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From Scatter-Free to Diffusive Propagation of Energetic Particles with Exact Solution of Fokker-Planck Equation

M. Malkov

in 35th International Cosmic Ray Conference

Contribution: pdf


Propagation of energetic particles through magnetized turbulent media
is reconsidered using the exact solution of Fokker-Planck equation.
This solution reveals that our understanding of cosmic ray (CR) transport
is inaccurate when it relies on a diffusive approximation for weakly scattered energetic
particles. The poor understanding of CR transport obscures their sources
and acceleration mechanisms. After the Fermi, PAMELA, and AMS-02 have
discovered the electron/positron and p/He spectral anomalies, it becomes
crucial to improve transport models for improving our understanding
of the anomalies. We discuss and simplify the exact solution of Fokker-Planck
equation [1] which accurately describes a ballistic,
diffusive and transdiffusive (intermediate between the first two)
propagation regimes. It is found that the transdiffusive phase lasts
for a (surprisingly) long time, about five scattering times ($5t_{c}$)
while starting as early as at $0.5t_{c}$. Since the scattering
time of CRs is energy dependent, $t_{c}=t_{c}\left(E\right)$, a significant part
of their spectrum propagates transdiffusively, thus requiring the exact solution
of Fokker-Planck equation.This limitation is particularly relevant to the heliospheric
modulation of galactic CRs.
We present a new,
simplified version of an exact Fokker-Planck propagator. It can easily
be employed in place of the Gaussian propagator, currently used in
major solar modulation and other CR transport models. Flaws in using
the telegraph equation to model the CR propagation before the onset of diffusive
regime are also briefly discussed.