Global compactly supported solutions of the mixed problem for the Vlasov-Poisson system and plasma confinement. Part 2.

The second mixed problem for the system of Vlasov-Poisson equations with an external magnetic field is considered. The unknown functions are the potential of a self-consistent electric field and two distribution functions of charged particles (positively charged ions and negatively charged electrons). If a large number of charged particles hit the wall of the vacuum chamber, the reactor may collapse. Therefore, an external magnetic field is created that holds the particles at some distance from the wall of the vacuum chamber. The report will formulate sufficient conditions to ensure plasma confinement, i.e. the location of the supports of the distribution functions of charged particles in spatial variables at some distance from the boundary of the domain. The main results will be presented with proofs. The report consists of 2 parts. Literature [1] A.L. Skubachevskii, The Vlas-Poisson statement for a two-component plasma with an external magnetic field// UMN, Vol.69, № 2 (2014), 107-148. [2] A.L.Skubachevskii, On the Existence of Global Solutions for the Vlasov–Poisson System in a Half-Space and Plasma Confinement, Lobachevskii J. of Math., V.45, № 2 (2024), 280-292.