  In plasmas, distribution functions often demonstrate long anisotropic tails
or otherwise significant deviations from local Maxwellians. The tails,
especially if they are pulled out from the bulk, pose a serious challenge for
numerical simulations as resolving both the bulk and the tail on the same mesh
is often challenging. A multi-scale approach, providing evolution equations for
the bulk and the tail individually, could offer a resolution in the sense that
both populations could be treated on separate meshes, or different reduction
techniques applied to the bulk and the tail population. In this letter, we
propose a multi-scale method which allows us to split a distribution function
into a bulk and a tail so that both populations remain genuine, non-negative
distribution functions and may carry density, momentum, and energy. The
proposed method is based on the observation that the motion of an individual
test particle in a plasma obeys a stochastic differential equation, also
referred to as a Langevin equation. This allows us to define transition
probabilities between the bulk and the tail and to provide evolution equations
for both populations separately.
