Ion beam propagation and radiative energy loss of electrons in background plasma

On the basis of Vlasov-Maxwell equations, ion beam propagation is discussed with beam of finite length. The beam velocity distribution function is assumed to have a form of product of a modification function g which depends on time and axial coordinate multiplied by a steady solution fb0 which is a known function of particle velocity and radial coordinate. This unknown function g depends upon the electrostatic and induced electric fields, so these electromagnetic field should be solved from the Maxwell equations by using beam distribution function and motion of electrons in background plasma. The background electron radiation plays an important role to determine the background plasma temperature