Incidence of an electron layer on an electrically insulated body with an unsteady self-consistent positive charge

Dynamics of an electron layer incident on the surface of an electrically insulated conducting body with an unsteady self-consistent positive charge is investigated. At the initial instant, the electron velocity is directed toward the body and the electron layer is not adjacent to the body surface. One-dimensional plane, cylindrical, and spherical electron motions in vacuum and against the background of motionless ions and neutral particles are considered. Exact analytical solutions to the set of nonlinear plasma hydrodynamics equations with absorbing boundary conditions for electrons are obtained. The spatial and time dependences of the electric field, electron density, and electron velocity are found. The time evolution of the surface charge density is determined.