Chemistry Reference
In-Depth Information
Assuming elastic electron-electron collisions, only, and no macroscopic forces,
the stationary solution of the BLME provides the well-known isotropic Maxwellian
velocity distribution function
exp
m
e
·
v
e
f
e
(
d
3
v
e
v
e
)
·
d
v
e
∼
−
·
(3.124)
2
·
k
B
T
e
and the normalized distribution function
f
e
(
v
e
)
, respectively, for the absolute value
of the electron velocity
m
e
2π
3
/
2
exp
,
dn
e
n
e
·
m
e
·
v
e
f
e
(
v
e
·
dv
e
=
v
e
)
=
4π
·
·
−
(3.125)
·
k
B
T
2
·
k
B
T
e
with
0
f
e
(
v
e
)
·
dv
e
=
1,
f
e
(
v
e
)
·
dv
e
=
f
e
(
ε
T
)
·
d
ε
T
, ε
T
=
m
e
/
2
·
v
e
and
dv
e
=
ε
T
)
−
1
/
2
(
d
ε
T
. The electron velocity distribution can be easily converted into
the electron energy distribution function (EEDF)
2
·
m
e
·
·
exp
dn
e
n
e
·
·
√
ε
T
·
ε
T
k
B
T
e
f
e
(
π
−
1
/
2
−
3
/
2
d
ε
T
=
ε
T
)
=
2
·
·
(
k
B
·
T
e
)
−
(3.126)
replacing the electron velocity
v
e
by the translational energy ε
T
.
The electrons in the high energetic tail of the distribution function (ε
T
>
ε
thres
)
are able for
excitation
and
ionization
of atoms and molecules and/or
dissociation
of
molecules. These inelastic collisions and the charged particle transport in gas dis-
charges due to electric field drift and diffusion cause deviations from the Maxwellian
distribution function. Consequently, the statistical description of the electron ensem-
ble in nonthermal plasma by means of the Maxwellian velocity distribution function
with the electron temperature
T
e
is strongly restricted. Nevertheless, the quantity
electron temperature is often applied to describe the nonthermal properties and to
determine the transport and rate coefficients in dependence on
T
e
.
In gas discharge physics it is often applied the EEDF in terms of voltage due to the
replacement of the translational energy by ε
T
=
e
·
U
,
d
ε
T
=
e
·
dU
, and
k
B
·
T
e
=
e
·
U
e
,
respectively
exp
.
√
U
dn
e
n
e
·
U
U
e
f
e
(
π
−
1
/
2
U
−
3
/
2
e
dU
=
U
)
=
2
·
·
·
·
−
(3.127)
Taking into account the influence of the macroscopic electric field, only, the calcula-
tion of the electron velocity distribution function using the BLME may be performed
by different approximations concerning the electric field strength in gas discharges.
For example, it is applied
1. The
two-term approximation
for weak electric field strength with the
isotropic Maxwellian
f
e
and the small anisotropic
f
e
term
v
e
)
+
v
e
v
e
·
f
e
(
v
e
)
=
f
e
(
f
e
.
(3.128)
