Walter RussellPosted by Hanne Thu, May 24, 2018 20:08:08A name given to manifestations of the magnetic
self-attraction of parallel electric currents having the same direction. The
effect at modest current levels of a few amperes can usually be neglected, but
when current levels approach a million amperes such as occur in
electrochemistry, the effect can be damaging and must be taken into account by
electrical engineers. The pinch effect in a gas discharge has been the subject
of intensive study, since it presents a possible way of achieving the magnetic
confinement of a hot plasma (a highly ionized gas) necessary for the successful
operation of a thermonuclear or fusion reactor.
The law of attraction which describes the interaction
between parallel electric currents was discovered by A. M. Ampère in 1820. For
a cylindrical wire of radius r meters carrying a total surface current of I
amperes, it manifests itself as an inward pressure on the surface (Fig. 1)
given by I2/2 × 107πr2 pascals. For the electric currents of normal experience,
this force is small and passes unnoticed, but it is significant that the
pressure increases with the square of the current, I2. For example, at 25,000
amperes the pressure amounts to about 1 atm (100 kilopascals) for a wire of 1-cm
radius, but at 106 amperes the pressure is about 1600 atm or about 12 tons
in.-2 (160 megapascals).

Pinch pressure on a current-carrying conductor
There are a number of ways in which the magnetic field of a
fusion reactor can be arranged around the plasma to hold it together, and one
of these methods is the pinch effect. A fusion reactor using this type of
confinement would ideally be a toroidal tube in which the confined plasma would
carry a large electric current induced in it by magnetic induction from a
transformer core passing through the major axis of the torus. The current would
have the double function of ohmically heating the plasma and compressing the
plasma toward the center of the tube.
Characteristically, as can be shown by
high-speed photography, the pinch forms at the inner surface of a discharge
tube wall and contracts radially inward, forming an intense line, the pinch, on
the axis; the pinch rebounds slightly; the contracted discharge rapidly
develops necks and kinks; and in a few microseconds all structure is lost in an
apparently turbulent glowing gas which fills the tube. Thus, the pinch turns
out to be unstable, and plasma confinement is soon lost by contact with the
wall. The cause of the instability is easily seen qualitatively: The pinch
confinement can be described as being caused by the magnetic field lines
encircling the pinch which are stretched longitudinally but which are in compression
transversely (Fig. 2). For a uniform cylindrical pinch, the magnetic pinch
pressure is everywhere equal to the outward plasma pressure, but at a neck or
on the inward side of a kink, the magnetic field lines crowd together, creating
a higher magnetic pressure than the outward gas pressure. Consequently, the neck contracts still further,
the kink cuts in on the concave side and bulges out on the convex side, and
both perturbations grow. The instability has a disastrous effect on the
confinement time.
Instability
The term theta pinch has come into wide usage to denote an
important plasma confinement system which relies on the repulsion of oppositely
directed currents and which is thus not in accord with the original definition
of the pinch effect (self-attraction of currents in the same direction). Plasma
confinement systems based on the original pinch effect are known as Z pinches.
Tokamak is essentially a low-density, slow Z pinch in a torus
with a very strong longitudinal field. The helical magnetic field lines,
resultant from the externally applied field and that of the pinch, do not
close, that is, do not complete one revolution of the minor axis in going
around the major axis of the torus once. This is known theoretically to prevent
the growth of certain helical distortions of the plasma. The performance of
tokamak experiments has raised the possibility of achieving a net power
balance. See Nuclear fusion
McGraw-Hill Concise Encyclopedia of Physics. © 2002 by The
McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia
(1979). It might be outdated or ideologically biased.
Pinch Effect
the tendency of an electric-current channel in a
compressible conducting medium to decrease its cross-section under the action
of the magnetic field produced by the current. The phenomenon was first
described in 1934 by the American scientist W. Bennett with respect to streams
of fast charged particles in a gas-discharge plasma. The term “pinch effect”
was introduced in 1937 by the British physicist L. Tonks in an investigation of
arc discharge.
The mechanism of the pinch effect can be
understood most easily through the example of a current I flowing along the
axis of a cylinder filled with a conducting medium. The lines of force of the
magnetic field generated by I have the form of concentric circles whose planes
are perpendicular to the axis of the cylinder. The electrodynamic force per
unit volume of a conducting medium with a current density j is equal to (1/c)
[jB] in the cgs system of units; the force is directed toward the axis of the
cylinder and tends to compress the medium. The state that arises is the pinch
effect. (Here, the square brackets indicate a vector product; c is the speed of
light in a vacuum; and B is the magnetic induction in the unit volume under
consideration.) The pinch effect may also be considered
a simple consequence of Ampere’s law, which describes the
magnetic attraction of the individual parallel current filaments whose
aggregate is the current cylinder. Magnetic compression is impeded by the
gas-kinetic pressure of the conducting medium resulting from the thermal motion
of the medium’s particles; the forces of this pressure are directed from the
axis of the current channel. When the current is sufficiently large, however,
the magnetic pressure differential becomes greater than the gas-kinetic
differential and the current channel contracts—the pinch effect arises.
