Transportation process of relativistic electron beam in gaz-plasma mediums and longitudinal magnetic field

The transportation modeling problem of relativistic electron beam in gaz-plasma medium and external longitudinal magnetic field is examined. The kinetic equation of the distribution function for quasistationary rotationally beams of relativistic electrons in paraxial approximation as well as a lack of collective azimuth movements is deduced. Preceding from this one the non-linear system of integral and differential equations for moments of the distribution function till second order inclusive is deduced. The obtained system is solving numerically in conformity with the focusing problem of electronic beam. The focusing is provided with using of external longitudinal magnetic field as well as presence of medium density gradient in to which the beam is injected. The system of differential equations is deduced by integration of moments ones through the coordinate space taking into account some approximations. The obtained equations describe integral features of the electron beams, which are used for the first approximate description of its transportation.