Chemistry Reference
In-Depth Information
TABLE 3.1
Phase and Group Velocity for Different Electric Field Frequencies in
Comparison with Electron Plasma Frequency (Collision-Free Case)
Angular Frequency
ω
Phase Velocity
c
ph
Group Velocity
c
gr
Comment
ω
<
ω
pe
Not defined
Not defined
No wave propagation
(
ε
<
0
)
(
ε
<
0
)
Total reflection
ω
=
ω
pe
c
ph
→∞
c
gr
=
0
No wave propagation
(
ε
=
0
)
(
ε
=
0
)
Total reflection
ω
>
ω
pe
c
ph
>
c
0
c
gr
<
c
0
Wave propagation
(
0
<
ε
<
1
)
(
0
<
ε
<
1
)
In the following, we will discuss the dispersion function (3.41) without collisions
(ν
e
=
0) as the simplest case
ω
2
1
c
0
·
k
(
ω
)
=
−
ω
pe
.
(3.42)
The phase and group velocity (
c
ph
and
c
gr
) are defined to (Table 3.1)
1
2
−
1
/
2
ω
pe
ω
ω
k
=
c
ph
=
c
0
·
−
,
(3.43)
1
2
1
/
2
ω
pe
ω
d
ω
dk
=
c
gr
=
c
0
·
−
.
(3.44)
A characteristic cutoff is observed in the dispersion function
k
at the electron
plasma frequency (see Figure 3.3). That means without external magnetic field no
electromagnetic wave propagation takes place below the electron plasma frequency
ω
pe
, or above the critical electron concentration
n
ec
(
ω
)
m
e
·
ε
0
n
ec
=
·
ω
pe
(3.45)
e
2
cm
−
3
10
10
2
.
n
ec
[
]=
1.24
·
·
(
ν
[
GHz
]
)
(3.46)
In the case of total reflection (ω
≤
ω
pe
or
n
e
≥
n
ec
), the penetration depth of the
electromagnetic wave δ can be estimated by
c
0
ω
pe
.
δ
≈
(3.47)
In a plasma with collisions (ν
e
=
, a damping of the
wave is observed. At frequencies below the electron plasma frequency the wave is
0) and high conductivity σ
(
ω
)
