Acceleration of cosmic rays in presence of magnetohydrodynamic fluctuations at small scales

Abstract

This work investigates the evolution of the distribution of charged particles due to the mechanism of stochastic turbulent acceleration (STA) in presence of small-scale turbulence with a mean magnetic field. STA is usually modelled as a biased random walk process in the momentum space of the non-thermal particles. This results in an advection-diffusion type transport equation for the non-thermal particle distribution function. Under quasilinear approximation, and by assuming turbulent spectra with power being available only in the sub-gyroscale range, we find that the Fokker-Planck diffusion coefficients $D_{\gamma \gamma }$ and $D_{\mu \mu }$ scale with the Lorentz factor $\gamma$ as: $D_{\gamma \gamma }\propto {\gamma }^{-2/3}$ and $D_{\mu \mu }\propto {\gamma }^{-8/3}$. We consider Alfvèn and fast waves in our calculations, and find a universal trend for the momentum diffusion coefficient irrespective of the properties of the small-scale turbulence. Such universality has already been reported regarding the spatial diffusion of the cosmic rays, and, here too, we observe a universality in the momentum diffusion coefficient. Furthermore, with the calculated transport coefficients, we numerically solve the advection-diffusion type transport equation for the non-thermal particles. We demonstrate the interplay of various mircophysical processes such as STA, synchrotron loss and particle escape on the particle distribution by systematically varying the parameters of the problem. We observe that the effect of the small-scale turbulence is more impactful for the high energy protons as compared to the electrons and such turbulence is capable of sustaining the energy of the protons from catastrophic radiative loss processes. Such a finding is novel and helps us to enhance our understanding about the hadronic emission processes that are typically considered as a competitor for the leptonic emission.

arXiv comment23 pages (including Appendix), 11 figures, Accepted to be published in MNRAS main journal

References in corpus (41)

• On The Non Thermal Emission and Acceleration of Electrons in Coma and Other Clusters of Galaxies
• Compressible Sub-Alfvenic MHD turbulence in Low-beta Plasmas
• Scattering of Cosmic Rays by Magnetohydrodynamic Interstellar Turbulence
• Transport of Cosmic Rays in Chaotic Magnetic Fields
• Stochastic Acceleration and the Evolution of Spectral Distributions in SSC Sources: A Self Consistent Modeling of Blazars' Flares
• Cosmic Ray Propagation: Nonlinear Diffusion Parallel and Perpendicular to Mean Magnetic Field
• Stochastic Acceleration of Electrons and Protons. I. Acceleration by Parallel Propagating Waves
• Relativistic Shocks: Particle Acceleration and Magnetization
• Scattering of energetic particles by anisotropic magnetohydrodynamic turbulence with a Goldreich-Sridhar power spectrum
• Long Term Evolution of Magnetic Turbulence in Relativistic Collisionless Shocks: Electron-Positron Plasmas
• Long-time evolution of magnetic fields in relativistic GRB shocks
• Wave damping by MHD turbulence and its effect upon cosmic ray propagation in the ISM
• Enhanced Magnetic Compressibility and Isotropic Scale-Invariance at Sub-Ion Larmor Scales in Solar Wind Turbulence
• Magnetic field evolution in relativistic unmagnetized collisionless shocks
• On the efficiency of Fermi acceleration at relativistic shocks
• Diffusion and drift of cosmic rays in highly turbulent magnetic fields
• Stochastic Acceleration in Relativistic Parallel Shocks
• Electron Acceleration and Efficiency in Nonthermal Gamma-Ray Sources
• Particle Acceleration by MHD Turbulence
• Numerical study of Cosmic Ray Diffusion in MHD turbulence
• Novel aspects of cosmic ray diffusion in synthetic magnetic turbulence
• Charged particle diffusion in isotropic random magnetic fields
• Generalized Fermi acceleration
• Regimes of cosmic-ray diffusion in Galactic turbulence
• Particle transport and heating in the microturbulent precursor of relativistic shocks
• Particle Transport in intense small scale magnetic turbulence with a mean field
• Power requirements for cosmic ray propagation models involving re-acceleration and a comment on second order Fermi acceleration theory
• Particle Acceleration in Shearing Flows: Efficiencies and Limits
• Adiabatic non-resonant acceleration in magnetic turbulence and hard spectra of gamma-ray bursts
• Relativistic Particle Transport and Acceleration in Structured Plasma Turbulence
• Self-Similar Collisionless Shocks
• A Classification Scheme For Turbulent Acceleration Processes In Solar Flares
• Transport of magnetic turbulence in Supernova remnants
• Ultrahigh-Energy Cosmic Ray Production by Turbulence in Gamma-Ray Burst Jets and Cosmogenic Neutrinos
• Blazar Spectra with Hard-sphere-like Acceleration of Electrons
• Perpendicular Diffusion of Energetic Particles: A Complete Analytical Theory
• Particle acceleration by slow modes in strong compressible MHD turbulence, with application to solar flares
• High Energy Cosmic-ray Diffusion in Molecular Clouds: A Numerical Approach
• On the broad-band synchrotron spectra of pulsar wind nebulae
• Stochastic Fermi Acceleration of sub-Relativistic Electrons and Its Role in Impulsive Solar Flares
• A corrugated termination shock in pulsar wind nebulae?

Cited by in corpus (2)

• Ultra-High-Energy Cosmic Rays Accelerated by Magnetically Dominated Turbulence
• Anisotropy and energy distribution of leptons and photons in radiative relativistic Alfvénic turbulence