Environmental Engineering Reference
In-Depth Information
5
Waves, Instabilities, and Structures in Excited and Ionized Gases
5.1
Instabilities of Excited Gases
5.1.1
Convective Instability of Gases
Currents in a plasma lead to its heating, and this may cause new forms of gas mo-
tion in accord with general laws of hydrodynamics [1-4]. In the first stage of trans-
formation of a quiet plasma into a moving plasma, where the motion supports the
heat transport, they may be considered as an instability of a motionless plasma. The
simple form of gas or plasma motion that increases the heat transport compared
with heat transport in a motionless gas is convection, which consists in the move-
ment of streams of hot gas to a cooler region and streams of cold gas to a warmer
region. The conditions for the development of this heat transport mechanism [1]
and the convective movement arising for a motionless gas will be considered below.
To find the stability conditions for a gas with a temperature gradient
dT
/
dz
oriented in the same direction as an external force [1], we assume the gas to be
in equilibrium with this external force. If the external force is directed along the
negative
z
-axis, the number density of gas molecules decreases with increasing
z
.
We consider two elements of gas of the same volume located a distance
dz
from
each other, and calculate the energy required to exchange them in terms of their
positions. The mass of the element with the smaller
z
coordinate is larger by
M
than that of the element with the larger coordinate, so the work required for the
exchange is
Δ
Mgdz
,where
g
is the force per unit mass exerted by an external
field. We ignore heat conductivity in this operation. The gas element initially at
larger
z
has its temperature increased by
Δ
T
as a result of this exchange, and
the element initially at smaller
z
is cooled by this amount. Hence, the heat energy
taken from a gas as a result of the transposition of the two elements is
C
p
Δ
Δ
MdT
D
MdT
/
m
,where
C
p
is the heat capacity of the gas per unit mass,
c
p
is the heat
capacity per molecule, and
m
is the molecular mass. The instability criterion states
that the above exchange of gas elements is energetically advantageous, and has the
c
p
Δ
