Comparison of the telegraph and hyperdiffusion approximations in cosmic-ray transport

Litvinenko, Yuri E.; Noble, Patrick

doi:10.1063/1.4953564

Cited by 17 publications

(15 citation statements)

References 40 publications

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“…No signatures of a well-known solution to the telegraph equation with the same initial condition (e.g., [16]) are present in the exact solution. The signatures are expected in the form of two sharp peaks attached to the oppositely propagating fronts.…”

Section: Discussionmentioning

confidence: 99%

“…As in many other asymptotic expansions, when applied outside of their validity range, higher order terms often make the approximation less accurate which was recently demonstrated in Ref. [16], using the numerical integration of Eq.(1). By contrast to the hyperdiffusive Chapman-Enskog expansion, the telegraph equation, as mentioned above, was intended to cover also the crossover phase, t ∼ t c .…”

Section: Diffusive (Hyperdiffusive) Propagation Regimementioning

confidence: 95%

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Exact solution of the Fokker-Planck equation for isotropic scattering

Malkov

2017

Phys. Rev. D

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Section: Discussionmentioning

confidence: 99%

Section: Diffusive (Hyperdiffusive) Propagation Regimementioning

confidence: 95%

Exact solution of the Fokker-Planck equation for isotropic scattering

Malkov

2017

Phys. Rev. D

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“…This was recently demonstrated in Ref. [13], by a numerical integration of Eq.(1). The results of this work are illustrated for t = t c in Fig.1.…”

Section: A Restricting Propagation Models By Limiting Casesmentioning

confidence: 56%

Propagating Cosmic Rays with exact Solution of Fokker-Planck Equation

Malkov

2018

Nuclear and Particle Physics Proceedings

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Shortfalls in cosmic ray (CR) propagation models obscure the CR sources and acceleration mechanisms. This problem became particularly obvious after the Fermi, Pamela, and AMS-02 have discovered the electron/positron and p/He spectral anomalies. Most of the CR models use diffusive propagation that is inaccurate for weakly scattered energetic particles. So, some parts of the spectra affected by the heliospheric modulation, for example, cannot be interpreted. I discuss and adopt an exact solution of the Fokker-Planck equation [1], which gives a complete description of a ballistic, diffusive and transdiffusive (intermediate between the first two) propagation regimes. I derive a simplified version of an exact Fokker-Planck propagator that can easily be employed in place of the Gaussian propagator, currently used in major Solar modulation and other CR transport models.

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“…The telegraph equation is also a convenient way to avoid numerical problems close to singular magnetic X-points, and may also allow for larger time steps in an explicit numerical scheme than that with the Fickian approach (Snodin et al 2006). Litvinenko & Noble (2016) compare numerical solutions of fluid equations for cosmic ray propagation that result from various approximations to the Fokker-Planck equation, including the telegraph equation, and confirm the relevance of this approximation. Our goal is to compare test-particle simulations of cosmic ray propagation with the telegraph-equation approximation to derive optimal parameters of the latter that can inform sub-grid models of cosmic ray propagation in a comprehensive MHD simulation of the multi-phase interstellar medium.…”

Section: Introductionmentioning

confidence: 73%

Fickian and non-Fickian diffusion of cosmic rays

Rodrigues

Snodin

Sarson

et al. 2019

Monthly Notices of the Royal Astronomical Society

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Fluid approximations to cosmic ray (CR) transport are often preferred to kinetic descriptions in studies of the dynamics of the interstellar medium (ISM) of galaxies, because they allow simpler analytical and numerical treatments. Magnetohydrodynamic simulations of the ISM usually incorporate CR dynamics as an advection–diffusion equation for CR energy density, with anisotropic, magnetic-field-aligned diffusion with the diffusive flux assumed to obey Fick’s law. We compare test particle and fluid simulations of CRs in a random magnetic field. We demonstrate that a non-Fickian prescription of CR diffusion, which corresponds to the telegraph equation for the CR energy density, can be easily calibrated to match the test particle simulations with great accuracy. In particular, we consider a random magnetic field in the fluid simulation that has a lower spatial resolution than that used in the particle simulation to demonstrate that an appropriate choice of the diffusion tensor can account effectively for the unresolved (subgrid) scales of the magnetic field. We show that the characteristic time that appears in the telegraph equation can be physically interpreted as the time required for the particles to reach a diffusive regime and we stress that the Fickian description of the CR fluid is unable to describe complex boundary or initial conditions for the CR energy flux.

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Comparison of the telegraph and hyperdiffusion approximations in cosmic-ray transport

Cited by 17 publications

References 40 publications

Exact solution of the Fokker-Planck equation for isotropic scattering

Exact solution of the Fokker-Planck equation for isotropic scattering

Propagating Cosmic Rays with exact Solution of Fokker-Planck Equation

Fickian and non-Fickian diffusion of cosmic rays

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