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Nonlinear electron kinetic structures are regularly observed in space andexperimental magnetized plasmas, called electron phase-space holes (EHs). Theexistence of EHs is conditioned and varies according to the ambient magneticfield and the parameters of the electron beam(s) that may generate them. Theobjective of this paper is to extend the 3D Bernstein-Greene-Kruskal (BGK)model with cylindrical geometry developed by Chen et al. (2004,2004) to includesimultaneously finite effects due to (i) the strength of the ambient magneticfield $\vec{B}_0$, by modifying the Poisson equation with a term derived fromthe electron polarization current, and (ii) the drift velocity $\vec{u}_e$ ofthe background plasma electrons with respect to the EH, by consideringvelocity-shifted Maxwellian distributions for the boundary conditions. Thisallows us to more realistically determine the distributions of trapped andpassing particles forming the EHs, as well as the width-amplitude relationshipsfor their existence.

3D cylindrical BGK model of electron phase-space holes with finite velocity and polarization drift