On a charge interacting with a plasma of unbounded mass (Q631357)

A system of one positive charge plus a positively charged plasma is considered in \(\mathbb{R}^2\), an infinite region. The term ``infinite'' refers to the main difference this approach is made for: the density is not supposed here to be bounded in contrast with the most existing literature. It is supposed that a background of continuous distribution of neutral particles in thermal equilibrium at high temperature is present (this is referred to as Vlasov-Helmholtz system). To avoid the problem of infinite energy, the finite energy of a region is introduces and it is proven that this function remains finite also at later times. The solution is determined and its existence is demonstrated, the desived properties are discussed.