Environmental Engineering Reference
In-Depth Information
5.5.7
Electric Domain
One of a variety of steady-state structures that can be formed by nonlinear pro-
cesses in a plasma is the electric domain - a perturbation of the electron number
density and the electric field in a gas discharge plasma that propagates with the
electron current. The physical picture of this phenomenon is as follows. The exter-
nal segment of an electric circuit that passes through a gas discharge has a large
resistance that maintains a constant electric current density in the discharge. This
constant current is
i
e
D
ewN
e
D
const ,
(5.155)
where
w
is the electron drift velocity and
N
e
is the electron number density. The de-
pendence of the electron drift velocity on the electric field strength has the behavior
shown in Figure 5.14, where two different electric current regimes are possible at
some values of the electric field strength. This behavior can preserve a perturbation
that propagates together with the current, meaning that it is a drift wave. Such a
perturbation is identified as the electric domain. Although this plasma structure
was discovered in a semiconductor plasma [80-83], it is of importance for a gas
discharge plasma [35].
To describe the electric domain, we use the continuity equation (4.1) and the
Poisson equation (1.4), which here take the forms
@
N
e
@
@
j
e
@
E
@
C
D
0,
D
4
π
e
(
N
0
N
e
) ,
(5.156)
t
@
x
x
where
j
e
is the electron flux,
E
is the electric field strength, and
N
0
is the equilibri-
um number density of electrons. We first treat these equations in a linear approxi-
mation so as to analyze the electric domain at low intensity. The electron flux can
be written
D
@
N
e
@
j
e
D
N
e
w
,
(5.157)
x
Figure 5.14
A nonmonotonic dependence of the electron drift velocity on the electric field
strength that can lead to the formation of a domain.
