Chemistry Reference
In-Depth Information
T
−
, the defined
electronegativity
α
0
at the sheath edge
will not be the same compared with the bulk plasma α
pl
. In the presheath the negative
ions are much more repelled then the electrons. By use of the Boltzmann relation for
electrons and negative ions in the presheath
But, for the condition
T
e
exp
−
exp
−
·
·
·
e
ϕ
pl
γ
e
ϕ
pl
n
e
(
)
=
n
e
,
pl
·
n
−
(
)
=
n
−
,
pl
·
0
0
(3.214)
k
B
·
T
e
k
b
·
T
e
it follows the expression for α
0
at the sheath edge in relation the α
pl
in the plasma bulk
exp
e
.
ϕ
pl
k
B
·
α
0
=
α
pl
·
·
(
1
−
γ
)
·
(3.215)
T
e
Further, taking into the consideration the energy conservation of negative ions, we
obtain
e
ϕ
pl
k
B
·
·
1
2
·
1
+
α
0
T
e
=
.
(3.216)
1
+
γ
·
α
0
Inserting (3.216) in (3.215) an expression for the bulk plasma electronegativity is
obtained
exp
(
.
1
+
α
0
)
·
(
γ
−
1
)
α
pl
=
α
0
·
(3.217)
2
·
(
1
+
γ
·
α
0
)
From (3.215) and (3.217) the electronegativity α
0
at the sheath edge and
e
ϕ
pl
/
k
B
T
e
can be calculated numerically if the bulk electronegativity α
pl
is known. The ratio
α
0
/
k
B
T
e
over α
pl
was firstly calculated by Boyd and Thomson [34]. For
the conditions α
pl
<
α
pl
and
e
ϕ
pl
/
30 the plasma sheath can be treated similar to electro-
positive plasmas which is relevant for most of the used nonthermal plasmas. Further
investigations by Braithwhite and Allen have also shown the additional formation of
a double layer at conditions with γ
2 and γ
>
>(
5
+
24
1
/
2
)
,see[35].
3.6.1.3 Multi-Species Plasmas
Generally, the nonthermal molecular plasmas may contain several kinds of positive
and negative ions, electrons, and neutral species. Some approximations are given in
the literature concerning the Bohm sheath criterion for multi-species plasma, by a
summation over several kinds of positive ions [33,36]
z
k
·
n
+
k
1
k
B
·
m
+
k
≤
(3.218)
n
e
·
ν
2
+
k
·
T
e
k
with
z
the charge number of the positive ion.
