σ ¼ Ài
e
2 n e
mω
ð2:3:27Þ
In this book, plasmas are frequently assumed collisionless; then the conductivity is
pure imaginary, and no net energy loss takes place for waves in plasmas. Such media
is called reactive media in comparison with the dissipative media. The RHS of
(2.2.2) is time averaged to give the energy loss rate of the wave in the form:
jE
h i ¼
1
2
σ r E
2
0
ð2:3:28Þ
where σ r is the real part of the conductivity.
When (2.2.2) is regarded as the energy propagation of the laser in plasmas, taking
the time average of the fields and use the following relations:
W
h i ¼
1
2
ε 0 E
2
0
S
h i ¼ W
h ic ¼ I L
ð2:3:29Þ
then one can obtain the following transport equation to laser intensity I L:
∂I L
∂t
þ c
∂I L
∂x
¼ À
ω
2
pe
ω
ωτ
1 þ ω 2 τ 2 I L
ð2:3:30Þ
In (2.3.30), a very important physical value ω pe is introduced. It is defined as:
ω pe ¼
e
2 n e
ε 0 m
1=2
ð2:3:31Þ
This is the electron plasma frequency or simply called plasma frequency and one
of the most important physical values in plasma physics. It is noted that in deriving
(2.3.22), it is assumed that ω/k ¼ c, but it is not satisfied in plasmas in general as seen
later.
It is clear that the coefficient of the RHS in (2.3.30) is absorption rate ν ab :
ν ab ¼
ω
2
pe
ω
ωτ
1 þ ω 2 τ 2 ¼
ω
2
pe
ω 2
ν
1 þ ν 2 =ω 2
ð2:3:32Þ
It has the following limiting dependence:
ωτ >> 1 ! ν ab ¼
ω
2
pe
ω 2 ν
ð2:3:33Þ
52
2 Laser Absorption by Coulomb Collision