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

A new approach is proposed to calculate the self‐consistent parallel electric field associated with the response of a plasma to quasi‐static electromagnetic perturbations (ω < k ‖ v A , where v A is the Alfvén velocity and k ‖ the parallel component of the wave vector). Calculations are carried out in the case of a mirror geometry, for ω < ω b (ω b being the particle bounce frequency). For the sake of simplification the β of the plasma is assumed to be small. Apart from this restriction, the full Vlasov‐Maxwell system of equations has been solved within the constraints described above (ω < k ‖ v A and ω < ω b ) by [ Le Contel et al. , this issue] (LC0, hereafter), who describe self‐consistently the radial transport of particles during the substorm growth 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 QNC implies (1) the existence of a global electrostatic potential Χ 0 which strongly modifies the perpendicular transport of the plasma and (2) the parallel 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 proportional to T e / T i does develop. We compute explicitly this potential drop in the case of the substorm growth phase modeled as in LC000. This potential drop has been calculated analytically for two regimes of parameters, and ( being the bounce averaged magnetic drift frequency equal to , where k y is the wave number in the y direction and the bounce averaged magnetic drift velocity). The first regime () corresponds to small particle energy and/or small k y , while the second regime (>) is adapted to large energies and/or large k y . In particular, in the limit and , where u y 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.