Plasma Expansion in a Magnetic Field

The expansion of a hot plasma in a magnetic field is treated. A background atmosphere may be present, but in examples emphasized the atmospheric pressure is low enough so that its influence is less than that of the magnetic field. The calculation begins after an initial collisional phase, during which free expansion transforms most of the energy into outward radial motion. It is demonstrated by means of a modified virial theorem that this initial outward momentum then dominates the dynamics until expansion is first halted by the field. Though allowed by the theorem, complications such as shock formation, plasma instability, and sweeping up an atmospheric mass comparable to that of the plasma have limited effect. We derive from the virial theorem a lower bound on the plasma radius as a function of time which compares well with simple models neglecting these complications.