Environmental Engineering Reference
In-Depth Information
the electron drift velocity is proportional to the electric field strength and inversely
proportional to the magnetic field strength. One can represent the drift velocity
w
of a charged particle in crossed electric
E
and magnetic
H
fields in the form
c
[
E
H
]
H
2
w
D
.
(4.138)
Let us find the electron temperature when an ionized gas is located in crossed
electric and magnetic fields. We use the balance equation for the electron energy
that has the form
Z
m
e
v
2
eEw
x
D
I
ea
(
f
0
)
d
v
.
2
Using (4.136) for the electron drift velocity and (3.18) for the collision integral, we
obtain by analogy with the derivation of (3.36)
˝
v
H
)
˛
Ma
2
3
2
2
C
ω
2
ν
/(
ν
T
e
T
D
.
(4.139)
h
v
2
ν
i
Evidently, in the limit of low magnetic fields
ω
ν
this formula is transformed
H
into (3.36). In the case
ν
D
const, this expression gives
Ma
2
T
e
T
D
3
ν
2
H
,
(4.140)
2
C
ω
and in the limit of strong magnetic field strengths
ω
ν
we have from this
H
Ma
2
3
Mc
2
E
2
3
H
2
T
e
T
D
2
H
D
.
(4.141)
ω
We now examine the case where a weakly ionized gas moves with an average
velocity
u
in a transverse magnetic field of strength
H
.Thenanelectricfieldof
strength
E
0
D
Hu
/
c
exists in the fixed frame of axes, where
c
is the light velocity.
This field creates an electric current that is used for the production of electric ener-
gy in magnetohydrodynamic generators [109-111]. The energy released in a plasma
under the action of this electric current corresponds to transformation of the flow
energy of a gas into electric and heat energies. In consequence, this process leads to
a deceleration of the gas flow and a decrease of the average gas velocity. In addition,
the generation of an electric field causes an increase in the electron temperature as
given by (4.141). The maximum increase in the electron temperature corresponds
to the limit
ω
ν
. In this limit, (4.141) becomes
H
Ma
2
3
1
3
Mu
2
T
e
T
D
H
D
.
(4.142)
2
ω
This value follows from (3.36) if electrons are in a gas in an induced electric field
of strength
E
0
D
Hu
/
c
.
