Analytical description of nonlinear cosmic ray scattering: isotropic and quasilinear regimes of pitch-angle diffusion

Shalchi, A.; Skoda, T.; Tautz, R. C.; Schlickeiser, R.

doi:10.1051/0004-6361/200912755

Cited by 63 publications

(37 citation statements)

References 39 publications

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“…Behind the shock little, if any, driving will transpire, and the spectrum is determined by cascading and damping until the energy reservoir at L max is drained. Shalchi et al (2009) have developed a second-order nonlinear theory of wave-particle interaction that for an assumed spectrum…”

Section: Small-scale Non-resonant Modesmentioning

confidence: 99%

Reacceleration of electrons in supernova remnants

Pohl

Wilhelm

Telezhinsky

2015

A&A

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Context. The radio spectra of many shell-type supernova remnants show deviations from those expected on theoretical grounds. Aims. In this paper we determine the effect of stochastic reacceleration on the spectra of electrons in the GeV band and at lower energies, and we investigate whether reacceleration can explain the observed variation in radio spectral indices. Methods. We explicitely calculated the momentum diffusion coefficient for 3 types of turbulence expected downstream of the forward shock: fast-mode waves, small-scale non-resonant modes, and large-scale modes arising from turbulent dynamo activity. After noting that low-energy particles are efficiently coupled to the quasi-thermal plasma, a simplified cosmic-ray transport equation can be formulated and is numerically solved. Results. Only fast-mode waves can provide momentum diffusion fast enough to significantly modify the spectra of particles. Using a synchrotron emissivity that accurately reflects a highly turbulent magnetic field, we calculated the radio spectral index and find that soft spectra with index α −0.6 can be maintained over more than 2 decades in radio frequency, even if the electrons experience reacceleration for only one acceleration time. A spectral hardening is possible but considerably more frequency-dependent. The spectral modification imposed by stochastic reacceleration downstream of the forward shock depends only weakly on the initial spectrum provided by, e.g., diffusive shock acceleration at the shock itself.

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Section: Small-scale Non-resonant Modesmentioning

confidence: 99%

Reacceleration of electrons in supernova remnants

Pohl

Wilhelm

Telezhinsky

2015

A&A

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“…(10) only requires that particle energies be "not too high" (Shalchi 2011), which has been specified by Shalchi et al (2009) through R = RL/l0 B 0 /δB, which assumption can be seen as fulfilled except perhaps for the highest energy value.…”

Section: Analytical Parallel Mean Free Pathmentioning

confidence: 99%

Simulating cosmic-ray transport with adiabatic focusing

Tautz

Dosch

Lerche

2012

A&A

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Context. Magnetized space plasmas such as the heliosphere contain a spatially variable guide magnetic field that is superposed by turbulence. Understanding the transport of energetic particles in such an environment is important for many applications. Aims. The modifications of the scattering mean free path caused by the effect of adiabatic focusing have so far been studied only analytically. Here, the exact analytical conditions are reproduced in a numerical simulation to allow for a detailed comparison. Methods. A Monte-Carlo simulation code was modified to include a guide magnetic field with a constant focusing length. The turbulence strength was kept constant either throughout the simulation space or relative to the variable background field strength. Results. In contrast to both quasi-linear and nonlinear analytical predictions, an increased parallel mean free path is found for almost all cases. Particle diffusion is found to be asymmetric depending on the initial particle velocity relative to the guide field. Conclusions. The increased parallel mean free path can be explained by a coherent particle motion toward lower magnetic field strengths. The possible reduction of the diffusion parameter is consequently obscured.

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“…In the following, we complement the work of Shalchi et al, 26 which is based on the SOQLT originally developed by Shalchi. 14 A. Specification of the turbulence model A further assumption, which is often used, is that the stochastic magnetic fields are replaced by the so-called magnetostatic slab model for which we assume dB i ðxÞ ¼ d B i ðzÞ.…”

Section: Second-order Quasilinear Theorymentioning

confidence: 99%

“…Shalchi et al 26 derived for the model spectrum (3) the following forms of the pitch-angle Fokker-Planck coefficient…”

Section: B Analytical Form Of D Llmentioning

confidence: 99%

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Analytical description of nonlinear particle transport in slab turbulence: High particle energies and stochastic acceleration

Shalchi

2012

Physics of Plasmas

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Pitch-angle scattering, parallel spatial diffusion, and stochastic acceleration of cosmic rays are investigated analytically. Based on a second-order quasilinear theory, we derive analytical expressions for the aforementioned transport parameters for all possible magnetic field strengths and particle energies. This work complements previous work where only parallel diffusion for low energetic particles was considered. Furthermore, we compute the first time the momentum diffusion coefficient. It is also shown that the relation between the momentum diffusion coefficient and the parallel spatial diffusion coefficient is more complicated than assumed in previous work.

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Analytical description of nonlinear cosmic ray scattering: isotropic and quasilinear regimes of pitch-angle diffusion

Cited by 63 publications

References 39 publications

Reacceleration of electrons in supernova remnants

Reacceleration of electrons in supernova remnants

Simulating cosmic-ray transport with adiabatic focusing

Analytical description of nonlinear particle transport in slab turbulence: High particle energies and stochastic acceleration

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