Shielding mechanisms' influence on the ratio of perpendicular to parallel scale lengths of multidimensional plasma electron hole equilibria are analyzed theoretically and computationally. It is shown that the ``gyrokinetic'' model, invoking perpendicular polarization, is based on a misunderstanding and cannot explain the observational trend that greater transverse extent accompanies lower magnetic field. Instead, the potential in the wings of the hole, outside the region of trapped-electron depletion, has isotropic shielding giving $\phi\propto { \rm e}^{ -r/L}/r$, with the shielding length $L$ equal to the Debye length for holes much slower than the electron thermal speed. Particle in cell simulations confirm the analysis.
Categories: physics.plasm-ph