Theory of Forbidden Zones in the Flow of a Magnetized Plasma

The theories of Alfvén and Karlson on the two-dimensional flow of a magnetized plasma are discussed. An analog mathematical model is introduced to clarify the various features of Karlson's exact theory of forbidden zones. It is shown that the boundary of the forbidden zone is a contour of constant magnetic field strength. Karlson's theory is generalized to include an arbitrary energy distribution in the plasma, and it is shown that the size of the forbidden zone is not unique. The physical processes which give rise to charge separation and the creation of high electric fields in the plasma are examined in detail, and an elementary derivation of the appropriate Poisson's equation is given.