Wall Stabilization Effects in Theta‐Pinch Configurations

If flux lines cannot penetrate into the conducting walls of a theta‐pinch coil, then a repulsion force arises as a diamagnetic plasma approaches the coil wall. This results from the three‐dimensional curvature of the flux lines when the plasma is near the wall. Neglecting changes in plasma shape, the stabilization energy is obtained by computing the energy needed to ``turn on'' the plasma surface currents in the presence of the coil wall. This is done accurately for spherical plasma shapes in cylindrical coils, and approximately for ellipsoidal shapes. The stabilization energy of spheres is proportional to the square of their volume, and becomes effective within a sphere diameter from the wall. It is approximately 10% of the energy needed to introduce the sphere into the coil center. Ellipsoids show roughly the same stabilization as spheres, but the force comes into play farther from the wall. By replacing the plasma with a conducting object of the same shape, an analog experiment is performed to determine the change in inductance as the object is moved about in the coil. For spheres and ellipsoids, agreement is found between the calculations and experiment. The experiment may be used to find the stabilization for complex shapes.