A Simple Model of Nonlinear Diffusive Shock Acceleration

Berezhko, E. G.; Ellison, Donald C.

doi:10.1086/307993

Cited by 315 publications

(482 citation statements)

References 37 publications

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“…The downstream region changes after the fluid speed becomes v box = 0 by microphysical dissipation processes. The gas subshock is just an ordinary discontinuous classical shock embedded in the comparably larger scale energetic particle shock (Berezhko & Ellison 1999). The value of v sub is determined by a sharp deflection of smooth curves in velocity profiles near the shock front, and the value of the subshock velocity increases from cases A, B, and C to Case D (i.e.…”

Section: Compression Ratiosmentioning

confidence: 99%

Monte Carlo simulations of a diffusive shock with multiple scattering angular distributions

Wang

Yan

2011

A&A

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Aims. We independently develop a simulation code following the previous dynamical Monte Carlo simulation of the diffusive shock acceleration under the isotropic scattering law during the scattering process, and the same results are obtained. Methods. Since the same results test the validity of the dynamical Monte Carlo method for simulating a collisionless shock, we extend the simulation toward including an anisotropic scattering law for further developing this dynamical Monte Carlo simulation. Under this extended anisotropic scattering law, a Gaussian distribution function is used to describe the variation of scattering angles in the particle's local frame. Results. As a result, we obtain a series of different shock structures and evolutions in terms of the standard deviation values of the given Gaussian scattering angular distributions. Conclusions. We find that the total energy spectral index increases as the standard deviation value of the scattering angular distribution increases, but the subshock's energy spectral index decreases as the standard deviation value of the scattering angular distribution increases.

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Section: Compression Ratiosmentioning

confidence: 99%

Monte Carlo simulations of a diffusive shock with multiple scattering angular distributions

Wang

Yan

2011

A&A

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“…14. As is well known for non-relativistic shocks undergoing efficient shock acceleration, the overall shock compression ratio must increase above the Rankine-Hugoniot value (e.g., Jones & Ellison 1991;Berezhko & Ellison 1999). For these examples, Rtot ≃ 12.…”

Section: Pion-decay Emissionmentioning

confidence: 93%

“…For more details on NL Fermi acceleration in non-relativistic shocks, the reader is directed to Berezhko & Ellison (1999); Malkov & Drury (2001);Caprioli et al (2010);Bykov et al (2014) and references therein.…”

Section: Pion-decay Emissionmentioning

confidence: 99%

Particle spectra and efficiency in nonlinear relativistic shock acceleration – survey of scattering models

Ellison

Warren

Bykov

2015

Mon. Not. R. Astron. Soc.

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We include a general form for the scattering mean free path, λ mfp (p), in a nonlinear Monte Carlo model of relativistic shock formation and Fermi acceleration. Particle-in-cell (PIC) simulations, as well as analytic work, suggest that relativistic shocks tend to produce short-scale, self-generated magnetic turbulence that leads to a scattering mean free path with a stronger momentum dependence than the λ mfp ∝ p dependence for Bohm diffusion. In unmagnetized shocks, this turbulence is strong enough to dominate the background magnetic field so the shock can be treated as parallel regardless of the initial magnetic field orientation, making application to γ-ray bursts (GRBs), pulsar winds, Type Ibc supernovae, and extra-galactic radio sources more straightforward and realistic. In addition to changing the scale of the shock precursor, we show that, when nonlinear effects from efficient Fermi acceleration are taken into account, the momentum dependence of λ mfp (p) has an important influence on the efficiency of cosmic-ray production as well as the accelerated particle spectral shape. These effects are absent in non-relativistic shocks and do not appear in relativistic shock models unless nonlinear effects are self-consistently described. We show, for limited examples, how the changes in Fermi acceleration translate to changes in the intensity and spectral shape of γ-ray emission from proton-proton interactions and pion-decay radiation.

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“…Note that incorporation of non-linear effects (e.g., strong shock modification) usually suggests values s < 2 at high energies (Berezhko and Ellison, 1999 …”

Section: Shock or First-order Fermi Accelerationmentioning

confidence: 99%

Fermi acceleration in astrophysical jets

Rieger

Bosch‐Ramon

Duffy

2007

The Multi-Messenger Approach to High-Energy Gamma-Ray Sources

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We consider the acceleration of energetic particles by Fermi processes (i.e., diffusive shock acceleration, second order Fermi acceleration, and gradual shear acceleration) in relativistic astrophysical jets, with particular attention given to recent progress in the field of viscous shear acceleration. We analyze the associated acceleration timescales and the resulting particle distributions, and discuss the relevance of these processes for the acceleration of charged particles in the jets of AGN, GRBs and microquasars, showing that multi-component powerlaw-type particle distributions are likely to occur.

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A Simple Model of Nonlinear Diffusive Shock Acceleration

Cited by 315 publications

References 37 publications

Monte Carlo simulations of a diffusive shock with multiple scattering angular distributions

Monte Carlo simulations of a diffusive shock with multiple scattering angular distributions

Particle spectra and efficiency in nonlinear relativistic shock acceleration – survey of scattering models

Fermi acceleration in astrophysical jets

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