Kinetic model for an auroral double layer that spans many gravitational scale heights

The electrostatic potential profile and the particle densities of a simplified auroral double layer are found using a relaxation method to solve Poisson's equation in one dimension. The electron and ion distribution functions for the ionosphere and magnetosphere are specified at the boundaries, and the particle densities are found from a collisionless kinetic model. The ion distribution function includes the gravitational potential energy; hence, the unperturbed ionospheric plasma has a density gradient. The plasma potential at the upper boundary is given a large negative value to accelerate electrons downward. The solutions for a wide range of dimensionless parameters show that the double layer forms just above a critical altitude that occurs approximately where the ionospheric density has fallen to the magnetospheric density. Below this altitude, the ionospheric ions are gravitationally confined and have the expected scale height for quasineutral plasma in gravity