The relativistic electron annulus is a critical component of the bumpy torus magnetic fusion concept. An analysis of the annulus is presented in which the ring steady state is determined by the explicit balance of quasi-linear heating and classical losses, i.e. collisions and synchrotron radiation. Both anisotropy and loss-cone effects are included in the formalism. It is demonstrated that a large number of electron cyclotron harmonics, not just the first and second, contribute in an appreciable way to annulus steady state and power balance. Without a loss cone, the analysis reproduces the relativistic passing electron population observed in bumpy tori on confined drift surfaces near the centre of the bumpy torus cross-section. Loss-cone effects permit an annulus population with large perpendicular pressure to exist. It is shown that the balance between quasi-linear heating and the classical losses cannot account for the experimental scaling of bumpy torus annulus temperature; therefore, processes not included in the classical ring power balance model must contribute in a non-trivial way to observed annulus properties.