This study considers the self-consistent formation and dynamics of electron clouds interacting with a background neutral gas through elastic and inelastic (ionization) collisions in coaxial geometries similar to gyrotron electron guns. These clouds remain axially trapped as the result of crossed magnetic field lines and electric equipotential lines creating potential wells similar to those used in Penning traps. Contrary to standard Penning traps, in this study, we consider a strong externally applied radial electric field which is of the same order as that of the space-charge field. In particular, the combination of coaxial geometry, strong radial electric fields, and electron collisions with the residual neutral gas (RNG) present in the chamber induce non-negligible radial particle transport and ionization. In this paper, the dynamics of the cloud density and currents resulting from electron–neutral collisions are studied using a 2D3V particle-in-cell code. Simulation results and parametric scans are hereby presented. Finally, a fluid model is derived to explain and predict the cloud peak density and peak radial current depending on the externally applied electric and magnetic fields, and on the RNG pressure.