Abstract
We consider the two-dimensional Vlasov-Poisson system to model a two-component plasma whose distribution function is constant with respect to the third space dimension. First, we show how this two-dimensional Vlasov-Poisson system can be derived from the full three-dimensional model. The existence of compactly supported steady states with vanishing electric potential in a three-dimensional ...
Abstract
We consider the two-dimensional Vlasov-Poisson system to model a two-component plasma whose distribution function is constant with respect to the third space dimension. First, we show how this two-dimensional Vlasov-Poisson system can be derived from the full three-dimensional model. The existence of compactly supported steady states with vanishing electric potential in a three-dimensional setting has already been investigated by in the literature. We show that these results can easily be adapted to the two-dimensional system. However, our main result is to prove the existence of compactly supported steady states even with a nontrivial self-consistent electric potential.
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