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