  Under low-collisionality conditions the isotropic part of the electron
velocity distribution function in a plasma becomes non-local and the electrons
can be described by a single global distribution function . This is also the
regime required for non-local collisonless (stochastic) heating in oscillating
and spatially inhomogeneous electric fields. Solution of the Boltzmann equation
under these conditions requires usually computationally involving
multi-dimensional PIC/MC simulations. The necessity of multi-dimensional
simulation arises mainly from the complicated time and space dependence of the
collisionless electron heating process. Here it is shown that a time, volume,
und solid angle averaged Fokker-Planck operator for the interaction of
electrons with an external field can replace the local Ohmic heating operator
resulting from a two-term approximation of the Boltzmann equation. This allows
consistent treatment of collisional as well as collisonless heating. This
operator combined with the dissipative operators for interaction with neutrals,
as resulting from the two-term approximation, plus an additional operator for
surface losses provide altogether a kinetic description for the determination
of the global static and isotropic distribution function of the system. The new
operators are relatively easy to integrate in classical local Boltzmann solvers
and allow for a fast calculation of the distribution function. As an example,
an operator describing non-local collisionless as well as collisional heating
in inductively coupled plasmas (ICPs) is derived. The resulting distribution
function can then be used to calculate rates and moments in a fluid model of
the plasma, similarly to the common practice in the local and highly
collisional case. A certain limitation of the above concept is the necessity of
using pre-defined field structures.
