The radial power transmission resulting from a particle beam of parabolic (quadratic) transverse charge distribution
have been studied theoretically. The particle beam is moving at constant speed down a resistive cylindrical pipe of finite
wall thickness. The wave equations for the electromagnetic fields induced by the beam motion inside the cylindrical pipe
have been derived and solved. The coefficient of radial power transmission through the beam-pipe wall have been obtained analytically and then analyzed numerically for different beam energies, different wall conductivities and different wave mode frequencies. The radial power transmission is found to increase with increasing beam energy, to decrease with
increasing wall conductivity and it is higher for the wave modes of lower frequencies.