Stabilization by Sheared Fields

The Princeton Gun Club was a small shack on the side of the runway of the Princeton airport and was purportedly used for skeet shooting at one time. It was an ideal location for a classified meeting of Project Sherwood in 1955. The Robin Hood connection came from one of the participants, James Tuck (Friar Tuck) of Los Alamos. Representatives of the four US laboratories working on fusion (Livermore, Oak Ridge, Los Alamos, and Princeton) fit into the small room. Edward Teller was there. After hearing about our trying to hold a plasma with a magnetic field, he exclaimed, “It’s like holding jello with rubber bands!” Indeed, the jello would squeeze out between rubber bands, exchanging places with an equal volume of rubber, so that the rubber bands were on the inside and the jello on the outside.

A solution to the basic interchange instability was formulated: weave the rubber bands into a mesh. In a toroidal magnetic field, this is done by magnetic shear. Figure 5.9 shows several magnetic surfaces in a torus, each containing magnetic field lines that are twisted. The twist angle, however, changes from surface to sur­face, so if a ripple starts on one surface and is aligned with the field lines there, as in Fig. 5.8, it finds itself misaligned with the field on the next surface. The differ­ence in pitch angle from one surface to another has been greatly exaggerated. It does not take a very fine mesh of field lines to kill the interchange instability; in fact, we will see later that the amount of twist is limited by another instability.

A graphic picture of how shear stabilization works was provided by an experi­ment by Mosher and Chen [4]. The plasma in Fig. 5.10 was in a straight cylinder with a magnetic field up out of the page. The shaded circle in the center represents a thick rod inside the plasma carrying a current into the page and creating a “poloidal” magnetic field that gives the field lines a helical twist. At the left, a bump on a magnetic surface is shown which might represent an instability getting started.3 In successive views to the right, the current in the rod is increased, twisting

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Fig. 5.9 A torus with a sheared helical field

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Fig. 5.10 Effect of shear on a bump in a plasma

the field lines more and more. Finally, at the right, the measurements show that the bump has been twisted into a thin spiral, so thin that the charges that create the electric field in the Rayleigh-Taylor instability (Fig. 5.8) can leak across the spiral, short-circuiting the electric field and killing the instability. In addition, short-circuiting by electrons moving in the toroidal direction (perpendicular to the page) also happens, and in fact is the main stabilizing effect of shear on the inter­change instability.

To summarize this first of many instabilities, we saw that a plasma cannot fall out of its magnetic container the way water falls out of a bottle because a plasma weighs practically nothing. Its gas pressure, however, is always pushing against the magnetic field. With the slightest perturbation, the plasma organizes itself to create an electric field that causes a tongue of plasma to leak out and a bubble of field to leak in. Being wise to the plasma’s tricks, we can thwart the plasma’s moves by short-circuiting its self-generated electric fields with magnetic shear.