  The time evolution of a two-component collisionless plasma is modeled by the
Vlasov-Poisson system. In this work, the setting is two and one-half
dimensional, that is, the distribution functions of the particles species are
independent of the third space dimension. We consider the case that an external
magnetic field is present in order to confine the plasma in a given infinitely
long cylinder. After discussing global well-posedness of the corresponding
Cauchy problem, we construct stationary solutions which indeed have support
away from their confinement device. Then, in the main part of this work we
investigate the stability of such steady states, both with respect to
perturbations in the initial data, where we employ the energy-Casimir method,
and also with respect to perturbations in the external magnetic field.
