On the Radial Evolution of κ-Distributions of Pick-up Protons in the Supersonic Solar Wind

Abstract:

It is well known that (pick-up) ions in the inner heliosphere do not
maintain Maxwellian distributions but tend to non-equilibrium distributions
with extended suprathermal tails. Such states have been classified as
quasi-equilibria which in many cases can well be described by so-called
κ-distributions. With the present study we start out from a phase space
transport equation for pick-up ions in the inner heliosphere that adequately
describes the most important processes such as injection, convection, cooling,
and diffusion in velocity space. Assuming that the underlying distribution
functions are κ-distributions, we proceed from this transport equation
to a second-order moment, i.e. pressure equation which represents an ordinary
differential equation for the adequate κ-parameter as function of the
heliocentric distance. This strategy allows one to describe the transition
from an initial Vasyliunas-Siscoe distribution to κ-distributions with
gradually more pronounced suprathermal tails. While the velocity-dependence of
the velocity diffusion coefficient determines the systematic reduction of the
parameter κ, the latter always has the (formal) asymptotic value
of 3/2. This translates into values of 1.5 < κ < 2.2
in the upstream region of the (upwind) solar wind termination shock that defines
the outer validity range of the model.