**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

**Abstract**

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.