Chemistry Reference
In-Depth Information
In order to use the PIC simulation method for collisional plasma modeling and
self-sustained discharges, the interaction between charge carriers and neutral par-
ticles has to be added. The inclusion of electron and ion collisions with neutral
particles is carried out by use of the Monte Carlo method described earlier and the
resulting simulation technique is called PIC-MCC, where MCC stands for Monte
Carlo collisions. The accuracy of this kinetic simulation technique is mainly limited
by the number of particles that can be treated in a simulation and the influence of
velocity space diffusion leading to numerical thermalization, as discussed in [41].
PIC and PIC-MCC codes on bounded plasmas are available (freely), for example,
from [42].
9.1.5.4 Hybrid Methods
Hybrid methods represent a compromise between the computationally faster fluid
models and the more detailed, but computationally very extensive, kinetic treatment
allowing a description of the nonequilibrium behavior of plasma species. In principle,
two different approaches have been established where the main difference concerns
the kinetic part of the hybrid method.
The first technique couples a fluid description of the slow species of the plasma,
that is, neutrals and slow charge carriers, with MC simulations for the fast species,
normally the electrons, providing the source functions of electron impact ionization
(and excitation) processes that are employed in the continuity equations of the fluid
module [43-45]. Concerning the transport coefficients of the charge carriers, most
of these hybrid models use ion mobilities as a function of the reduced electric field
|
E
=
α
n
α
and a constant experimental value for the electron mobility
at a low value of
|
/
n
with
n
|
E
|
/
n
. To get the diffusion coefficients of the charge carriers, the
Einstein relation [7]
D
α
μ
α
=
k
B
T
α
e
0
(9.51)
is usually utilized, where for the electrons in particular, a characteristic energy
k
B
T
e
/
e
0
of 1 eV is normally used. This hybrid approach has so far been applied successfully
to studies of DC discharge plasmas in one and two space dimensions as well as to
RF and transient, spatially 1D glow discharges. It profits from its large flexibility
particularly of the MC simulations.
The second hybrid approach combines a system of fluid equations for the plasma
species with the solution of the Boltzmann equation of the electrons to take into
account the nonequilibrium behavior of the electrons. Although the solution of the
kinetic equation for the electrons can become mathematically complicated and com-
putationally very time consuming for complex geometries, this approach has the
advantage that it allows to accurately treat the nonlocal electron transport and to
directly derive the transport and rate coefficients of the electrons. For instance, the
rate coefficient
k
i
α
(
)
of an inelastic collision process of electrons with neutral
heavy particles of species α gets the representation
x
,
t
