Equipotential model for auroral arcs: The theory of two-dimensional laminar electrostatic shocks

The two-dimensional current-driven shock theory of Swift (1976) is reformulated in a way that removes previous restrictions on the shock thickness in relation to an ion gyrodiameter and also makes it possible to include effects of finite gyrational energy of the ions. The theory is applied to a shock model consisting of cold streaming electrons of magnetospheric origin and streaming ions of ionspheric origin, and it is shown that shock widths will be slightly less than the gyrodiameter of an ion whose energy is equal to the maximum potential difference across the shock. It is also shown that ions in passing through the shock may gain gyrational energy on the order of 10% of the parallel and the E x B energy gain. The theory also requires that the electron beam flux be largest on field lines where the precipitating electron experiences the largest energy gain