  During periods of intense geomagnetic activity, strong electric fields and
currents penetrate from the magnetosphere into high-latitude ionosphere where
they dissipate energy, form electrojets, and excite plasma instabilities in the
E-region ionosphere. These instabilities give rise to plasma turbulence which
induces non-linear currents and strong anomalous electron heating (AEH) as
observed by radars. These two effects can increase the global ionospheric
conductances. This paper analyzes the energy budget in the electrojet, while
the companion paper applies this analysis to develop a model of anomalous
conductivity and frictional heating useful in large-scale simulations and
models of the geospace environment. Employing first principles, this paper
proves for the general case an earlier conjecture that the source of energy for
plasma turbulence and anomalous heating equals the work by external field on
the non-linear current. Using a two-fluid model of an arbitrarily magnetized
plasma and the quasilinear approximation, this paper describes the energy
conversion process, calculates the partial sources of anomalous heating, and
reconciles the apparent contradiction between the inherently 2-D non-linear
current and the 3-D nature of AEH.
