pinch effect

n.
Radial constriction of flowing plasma or other matter carrying an electric current, caused by the magnetic field that is produced by the current.

A 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. Arrows at left show direction of pinch pressure.

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. (a) Sausage type. (b) Kink type.

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 also Nuclear fusion.

---