Environmental Engineering Reference
In-Depth Information
and defining in this manner the coefficient
D
a
of ambipolar diffusion and account-
ing for the plasma quasineutrality, one finds for the coefficient of ambipolar diffu-
sion
N
e
D
N
i
D
N
D
e
K
e
K
i
.
D
a
D
D
i
C
(4.120)
In the case of a Maxwell distribution function for electrons and ions that corre-
sponds to the regime of a high number density of electrons, this formula has the
form
D
i
1
,
T
a
T
i
D
a
D
C
(4.121)
where
T
a
and
T
i
are the temperatures of electrons and ions, and the effective elec-
tron temperature due to ambipolar diffusion is
eD
e
dw
e
/
dE
a
T
a
D
,
(4.122)
where
w
e
is the electron drift velocity under the action of the ambipolar electric
field strength that occurs due to charge separation because of ambipolar diffusion.
If external fields are absent and electrons are characterized by the Maxwell dis-
tribution function with a gas temperature, we have
T
a
D
T
,
D
a
D
2
D
i
.
In the case of the Maxwell distribution function for electrons with electron temper-
ature
T
e
, the coefficient of ambipolar diffusion is given by
D
i
1
.
T
e
T
i
D
a
D
C
(4.123)
If a plasma in located in an electric field and ambipolar diffusion proceeds in the
field direction
z
,wehaveforthetotalelectricfieldinaplasma
E
E
a
,where
E
z
is an external electric field, and the effective temperature of ambipolar diffusion
is
D
E
z
C
eD
e
dw
e
/
dE
,
T
a
D
(4.124)
where
T
a
accounts for the direction of an ambipolar field along an external field,
and
D
e
is the coefficient of longitudinal diffusion of electrons in an external elec-
tric field. This type of ambipolar diffusion is realized in gas discharge near the
anode. Note that in a general case this ambipolar temperature
T
a
differs from the
Townsend characteristic electron temperature
T
ef
defined according to (4.82):
eD
e
K
e
D
eD
e
E
w
e
T
ef
D
.
