  We address the existence of stationary solutions of the Vlasov-Poisson system
on a domain $\Omega\subset\mathbb{R}^3$ describing a high-temperature plasma
which due to the influence of an external magnetic field is spatially confined
to a subregion of $\Omega$. In a first part we provide such an existence result
for a generalized system of Vlasov-Poisson type and investigate the relation
between the strength of the external magnetic field, the sharpness of the
confinement and the amount of plasma that is confined measured in terms of the
total charges. The key tools here are the method of sub-/supersolutions and the
use of first integrals in combination with cutoff functions. In a second part
we apply these general results to the usual Vlasov-Poisson equation in three
different settings: the infinite and finite cylinder, as well as domains with
toroidal symmetry. This way we prove the existence of stationary solutions
corresponding to a two-component plasma confined in a Mirror trap, as well as a
Tokamak.
