Environmental Engineering Reference
In-Depth Information
for electron velocities, which is characterized by the electron temperature
T
e
,the
Townsend energy coefficient of electrons is
T
e
T
η
D
.
Experimentally, the Townsend energy coefficient may be determined [38, 39] by a
simultaneous measurement of the transverse diffusion coefficient of electrons and
their mobility in an electric field when a pulsed electron beam of a certain width is
injected in a drift chamber with a certain electric field strength. Then the electron
drift velocity follows from measurement of time the beam takes to pass through a
drift chamber, and the coefficient of transverse diffusion results from broadening
of this beam during the drift time.
Under these conditions, the effective electron temperature
T
ef
,whichisnamed
the characteristic energy [37, 38], in the regime of a low electron number density
on the basis of the Townsend energy coefficient is
eD
?
K
e
T
ef
D
η
T
D
.
(4.82)
Using (3.26) for the electron drift velocity and (4.64) for the diffusion coefficient,
we obtain for the Townsend energy coefficient
m
e
v
T
1
v
1
2
d
d
3
ν
v
η
D
.
(4.83)
ν
2
v
If the rate of elastic electron-atom collisions
ν
is independent of the electron ve-
locity, this equation gives
m
e
v
.
2
η
D
(4.84)
3
T
In this case the Townsend energy coefficient is the ratio of the mean electron energy
to the mean energy of the atom. Such a relation holds both for the case
ν
D
const
and for a Maxwell distribution function for electrons.
In the regime of a low number density of electrons, when the electron velocity
distribution function is given by (3.27), the expression (4.83) for the Townsend
energy coefficient takes the following form in the limit of low electron number
density
˝
v
ν
˛
2
/
η
D
,
(4.85)
h
v
2
/
ν
(1
C
Mu
2
/3
T
)
i
where
u
). In particular, if the electric field is strong and the electron-
atom cross section does not depend on the electron velocity
D
eE
/(
m
e
ν
ν
D
v
/
λ
,wherethe
mean free path of electrons
λ
is independent of the collision velocity, we have
1.14
m
e
v
.
2
η
D
3
T
