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Register a new userTurbulence Dissipation and Particle Injection in Non-Linear Diffusive Shock Acceleration with Magnetic Field Amplification
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The highly amplified magnetic fields suggested by observations of some supernova remnant (SNR) shells are most likely an intrinsic part of efficient particle acceleration by shocks. This strong turbulence, which may result from cosmic ray driven instabilities, both resonant and non-resonant, in the shock precursor, is certain to play a critical role in self-consistent, nonlinear models of strong, cosmic ray modified shocks. Here we present a Monte Carlo model of nonlinear diffusive shock acceleration (DSA) accounting for magnetic field amplification through resonant instabilities induced by accelerated particles, and including the effects of dissipation of turbulence upstream of a shock and the subsequent precursor plasma heating. Feedback effects between the plasma heating due to turbulence dissipation and particle injection are strong, adding to the nonlinear nature of efficient DSA. Describing the turbulence damping in a parameterized way, we reach two important results: first, for conditions typical of supernova remnant shocks, even a small amount of dissipated turbulence energy (~10%) is sufficient to significantly heat the precursor plasma, and second, the heating upstream of the shock leads to an increase in the injection of thermal particles at the subshock by a factor of several. In our results, the response of the non-linear shock structure to the boost in particle injection prevented the efficiency of particle acceleration and magnetic field amplification from increasing. We argue, however, that more advanced (possibly, non-resonant) models of turbulence generation and dissipation may lead to a scenario in which particle injection boost due to turbulence dissipation results in more efficient acceleration and even stronger amplified magnetic fields than without the dissipation.
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We present a nonlinear Monte Carlo model of efficient diffusive shock acceleration (DSA) where the magnetic turbulence responsible for particle diffusion is calculated self-consistently from the resonant cosmic-ray (CR) streaming instability, together with non-resonant short- and long-wavelength CR-current-driven instabilities. We include the backpressure from CRs interacting with the strongly amplified magnetic turbulence which decelerates and heats the super-alfvenic flow in the extended shock precursor. Uniquely, in our plane-parallel, steady-state, multi-scale 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 with the shock structure, precursor heating, magnetic field amplification (MFA), and scattering center drift relative to the background plasma. In addition, we show how the cascade of turbulence to shorter wavelengths influences the total shock compression, the downstream proton temperature, the magnetic fluctuation spectra, and accelerated particle spectra. A parameter survey is included where we vary shock parameters, the mode of magnetic turbulence generation, and turbulence cascading. From our survey results, we obtain scaling relations for the maximum particle momentum and amplified magnetic field as functions of shock speed, ambient density, and shock size.
Fast collisionless shocks in cosmic plasmas convert their kinetic energy flow into the hot downstream thermal plasma with a substantial fraction of energy going into a broad spectrum of superthermal charged particles and magnetic fluctuations. The superthermal particles can penetrate into the shock upstream region producing an extended shock precursor. The cold upstream plasma flow is decelerated by the force provided by the superthermal particle pressure gradient. In high Mach number collisionless shocks, efficient particle acceleration is likely coupled with turbulent magnetic field amplification (MFA) generated by the anisotropic distribution of accelerated particles. This anisotropy is determined by the fast particle transport making the problem strongly nonlinear and multi-scale. Here, we present a nonlinear Monte Carlo model of collisionless shock structure with super-diffusive propagation of high-energy Fermi accelerated particles coupled to particle acceleration and MFA which affords a consistent description of strong shocks. A distinctive feature of the Monte Carlo technique is that it includes the full angular anisotropy of the particle distribution at all precursor positions. The model reveals that the super-diffusive transport of energetic particles (i.e., Levy-walk propagation) generates a strong quadruple anisotropy in the precursor particle distribution. The resultant pressure anisotropy of the high-energy particles produces a non-resonant mirror-type instability which amplifies compressible wave modes with wavelengths longer than the gyroradii of the highest energy protons produced by the shock.
We present a theory for the generation of mesoscale ($kr_{g}ll 1$, where $r_{g}$ is the cosmic ray gyroradius) magnetic fields during diffusive shock acceleration. The decay or modulational instability of resonantly excited Alfven waves scattering off ambient density perturbations in the shock environment naturally generates larger scale fields. For a broad spectrum of perturbations, the physical mechanism of energy transfer is random refraction, represented by diffusion of Alfven wave packet in $k-$space. The scattering field can be produced directly by the decay instability or by the Drury instability, a hydrodynamic instability driven by the cosmic ray pressure gradient. This process is of interest to acceleration since it generates waves of longer wavelength, and so enables the confinement and acceleration of higher energy particles. This process also limits the intensity of resonantly generated turbulent magnetic field on $r_{g}$ scales.
The present article investigates magnetic amplification in the upstream medium of SNR blast wave through both resonant and non-resonant regimes of the streaming instability. It aims at a better understanding of the diffusive shock acceleration (DSA) efficiency considering various relaxation processes of the magnetic fluctuations in the downstream medium. Multi-wavelength radiative signatures coming from the SNR shock wave are used in order to put to the test the different downstream turbulence relaxation models. We confirm the result of Parizot et al (2006) that the maximum CR energies should not go well beyond PeV energies in young SNRs where X-ray filaments are observed. In order to match observational data, we derive an upper limit on the magnetic field amplitude insuring that stochastic particle reacceleration remain inefficient. Considering then, various magnetic relaxation processes, we present two necessary conditions to achieve efficient acceleration and X-ray filaments in SNRs: 1/the turbulence must fulfil the inequality $2-beta-delta_{rm d} ge 0$ where $beta$ is the turbulence spectral index while $delta_d$ is the relaxation length energy power-law index; 2/the typical relaxation length has to be of the order the X-ray rim size. We identify that Alvenic/fast magnetosonic mode damping does fulfil all conditions while non-linear Kolmogorov damping does not. Confronting previous relaxation processes to observational data, we deduct that among our SNR sample, the older ones (SN1006 & G347.3-0.5) fail to verify all conditions which means that their X-ray filaments are likely controlled by radiative losses. The younger SNRs, Cas A, Tycho and Kepler, do pass all tests and we infer that the downstream magnetic field amplitude is lying in the range of 200-300 $mu$ Gauss.
We model the multi-wavelength emission in the southern hotspot of the radio quasar 4C74.26. The synchrotron radio emission is resolved near the shock with the MERLIN radio-interferometer, and the rapid decay of this emission behind the shock is interpreted as the decay of the amplified downstream magnetic field as expected for small scale turbulence. Electrons are accelerated to only 0.3 TeV, consistent with a diffusion coefficient many orders of magnitude greater than in the Bohm regime. If the same diffusion coefficient applies to the protons, their maximum energy is only ~100 TeV.
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