Environmental Engineering Reference
In-Depth Information
4.5.8
Pinch Effect
We next analyze shrinkage under the action of a magnetic field for a cylindrical
plasma column maintained by a direct current [120, 121]. Here the magnetic lines
of force are cylinders, and because of the axial symmetry, (4.161) for the direction
perpendicular to the field and current has the form
p
H
2
8
r
C
D
0 .
(4.163)
π
H
2
/(8
The solution of this equation shows that the total pressure
p
), which is
the sum of the gas-kinetic pressure and the magnetic field pressure, is independent
of the transverse coordinate. Let the radius of the plasma column be
a
and the
current in it be
I
, so the magnetic field at the surface of the column is
H
C
π
2
I
/(
ca
).
The total pressure outside the column near its surface is equal to the magnetic field
pressure
I
2
/(2
D
c
2
a
2
), and the total pressure inside the plasma column is equal to
the gas-kinetic pressure
p
. Equating these two pressures, we find the radius of the
plasma column to be [121]
π
I
c
p
2
a
D
.
(4.164)
π
p
An increase in the current of the plasma column is accompanied by a correspond-
ing increase in the magnetic field, which gives rise to a contraction of the plasma
column. This phenomenon is called the pinch effect, and the state of the plasma
column itself is known as
z
-pinch.
4.5.9
Reconnection of Magnetic Lines of Force
In a cold plasma of high conductivity, magnetic lines of force are frozen in the
plasma. This means that internal magnetic fields support electric currents inside
the plasma. But plasma motion and the interaction of currents may cause a short
circuit of some currents. This leads to an instability called the reconnection of mag-
netic lines of force [122]. As a result of this process, the energy of the magnetic
fields is transformed into plasma energy in an explosive process that generates
plasma fluxes. This phenomenon is observed in solar plasmas. Various solar plas-
ma structures, such as spicules and prominence, result from this phenomenon.
We consider first a simple example of this phenomenon, when there are two
antiparallel currents of amplitude
I
located a distance 2
a
apart, and with length
l
a
. We assume these currents have transverse dimensions that are small com-
pared with
a
. Taking the direction of the currents to be along the
z
-axis, taking the
planeofthecurrentstobethe
xz
plane, and placing the origin of the coordinates
in the middle of the currents, we find the magnetic field strength at distances
r
l
