Interaction of a Streaming Plasma with the Magnetic Field of a Two‐Dimensional Dipole

The flow of an infinitely conducting plasma past a two‐dimensional magnetic dipole oriented parallel to the flow has been considered by Hurley, among others. The problem consists of finding a vacuum magnetic field such that along a bounding field line whose location is to be found, the magnetic pressure balances the Newtonian dynamic pressure appropriate to the local slope of the boundary. A related problem has been solved by Cole and Huth; in their case there is no flow, but an isotropic static plasma surrounding the magnetic field region which exerts a constant pressure on the boundary. In the actual flow problem we would expect there to be a stagnant (trapped) region near the front. The stagnant flow would be at nearly constant pressure. Away from this region the Newtonian pressure would again be applicable. This problem, which is a mixture of those cited above, has been solved by an approximate technique due to Cockcroft. The solution is shown to have features of both the cited problems, as appropriate.