Thin E-layer equilibria

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Abstract
The equilibrium of an infinitely long, thin E layer under the influence of external and self-fields is studied. The canonical angular momentum and the total energy per particle are constant in this analysis. The results can be summarized as follows: (1) with complete charge neutralization, as the number of particles N increases, the E-layer radius R e tends toward the value Re = (RwRc)1/2, where R w and R c are the radii of the outer and inner conducting walls, respectively, (2) the total kinetic energy per particle initially decreases as N increases; (3) the axial temperature increases with N so as to maintain stability with respect to the tearing mode; and (4) the current per unit length saturates at a value well beyond that required for field reversal.