Consequences of particle conservation along a flux surface for magnetotail tearing

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 < n(1) >, where n(1) 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 < n(1) > can be calculated as a function of the perturbation vector potential component A(1y) (assuming magnetotail coordinates) independent of the potential components A(1x) and A(1z) and independent of the scalar potential phi. 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 < n(1) > exactly matches the results obtained previously by Lembege 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 < n(1) > is independent of B-y, the guide component of the magnetic field, so the inclusion of a guide field does not alter the tearing stabilization condition.