A flux preserving method of coupling first and second order equations to simulate the flow of plasma between the protonosphere and the ionosphere

This paper describes a numerical method developed to solve the interhemispheric flow of thermal plasma, heat and momentum along closed magnetic field tubes in the plasmasphere. The essence of our technique incorporates the best aspects of two former approaches into a single unified code. The first is the so-called shooting or searching method, which employs integro-differential equations, and the second involves the solution of second order nonlinear partial differential equations by conventional iterative techniques. The former method attains optimal performance above -2000 km, and the latter below this altitude. The combined approach yields a satisfactory solution over an entire geomagnetic flux tube, encompassing two low altitude regimes, in the northern and southern ionospheres, and a high altitude regime spanning the distance between them. We demonstrate that the solution is stable and simulate the collapse of the postsunset ionosphere.