The pinch effect requires that the concentrations of the
carriers of charges of opposite signs in the medium be approximately equal. In
fluxes of carriers of charges of one sign, the electric field of the space
charge effectively impedes current contraction. When sufficiently large
currents pass through a gas, the gas changes to the state of a completely
ionized plasma consisting of charged particles of both signs; the pinch effect
squeezes the plasma column away from the walls of the chamber in which the
discharge occurs. The conditions are thus created for magnetic thermal
insulation of the plasma. This property of powerful self-constricting
discharges, which are called pinches, explains scientists’ interest in the pinch
effect as the simplest and most encouraging mechanism for the confinement of
high-temperature plasma. Such confinement is of importance in the problem of
controlled thermonuclear fusion.
The conditions under which the gas-kinetic pressure of the
plasma nk(Te + Ti) becomes equal to the magnetic pressure of the field of the
current I are given by Bennett’s equation (2I/cr)2/8π = nk(Te + Ti). Here, n is
the number of particles per unit volume, r is the pinch radius, Te and Ti are
the electron and ion temperatures, respectively, n is the number of electrons
per unit volume and is equal to the number of ions because of the quasi-neutrality
of the plasma, and k is the Boltzmann constant. It follows from Bennett’s
formula that the large, but quite feasible, current of ~ 106 amperes (A) is
required to attain the minimum temperature (T ~ 108°K) at which thermonuclear
fusion may be of interest as an energy source.
Investigation of pinches in deuterium began simultaneously
in 1950 and 1951 in the USSR, the USA, and Great Britain within the framework
of national programs for controlled thermonuclear fusion. Attention was paid
primarily to two types of pinches—linear and toroidal. It was believed that
when a current passed through the pinch, the plasma would be heated not only
through Joule heating but also by adiabatic compression of the pinch—that is,
by compression occurring without exchange of energy with the environment.
The early experiments, however, showed that the pinch effect
is accompanied by the development of various plasma instabilities. Necks
(“sausage” deformations), kinks, and helical disturbances are formed. The
growth of these perturbations occurs extraordinarily quickly and results in the
breakdown of the pinch—the pinch ruptures or plasma is thrown onto the wall of
the chamber. Simple pinches were found to be subject to practically all the
types of instabilities of a high-temperature plasma and thus can be used to
study these instabilities and to test various methods of stabilizing the plasma
column.
A current of ~106 A in linear pinch units is produced by the
discharge of powerful condenser batteries across a gas-filled gap. In some
cases, the rate of current growth may be ~1012 A/sec. The most important factor
here is not Joule heating but the electrodynamic acceleration of the thin outer
layer, or skin, of the current column toward its axis with the accompanying
formation of a powerful shock wave that converges on the axis. The conversion
of the energy accumulated by the wave into thermal energy creates a plasma with
a temperature much greater than Joule heating could produce. On the other hand,
the conversion of the energy of the electric current in a pinch into thermal
energy becomes considerably more efficient when the turbulence that arises with
the development of microinstabilities begins to make the decisive contribution
to the electrical resistance of the plasma.
Under certain conditions, powerful pulsed pinches in
rarefied deuterium become sources of hard radiation, including neutron
radiation and X rays. This phenomenon was discovered in the USSR in 1952.
Although the problem of controlled thermonuclear fusion has
not been solved for even the simplest pinches, self-constricting discharges
have been of great importance for plasma research. They have permitted the
obtaining of a dense plasma with a lifetime that, although short, is sufficient
to study the physics of the pinch effect, to create various methods of plasma
diagnostics, and to develop a modern theory of plasma processes. The evolution
of apparatus making use of the pinch effect has led to the development of many
types of plasma devices in which the instabilities of the pinch effect are
stabilized by external magnetic fields—for example, Tokamaks and θ pinches—or
are used to produce a short-lived high-density plasma in fast processes (plasma
focus, micropinches). For this reason, systems based on the pinch effect occupy
at the present time an important place in programs for controlled thermonuclear
fusion in the USSR, the United States, and the European Atomic Energy
Community.
The pinch effect occurs not only in a gas discharge but also
in a solid-state plasma, particularly in the strongly degenerate electron-hole
plasma of semiconductors.
REFERENCES
Artsimovich, L. A. Elementarnaia fizika plazmy, 3rd ed.
Moscow, 1969.
Post, R. Vysokotemperaturnaia plazma i upravliaemye termoiadernye reaktsii.
Moscow, 1961. (Translated from English.)
Steele, M., and B. Vural. Vzaimodeistvie voln v plazme tverdogo tela. Moscow,
1973. (Translated from English.)
T. I. FILIPPOVA and N. V. FILIPPOV
The Great Soviet Encyclopedia, 3rd Edition (1970-1979). ©
2010 The Gale Group, Inc. All rights reserved.