Vlasov-Poisson Equations for Two-Component Plasma: A Scoping Review

Background. According to the state of the contemporary science and based on the challenges the mankind faces, the aggravation of the energy issue, the increased interest in thermonuclear energy, the lack of scoping reviews on the topic “Vlasov-Poisson equations for two-component plasma” actualize the need for this work. Purpose. The purpose of this scoping review is to provide a comprehensive analysis of the results of works devoted to the study of the system of Vlasov-Poisson equations for a two-component plasma written within the period from 2014 to 2022. An overview of fundamental results (theorems, found solutions and estimates) for various domains in space or other special conditions in the system of equations under study will be presented. Methods: This review was conducted in accordance with the PRISMA-ScR guidelines for the search and selection of studies. Sources published between 2014 and 2022 were searched against the Springer database. Articles and original studies were selected according to the principle that they should strictly correspond to the topic of this review, as well as to a number of criteria described in the protocol. Results. This review included 20 studies from 49 search results. In the studies under consideration, it was revealed that the most studied problem is the first mixed problem for an infinite cylinder, the most common method was the study of stationary solutions. The problem for a toroidal field turned out to be the least studied. Conclusion. The results of this review may be useful to specialists in the field of mathematical physics, young scientists interested in progress in the study of this problem.