Exact, Analytic, Self-consistent 2-D X-point Model

We have developed an exact analytic model of a two-dimensional X-point structure in a Maxwellian plasma that is self-consistent. A similar approach was used by Harris (1962) to develop an exact analytic one-dimensional current sheet model that has proved quite useful as a basis for studies of collisionless space plasmas in many contexts. Kan (1973) showed how this same formalism could be extended to two-dimensional current sheets. We now show how exact analytic expressions for plasma and magnetic field structures in the vicinity of an X-point can be developed. The plasma model has arbitrary electron to ion mass and temperature ratios and has several adjustable parameters that allow flexibility for adapting the model to particular observed geometries and scale lengths. In the current state of the work the flows and currents are perpendicular to the plane of the X-point structure but extensions of the model to allow flows in the plane may be accomplished by perturbation methods.