@ARTICLE{2018ApJ...868L..28E,
       author = {Effenberger, Frederic and Petrosian, Vah'e},
        title = "{The Relation between Escape and Scattering Times of Energetic Particles in a Turbulent Magnetized Plasma: Application to Solar Flares}",
      journal = {The Astrophysical Journal Letters},
     keywords = {cosmic rays, diffusion, magnetic fields, scattering, Sun: heliosphere, Sun: particle emission, Astrophysics - High Energy Astrophysical Phenomena, Physics - Space Physics},
         year = "2018",
        month = "Dec",
       volume = {868},
       number = {2},
          eid = {L28},
        pages = {L28},
     abstract = "{A knowledge of the particle escape time from the acceleration regions of
        many space and astrophysical sources is of critical importance
        in the analysis of emission signatures produced by these
        particles and in the determination of the acceleration and
        transport mechanisms at work. This Letter addresses this general
        problem, in particular in solar flares, where in addition to
        scattering by turbulence, the magnetic field convergence from
        the acceleration region toward its boundaries also influences
        the particle escape. We test an (approximate) analytic relation
        between escape and scattering times, and the field convergence
        rate, based on the work of Malyshkin & Kulsrud, valid for
        both strong and weak diffusion limits and isotropic pitch-angle
        distributions of the injected particles, with a numerical model
        of particle transport. To this end, a kinetic Fokker-Planck
        transport model of particles is solved with a stochastic
        differential equation scheme, assuming different initial pitch-
        angle distributions. This approach enables further insights into
        the phase-space dynamics of the transport process, which would
        otherwise not be accessible. We find that in general the
        numerical results agree well with the analytic equation for the
        isotropic case; however, there are significant differences in
        the weak diffusion regime for non-isotopic cases, especially for
        distributions beamed along the magnetic field lines. The results
        are important in the interpretation of observations of energetic
        particles in solar flares and other similar space and
        astrophysical acceleration sites, and for the determination of
        acceleration-transport coefficients, commonly used in Fokker-
        Planck-type kinetic equations.}",
          doi = {10.3847/2041-8213/aaedb3},
archivePrefix = {arXiv},
       eprint = {1808.07308},
 primaryClass = {astro-ph.HE},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2018ApJ...868L..28E},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}