Self-consistent quasi-static parallel electric field associated with substorm growth phase

A new approach is proposed to calculate the self-consistent parallel electr ic field associated with the response of a plasma to quasi-static electroma gnetic perturbations (omega < k(parallel to)v(A), where v(A) is the Alfven velocity and k(parallel to) the parallel component of the wave vector). Cal culations are carried out in the case of a mirror geometry, for omega < ome ga(b) (omega(b) being the particle bounce frequency). For the sake of simpl ification the beta of the plasma is assumed to be small. Apart from this re striction, the full Vlasov-Maxwell system of equations has been solved with in the constraints described above (omega < k parallel to v(A) and omega < omega(b)) by [Le Contel et al., this issue] (LC00, hereafter), who describe self-consistently the radial transport of particles during the substorm gr owth phase. LC00 used an expansion in the small parameter T-e/T-i (T-e/T-i is typically 0.1 to 0.2 in the plasma sheet) to solve the quasi-neutrality condition (QNC). To the lowest order in T-e/T-i < 1, they found that the QN C implies (1) the existence of a global electrostatic potential Phi(0) whic h strongly modifies the perpendicular transport of the plasma and (2) the p arallel electric field vanishes. In the present study, we solve the QNC to the next order in T-e/T-i and show that a field-aligned potential drop prop ortional to T-e/T-i does develop. We compute explicitly this potential drop in the case of the substorm growth phase modeled as ill LC00. This potenti al drop has been calculated analytically for two regimes of parameters, <(o mega(d))over bar> < omega and <(omega(d))over bar> > omega (<(omega(d))over bar> being the bounce averaged magnetic drift frequency equal to k(y)<(v(d ))over bar>, where k(y) is wave wave number in the y direction and <(v(d))o ver bar> the bounce averaged magnetic drift velocity). The first regime (<( omega(d))over bar> < omega) corresponds to small particle energy and/or sma ll k(y), while the second regime (<(omega(d))over bar> > omega) is adapted to large energies and/or large k(y). In particular, in the limit <(omega(d) )over bar> < omega and \<(v(d))over bar>\ < \<(u(y))over bar>\, where uy is the diamagnetic velocity proportional to the pressure gradient, we find a parallel electric field proportional to the pressure gradient and directed toward the ionosphere in the dusk sector and toward the equator in the dawn sector. This parallel electric field corresponds to a potential drop of a few hundred volts that can accelerate electrons and produce a differential drift between electrons and ions.