Finite gyroradius multidimensional electron hole equilibria

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