Chemistry Reference
In-Depth Information
TABLE 3.2
Diffusion Lengths for Different Geometries of the
Diffusion Problem
Symmetry of the Problem
(
1
/)
2
Cylinder (radius
R
, length
L
)
(
2.4
/
R
)
2
+
(
π
/
L
)
2
Sphere (radius
R
)
(
π
/
R
)
2
Parallelepiped (side lengths
L
1
,
L
2
,
L
3
)
(
π
/
L
1
)
2
+
(
π
/
L
2
)
2
+
(
π
/
L
3
)
2
Source:
Raizer, Y.P.,
Gas Discharge Physics
, Springer-Verlag, Berlin,
Germany, 1991.
By use of the ambipolar diffusion coefficient for a nitrogen plasma, discussed
above the typical diffusion time constant at a total pressure of 100 Pa (1 mbar) in a
spherical geometry with radius
R
10
−
2
s.
Inthecaseofthree-componentplasmas,consistingofpositiveandnegativeionsas
well as electrons, three ambipolar diffusion coefficients
D
a
+
,
D
a
−
, and
D
ae
are defined
by use of the condition for quasi-neutrality
n
+
=
=
20 cm of the plasma vessel gets about 2.4
·
n
e
+
n
−
and the electronegativity
α
=
n
−
/
n
e
[4]
b
e
D
+
+
b
+
D
e
(
1
+
α
)(
∇
n
e
/
∇
n
+
)
+
b
−
D
+
α
+
b
+
D
−
(
1
+
α
)(
∇
n
−
/
∇
n
+
)
D
a
+
=
,
b
e
+
b
−
α
+
b
+
(
1
+
α
)
(3.55)
b
+
D
e
(
1
+
α
)
+
b
e
D
+
(
∇
n
+
/
∇
n
e
)
+
b
−
D
e
α
−
b
e
D
−
(
∇
n
−
/
∇
n
e
)
D
ae
=
,
(3.56)
b
e
+
b
−
α
+
b
+
(
1
+
α
)
b
+
D
−
(
1
+
α
)
+
b
−
D
+
(
∇
n
+
/
∇
n
−
)
+
b
e
D
−
−
b
−
D
e
α
(
∇
n
e
/
∇
n
−
)
D
a
−
=
.
(3.57)
b
e
+
b
−
α
+
b
+
(
1
+
α
)
These equations for the ambipolar diffusion coefficient can be approximated to
specific cases, e.g., for weak, strong, or very strong electronegativity α.
3.1.6 M
OTION OF
C
HARGED
S
INGLE
P
ARTICLE IN
H
OMOGENEOUS
M
AGNETIC
F
IELD
3.1.6.1 Cyclotron Motion
Firstly, we consider the motion of a single particle (charge
q
and mass
m
)
with a component of velocity perpendicular to a homogeneous magnetic field
B
=
B
·
e
z
=
const
.
⎛
⎞
⎛
⎞
⎛
⎞
⎛
⎞
˙
v
x
˙
v
x
v
y
v
z
0
0
B
+
v
y
·
B
⎝
⎠
=
⎝
⎠
×
⎝
⎠
=
⎝
⎠
.
m
·
v
y
˙
q
·
q
·
−
v
x
·
B
(3.58)
v
z
0
