Cosmic rays are fast charged particles which are accelerated to very
high energies and move vast distance in the collisionless, turbulent
plasmas of space. They are studied both for their intrinsic interest
and as probes of distant plasmas. A robust and successful paradigm for
their acceleration and transport has been developed, involving a
statistical description of the particle motions in terms of the
statistical properties of the ambient turbulent electromagnetic field.
For the most part, we are interested in particles moving at nearly the
speed of light, for which the relevant turbulent fluctuations are
hydromagnetic. In this limit, the magnetic field has the most important
effect, and it changes slowly, so a quasistatic approximation may be
used. Often, a description in terms of a Fokker-Planck, or diffusion
approximation is adequate to provide considerable quantitative insight
into a variety of astrophysical and space physics phenomena.
More-recent steps beyond this basic picture to include the reaction of
the cosmic rays back on the ambient plasma and non-diffusive effects
will be discussed. The ideas will be illustrated by discussion of
applications to specific observed phenomena.
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