On classical solutions of Vlasov–Poisson system with external magnetic field

We consider the second mixed problem for the Vlasov–Poisson system with external magnetic field in a half–space. This problem models the kinetics of high temperature plasma in a fusion reactor.
If plasma reaches a boundary of the domain, it can lead to the destruction of the reactor. Therefore we study solutions of the above mentioned mixed problem such that the supports of density distribution functions of charged particles are located strictly inside the domain. For this purpose we use an external magnetic field.
It will be obtained sufficient conditions for external magnetic field, which provide existence of global classical solutions having supports of density distribution functions inside the domain [1].
The work is sponsored by the Ministry of Science and Higher Education of the Russian Federation (Megagrant, No. 075-15-2022-1115).