Finite gyroradius multidimensional electron hole equilibria

Finite electron gyroradius influences on the trapping and charge density distribution of electron holes of limited transverse extent are calculated analytically and explored by numerical orbit integration in low to moderate magnetic fields. Parallel trapping is shown to depend upon the gyroaveraged potential energy and to give rise to gyroaveraged charge deficit. Both types of average are expressible as convolutions with perpendicular Gaussians of width equal to the thermal gyroradius. Orbit-following confirms these phenomena but also confirms for the first time in self-consistent potential profiles the importance of gyrobounce resonance detrapping and consequent velocity diffusion on stochastic orbits. The averaging strongly reduces the trapped electron deficit that can be sustained by any potential profile whose transverse width is comparable to the gyroradius rg. It effectively prevents equilibrium widths smaller than ∼ r g for times longer than a quarter parallel-bounce-period. Avoiding gyrobounce resonance detrapping is even more restrictive, except for very small potential amplitudes, but it takes multiple bounce periods to act. Quantitative criteria are given for both types of orbit loss.