroradii. Then, in the nonlinear stage, most unstable modes migrate to larger and larger wavelengths, eventually becoming resonant in wavelength with the driving ions, which start diffuse. Ahead of strong shocks we distinguish two regions, separated by the freeescape boundary: the far upstream, where field amplification is provided by the current of escaping ions via NRH instability, and the shock precursor, where energetic particles are effectively magnetized, and field amplification is provided by the current in diffusing ions. The presented scalings of magnetic field amplification enable the inclusion of selfconsistent microphysics into phenomenological models of ion acceleration at nonrelativistic shocks.},
doi = {10.1088/0004637X/794/1/46},
journal = {Astrophysical Journal},
number = 1,
volume = 794,
place = {United States},
year = {Fri Oct 10 00:00:00 EDT 2014},
month = {Fri Oct 10 00:00:00 EDT 2014}
}

We use twodimensional and threedimensional hybrid (kinetic ionsfluid electrons) simulations to investigate particle acceleration and magnetic field amplification at nonrelativistic astrophysical shocks. We show that diffusive shock acceleration operates for quasiparallel 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 powerlaw spectra ∝p {sup –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 quasiparallel strong shocks, where 10%20% ofmore »

Simulations of ion acceleration at nonrelativistic shocks. III. Particle diffusion
We use large hybrid (kineticprotonsfluidelectrons) simulations to investigate the transport of energetic particles in selfconsistent electromagnetic configurations of collisionless shocks. In previous papers of this series, we showed that ion acceleration may be very efficient (up to 10%20% in energy), and outlined how the streaming of energetic particles amplifies the upstream magnetic field. Here, we measure particle diffusion around shocks with different strengths, finding that the mean free path for pitchangle scattering of energetic ions is comparable with their gyroradii calculated in the selfgenerated turbulence. For moderately strong shocks, magnetic field amplification proceeds in the quasilinear regime, and particles diffusemore » 
ION ACCELERATION IN NONRELATIVISTIC ASTROPHYSICAL SHOCKS
We explore the physics of shock evolution and particle acceleration in nonrelativistic collisionless shocks using hybrid simulations. We analyze a wide range of physical parameters relevant to the acceleration of cosmic rays (CRs) in astrophysical shock scenarios. We show that there are fundamental differences between high and low Mach number shocks in terms of the electromagnetic turbulence generated in the preshock zone; dominant modes are resonant with the streaming CRs in the low Mach number regime, while both resonant and nonresonant modes are present for high Mach numbers. Energetic powerlaw tails for ions in the downstream plasma account for upmore » 
SIMULATIONS AND THEORY OF ION INJECTION AT NONRELATIVISTIC COLLISIONLESS SHOCKS
We use kinetic hybrid simulations (kinetic ionsfluid electrons) to characterize the fraction of ions that are accelerated to nonthermal energies at nonrelativistic collisionless shocks. We investigate the properties of the shock discontinuity and show that shocks propagating almost along the background magnetic field (quasiparallel shocks) reform quasiperiodically on ion cyclotron scales. Ions that impinge on the shock when the discontinuity is the steepest are specularly reflected. This is a necessary condition for being injected, but it is not sufficient. Also, by following the trajectories of reflected ions, we calculate the minimum energy needed for injection into diffusive shock acceleration, asmore » 
Magnetic field amplification in nonlinear diffusive shock acceleration including resonant and nonresonant cosmicray driven instabilities
We present a nonlinear Monte Carlo model of efficient diffusive shock acceleration where the magnetic turbulence responsible for particle diffusion is calculated selfconsistently from the resonant cosmicray (CR) streaming instability, together with nonresonant short and longwavelength CRcurrentdriven instabilities. We include the backpressure from CRs interacting with the strongly amplified magnetic turbulence which decelerates and heats the superAlfvénic flow in the extended shock precursor. Uniquely, in our planeparallel, steadystate, multiscale model, the full range of particles, from thermal (∼eV) injected at the viscous subshock to the escape of the highest energy CRs (∼PeV) from the shock precursor, are calculated consistently withmore »