The self‐consistent equilibrium configurations available to low‐density (q= &ohgr;p2/&ohgr;c2≪ 1) toroidal electron clouds under the influence of an external magnetic field and the electric fields due to space and image charges are discussed. The equilibria are dynamic rather than static, but steady. ▿B, centrifugal, and other drifts are shown to be unimportant, in contrast to the situation in toroidal neutral plasmas. Typical equilibria are shown in detail, to zero order inq. The construction of equilibria accurate to orderqis shown to be possible but is not carried out in detail. Questions relating to the stability of these equilibria are not treated.