Generalized adiabatic theory applied to the magnetotail current sheet

We use the generalized first adiabatic invariant, an extension of the magnetic moment for regions of large field gradients, to treat particles in the magnetotail current sheet. The equations of motion can be expressed in terms of drift parameters which vary slowly and smoothly at the drift rate, not at the gyration rate. The analysis leads to boundaries in phase space which form a generalized loss cone and separate particles drifting into and out of the layer from particles trapped within the layer. These boundaries can be used in the moment integrals for densities and currents when the drifting particles differ in temperature, or in other properties, from the trapped population, as has been suggested by observations. We give examples of how different kinds of particle orbits contribute to the spatial profiles of density and current and thus to the field structure of the current sheet. We find that the parallel pressure of the drifting particles must exceed the transverse pressure for self-consistent solutions to exist, and based on this result, we give examples of fully self-consistent solutions using bi-Maxwellian ion and Maxwellian electron distributions. We give a proof, using generalized adiabatic theory, of Cowley's (1978a) theorem that particles trapped in the current layer experience zero net drift.Paper dedicated to Professor Hannes Alfvén on the occasion of his 80th birthday, 30 May 1988.