Non‐linear particle acceleration at non‐relativistic shock waves in the presence of self‐generated turbulence

INAF – Osservatorio Astrofisico di Arcetri, Largo E. Fermi, 5, 50125, Firenze, Italy
Monthly Notices of the Royal Astronomical Society (Impact Factor: 5.11). 09/2006; 371(3):1251 - 1258. DOI: 10.1111/j.1365-2966.2006.10739.x


Particle acceleration at astrophysical shocks may be very efficient if magnetic scattering is self-generated by the same particles. This non-linear process adds to the non-linear modification of the shock due to the dynamical reaction of the accelerated particles on the shock. Building on a previous general solution of the problem of particle acceleration with arbitrary diffusion coefficients, we present here the first semi-analytical calculation of particle acceleration with both effects taken into account at the same time; charged particles are accelerated in the background of Alfvén waves that they generate due to the streaming instability, and modify the dynamics of the plasma in the shock vicinity.

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    • "This idea is motivated by cosmicray source candidates like pulsars and supernova remnants being rather young (see, e.g. [39] [17] [25] [14]) and therefore mostly confined to the vicinity of the star-formation regions and thus to the vicinity of the spiral arms. Just recently, supernova remnants (SNRs) have received observational support as sources of cosmic rays (see [2]), supporting the link between cosmic-ray sources candidates and star-forming regions. "
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    • "Direct numerical simulations of the CR-modified shock by particlein-cell technique are nonfeasible by now because of the wide dynamical range of the simulation that requires extreme computing resources. Nevertheless, an approximate iterative approach (e.g., within the Monte Carlo model discussed in Vladimirov et al. (2008) or semi-analytical kinetic models developed by Malkov (1997); Amato and Blasi (2006)) can be used to derive the steady-state distribution function consistent with the shock compression. These approximate models assume some diffusion model and parameterize the microphysical processes of magnetic field amplification and plasma heating. "
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    • "The case of Tycho is instructive as an illustration of the level of credibility of calculations based on the theory of NLDSA: the different techniques agree fairly well (see (Caprioli et al, 2010) for a discussion of this point) as long as only the dynamical reaction of accelerated particles on the shock is included. When magnetic effects are taken into account, the situation becomes more complex: in the calculations based on the semi-analytical description of Amato and Blasi (2006) the field is estimated from the growth rate and the dynamical reaction of the magnetic field on the shock is taken into account (Caprioli et al, 2008, 2009b). Similar assumptions are adopted by Vladimirov et al (2008), although the technique is profoundly different. "
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