Relativistic Sheet Pinches with Current Shear

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A new class of self-consistent, one-dimensionally confined, neutral solutions to the stationary Vlasov and Maxwell equations is presented. Apart from the special cases of conventional sheet pinches, these equilibria all display current shear (which, in analogy with magnetic shear, is defined as rotation of the current vector as the plasma is traversed in the confined direction). The new solutions are obtained numerically, after the relativistic Vlasov-Maxwell problem has been reduced to a single second-order nonlinear ordinary differential equation for the critical component of the self-consistent vector potential. The physical properties of representative equilibria are given in graphical form. Included in addition to thin sheet pinches are broader configurations with a region of nearly uniform plasma number density, bounded by rather sharp plasma/magnetic-field interfaces.