2020/08/31 by Martin Lemoine, Mikhail Malkov, Mikhail A. Malkov
Environmental Science · Physics and Astronomy · #Acceleration #Classical mechanics #Climate variability and models #Conservation law #Cosmology and Gravitation Theories #Mechanics #Momentum (technical analysis) #Monte Carlo method #Particle acceleration #Phase space #Phenomenology (philosophy) #Physics #Position and momentum space #Power law #Quantum mechanics #Solar and Space Plasma Dynamics #Statistical physics #Statistics #Stochastic process #Turbulence #astro-ph.HE #physics.plasm-ph
paper · pdf · doi:10.1093/mnras/staa3131
12 pages, 13 figures; version to appear in MNRAS (minor edits)
openalex publication_date 2020/10/10 · arxiv created 2020/11/18 · arxiv updated 2020/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
ABSTRACT Numerical simulations of particle acceleration in magnetized turbulence have recently observed power-law spectra where pile-up distributions are rather expected. We interpret this as evidence for particle segregation based on acceleration rate, which is likely related to a non-trivial dependence of the efficacy of acceleration on phase space variables other than the momentum. We describe the corresponding transport in momentum space using continuous-time random walks, in which the time between two consecutive momentum jumps becomes a random variable. We show that power laws indeed emerge when the experimental (simulation) time-scale does not encompass the full extent of the distribution of waiting times. We provide analytical solutions, which reproduce dedicated numerical Monte Carlo realizations of the stochastic process, as well as analytical approximations. Our results can be readily extrapolated for applications to astrophysical phenomenology.