Self-consistent quasi-static radial transport during the substorm growth phase

We develop a self-consistent description of the slowly changing magnetic configuration of the near-Earth plasma sheet (NEPS) during substorm growth phase. This new approach is valid for quasi-static fluctuations omega < k(parallel to)v(A) (v(A) being the Alfven velocity), with characteristic frequency lower than the bounce frequencies of electrons and ions (omega < omega(bi),omega(be)), and for spatial scales larger than the ion Larmor radius. The basic equations are obtained from a linearization of the cyclotron and bounce-averaged Vlasov equation, together with Maxwell equations, The Vlasov-Maxwell system of equations is solved for the quasi-dipolar NEPS region. Using a 2-D dipole for the equilibrium, we calculate analytically the perturbed components of the electromagnetic field as a function of an external forcing current. The quasi-neutrality condition (QNC) is solved via an expansion in the small parameter T-e/T-i (T-e/T-i is the ratio between the electronic and ionic temperatures). To the lowest order in T-e/T-i, we find that the enforcement of QNC implies the presence of a global electrostatic potential which is constant for a given magnetic field line but varies across the magnetic field. The corresponding electric field shields the effect of the inductive component of the electric field, thereby producing a partial reduction of the motion that would correspond to the inductive electric field. Furthermore, we show that enforcing the QNC implies a field:aligned potential drop which is computed to the next order in T-e/T-i in a companion paper [Le Contel ct at, this issue]. In the present paper, we show that the direction of the azimuthal electric field varies along; the field line, thus the equatorial electric field cannot be mapped onto the ionosphere. Furthermore during the growth phase, the (total) azimuthal electric field is directed eastward, close to the equator, and westward, off-equator. Thus large equatorial pitch angle particles drift tailward, whereas small pitch angle particles drift earthward.