  We have developed an analytic model to describe coupling of plasma and
neutral fluids in the partially ionized heliosphere plasma medium. The sources
employed in our analytic model are based on a $\kappa$-distribution as opposed
to the Maxwellian distribution function. Our model uses the
$\kappa$-distribution to analytically model the energetic neutral atoms that
result in the heliosphere partially ionized plasma from charge exchange with
the protons and subsequently produce a long tail which is otherwise not
describable by the Maxwellian distribution. We present our analytic formulation
and describe major differences in the sources emerging from these two distinct
distributions.
