Consequences of particle conservation along a flux surface for magnetotail tearing

Abstract

The energy principle for magnetotail tearing is reexamined using conservation of electron particle number along a flux surface as a means of calculating the volume‐integrated perturbed number density 〈 n1 〉, where n1 is the perturbed electron number density and the angle brackets denote integration along a field line. It is shown that if the electron response is magnetohydrodynamic, then 〈 n1 〉 can be calculated as a function of the perturbation vector potential component A1y (assuming magnetotail coordinates) independent of the potential components A1x and A1z and independent of the scalar potential ϕ. This result holds as long as the equilibrium and the tearing perturbations are two‐dimensional, independent of the y coordinate. In the case of a parabolic field model, the resulting 〈 n1 〉 exactly matches the results obtained previously by Lembége and Pellat [1982], who used the kinetic drift equation to calculate the electron response. Thus the compressional stabilization of the tearing mode is a direct consequence of, and can be completely calculated from, the conservation of electron particle number along the field line. Further, it is shown that 〈 n1 〉 is independent of By, the guide component of the magnetic field, so the inclusion of a guide field does not alter the tearing stabilization condition.