Analysis of the Transition Region between a Uniform Plasma and its Confining Magnetic Field. II

The case of one-dimensional geometry for the transition region separating a uniform plasma from its confining magnetic field is considered. The magnetic-field profile within the boundary layer is determined by the current distribution, i.e., by the paths of the ions and electrons. The paths of these particles, on the other hand, are determined by the fields in which they move. An exact, self-consistent solution of Maxwell's equations and the equations of motion of the particles is obtained. A detailed analysis is made for a hydrogen plasma. These results are then compared with those of a plasma whose positive constituent is the proton and whose negative constituent has a mass which approaches zero and a speed which approaches infinity in such a way that the energy remains finite. The transition layer thickness for these two plasmas agree to one part in 106. It is shown that this latter case is equivalent to treating the electrons of the hydrogen plasma in the guiding-center approximation.