Environmental Engineering Reference
In-Depth Information
for the oscillation amplitudes. Solution of these equations shows that the oscilla-
tions increase with the dependence
a
,
b
exp(
γ
t
), with
r
m
e
r
m
e
1
4
ω
1
4
ω
eE
0
m
e
e
e
γ
D
u
0
k
i
D
k
i
.
(5.127)
m
i
ω
m
i
ω
ω
i
i
0
Thus, the initial plasma wave is unstable. It can decay into a plasma wave of a lower
frequency and the ion sound. This instability is also known as decay instability. The
exponential growth parameter of the new wave is proportional to the amplitude of
the decaying wave.
5.5
Ionization Instabilities and Plasma Structures
5.5.1
Drift Waves
A laboratory ionized gas is usually maintained by an external electric field that
generates an electric current and causes ionization of the gas. Electrons are the
principal plasma component in the sense that electrons contribute most of the
total electric current, and formation of new charged particles is due to collisions
of electrons with gas atoms or molecules. Perturbations of the electron number
density are thus of central importance to the properties of the plasma.
To examine the simplest form of perturbations in the plasma, we begin with the
continuity equation (4.1)
@
N
e
@
C
div
j
D
0
t
for electrons, and we assume that the electron flux
j
is determined solely by the
electron drift in an external electric field. The current is then
j
D
w
N
e
,where
w
is
the electron drift velocity. Using expansion (5.48) for a perturbation to the electron
number density, we obtain the dispersion relation
ω
D
kw
.
(5.128)
That is, there is a wave associated with the perturbation that propagates together
with the electric current. In other words, the perturbation moves together with
the electric current. Such waves which transfer plasma perturbation by an electric
current are drift waves.
Damping or amplification of these waves can occur by several mechanisms. One
such mechanism is the diffusive motion of the electrons. The electron flux is then
j
D
w
N
e
N
e
,where
D
is the diffusion coefficient for electrons in a gas, and
the dispersion relation that follows from the continuity equation for electrons has
the form
D
r
iDk
2
.
ω
D
kw
(5.129)
