Environmental Engineering Reference
In-Depth Information
Ta b l e 4 . 17
The boundary reduced cluster radius for transition between the kinetic and diffusion
regimes of cluster drift for gases at room temperature.
Gas
He
Ne
Ar
Kr
Xe
H
2
N
2
O
2
r
0
,10
14
cm
2
N
8.0
5.8
2.8
2.2
1.5
5.1
2.7
2.7
Table 4.17 gives the values of the boundary number density of atoms on the basis
of this formula, and the values of the gas-kinetic cross sections
g
are taken from
Table 4.5. Note that the boundary cluster radius does not depend on the cluster
material.
σ
4.4.6
Ambipolar Diffusion
Violation of plasma quasineutrality creates strong electric fields within the plasma.
The fields between electrons and ions are associated with attractive forces, tending
to move them together. The specific regime of plasma expansion in a gas results
from a higher mobility of electrons than ions. But separation of electrons and ions
in a gas creates an electric field that slows the electrons and accelerates the ions.
This establishes a self-consistent regime of plasma motion called ambipolar dif-
fusion and is typical for gas discharge [95, 96]. We shall examine this regime and
establish the conditions necessary to achieve it.
We consider transport of electrons and ions in a weakly ionized gas in which the
number densities of electrons and ions are similar and are small compared with
the number density of atoms. In this case fluxes of electrons
j
e
and ions
j
i
are given
by
j
e
D
K
e
N
e
E
a
D
e
r
N
e
,
j
i
D
K
i
N
i
E
a
D
i
r
N
i
.
(4.117)
Here
N
e
and
N
i
are the number densities of electrons and ions,
K
e
and
D
e
are the
mobility and the diffusion coefficient of electrons,
K
i
and
D
i
are the mobility and
diffusion coefficients of ions,
E
a
is the electric field strength due to separation of
electron and ion charges, and we take into account that the force from this electric
field acts on electrons and ions in different directions. Since the quasineutrality of
this plasma is conserved in the course of its evolution, the electron and ion fluxes
are equal:
j
e
D
j
i
. From this it follows that because
K
e
K
i
and
D
e
D
i
,in
scales of electron values we have
j
e
D
0. From this we find the electric field strength
created by a charge separation:
D
e
N
e
N
e
K
e
r
E
a
D
.
(4.118)
Ta k i n g t h e p l a s m a fl u x a s
j
D
j
i
D
D
a
r
N
(4.119)
