Plasma equilibrium in a toroidal chamber with a travelling magnetic field

The displacement was found of the center of a plasma column in a toroidal chamber that is maintained in equilibrium by the average pressure of the high-frequency travelling magnetic field H and the dc magnetic field of the longitudinal surface currents. The travelling hf magnetic field is created by passing ac currents with specially selected phases through the annular conductors enveloping the chamber. It is assumed that these conductors do not affect the distribution of the dc magnetic field, which is assumed to be the same as in a single ideally conducting toroid. The solution is performed in assuming that toroidality is small (expansion in powers with respect to 1/R; R is the large radius of the torus).The conditions for detachment of the column from the chamber walls in a quasi-static regime, is evaluated in the following manner. Let a plasma column of radius α be in equilibrium in a cylindrical chamber of radius b (R = ∞) at a distance δ from the walls. If the column is bent into a torus, then for detachment of the plasma from the chamber walls it is necessary that δ be larger than the displacement of the center of the plasma column Δ (a,b) = b – δ. The condition for detachment, δ > Δ (b – δ, b), limits β, the ratio of plasma pressure to full magnetic-field pressure (time average of H plus ).In a concrete case that is close to the experiments described in ref. 1 (R=35 cm, b=4 cm, and 12 waves of the travelling magnetic field fill the length of the torus), the formula is h = a/Hb is the ratio of x at the surface of the plasma column to H near the current conductors (on the surface of the chamber). From this formula it follows that for large longitudinal currents (h2 > 0.49), detachment is impossible. From table I we can find the maxima of β for which, with preset h2, a column can exist that is detached from the chamber walls. As is seen from this table, the conditions for detachment are very stringent.