We present a one-dimensional model which gives a novel physical interpretation to the specific state of an ensemble of electrons continuously injected into an electrostatic potential well immersed in a strong applied magnetic field preventing radial expansion. When the space-charge field of the electrons accumulated in the potential well compensates the external electrostatic field, a force-free steady-state of the electron cloud forms. This state of equilibrium is known in another context as a squeezed state of an electron beam. It is shown that the spatial distribution of the electron number density in this steady-state correlates with the shape of the potential well. Perturbations of the steady-state propagate along the electron cloud in the form of Trivelpiece-Gould modes.
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