On the equilibrium of electron clouds in toroidal magnetic fields

The self -consistent equilibrium configurations available t o low 2 density (q = o /w << 1) toroidal electron clouds under the influence of an external magnetic field and the electric fields due to space and image charges a r e discussed.static, but steady.unimportant, in contrast to the situation in toroidal neutral plasmas.Typical equilibria a r e shown in detail, to zero o r d e r in q .The construction of equilibria accurate to o r d e r q is shown to be possible but is not c a r r i e d out in detail. P CThe equilibria are dynamic r a t h e r than VB , centrifugal and other drifts are shown t o be