Chemistry Reference
In-Depth Information
C
m
A
k
f
k
f
m
σ
klmn
v
kl
=
v
k
-
v
l
d
Ω = sin ϑ ·
d
ϑ ·
d
φ
f
l
f
n
B
l
D
n
FIGURE 3.23
Scheme of the binary collision process between particles A
k
and B
l
with
velocity distribution function
f
k
and
f
l
, the relative velocity
v
kl
, and the collision cross
section σ
klmn
.
consumption of particles
i
in collisions. Thereby, the different velocity distribution
functions
f
k
,
f
l
and
f
m
,
f
n
in (3.121) consider all binary collisions which are related
to the particle
i
(
i
v
kl
=
|
v
l
|
klmn
) with the relative velocity
v
r
=
v
k
−
and collision
)
cross section σ
klmn
(
depending on the relative velocity and the solid angle.
In the case of elementary processes which involve a third collision partner, e.g.,
in the case of the three-body recombination or the chemical reaction of third order at
higher gas pressure, the collision term contains a triple collision integral, respectively.
A lot of knowledge about the manifold elementary collision processes is nec-
essary, in particular, the collision cross sections in dependence on the translational
energy of the collision partners and their internal quantum states to solve the BLME
for selected kind of plasma species
i
.
v
r
,
3.4.2 E
LECTRON
E
NERGY
D
ISTRIBUTION
F
UNCTION IN
N
ONTHERMAL
P
LASMAS
In nonthermal plasma physics and chemistry the calculation of the
electron velocity
distribution function
is the fundamental task
v
e
×
B
E
ext
+
E
ρ
+
df
e
dt
=
∂
f
e
∂
v
e
·
∂
f
e
∂
·
∂
f
e
∂
t
+
r
−
e
m
e
v
∂
coll
=
f
e
∂
C
el
C
inel
n
=
+
(3.122)
t
n
considering electric and magnetic fields and the terms for elastic electron collisions
and the summation over all inelastic collisions involving electrons [31].
Neglecting the magnetic field, the electric field
E
=
E
ext
+
E
ρ
from external
sources and the electric space charges
e
div
E
ρ
=
ε
0
·
ρ
=
(
f
ion
−
f
e
)
·
d
3
v
(3.123)
has to be considered for the macroscopic force in gas discharges.
