Synthetic multidimensional plasma electron hole equilibria

Methods for constructing synthetic multidimensional electron hole equilibria without using particle simulation are investigated. Previous approaches have various limitations and approximations that make them unsuitable within the context of expected velocity diffusion near the trapped-passing boundary. An adjustable model of the distribution function is introduced that avoids unphysical singularities there, and yet is sufficiently tractable analytically to enable prescription of the potential spatial profiles. It is shown why simple models of the charge density as being a function only of potential cannot give solitary multidimensional electron holes, in contradiction of prior suppositions. Fully self-consistent axisymmetric electron holes in the drift-kinetic limit of electron motion (negligible gyro-radius) are constructed and their properties relevant to observational interpretation and finite-gyro-radius theory are discussed.