Two-Dimensional, Time-Independent Solutions for Plasma Moving through a Uniform Transverse Magnetic Field

If particle gyroradii and drift velocities are small in a collisionless plasma which is infinite and uniform in the direction of the straight magnetic field B, it may be shown in the time-independent case that particle densities and B are constant on any surface of constant electrostatic potential. Using the magnetohydrodynamic equation of motion, it follows that the particles move very nearly along these equipotential surfaces, and an expression for the charge density may be derived. From the resulting Poisson equation, solutions for plasma crossing a uniform B0 field may be obtained; collectively these solutions may appropriately be termed the ``double-vortex'' model from their drift velocity patterns.