Environmental Engineering Reference
In-Depth Information
where the specific functions chi(
x
)andshi(
x
)aregivenby[36]
Z
x
Z
x
cosh
t
1
sinh
t
t
chi(
x
)
D
C
C
ln
x
C
dt
, i
x
)
D
dt
,
t
0
0
and
C
D
0.577 is the Euler constant. The limiting expressions for this function are
given by
1
2
ln
1
e
2
C
6
20
D
I
Φ
D
Φ
(
)
1
,
1
(
)
,
1.
Figure 3.6 represents the dependence
Φ
(
), and also its simple approximation
/6)
1
.
Let us consider the limiting cases for the electron drift velocity. At low values of
(1
C
(alowdegreeofgasionization)wehave
ea
1
2
ln
1
e
2
C
Σ
D
Σ
.
e
At high values of
(a high degree of gas ionization), when scattering by ions dom-
inates, the electron drift velocity is given by
ea
1
ei
1
6
Σ
20
20
Σ
D
D
Σ
,
e
where
w
ei
is determined by (3.29).
Let us apply the above results for electron drift in helium. Being guided by the
electron temperature
T
e
1 eV, we take the diffusion cross section in scattering of
an electron by a helium atom to be
6Å
2
. Correspondingly,
σ
D
, which charac-
ea
terizes the ratio of ion and atom number densities, is
N
i
N
a
π
Λ
T
e
σ
ea
D
e
4
ln
N
i
N
a
1100
T
e
D
,
Figure 3.6
Function (3.45), which characterizes the conductivity of an ionized gas (3.44).
