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We address the existence of stationary solutions of the Vlasov-Poisson system on a domain Ω ⊂ R 3 describing a high-temperature plasma which due to the influence of an external magnetic field is spatially confined to a subregion of Ω. 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 confineddoi:10.3934/krm.2021004 fatcat:ciryeujdwrhrzokogt7jk3hh7u