Power transmission of a particle beam moving in a resistive cylindrical tube

The radial power transmission resulting from a particle beam of parabolic (quadratic) transverse charge distributionhave been studied theoretically. The particle beam is moving at constant speed down a resistive cylindrical pipe of finitewall thickness. The wave equations for the electromagnetic fields induced by the beam motion inside the cylindrical pipehave 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 withincreasing wall conductivity and it is higher for the wave modes of lower frequencies.