Analytical calculation of the longitudinal space charge and resistive wallimpedances in a smooth cylindrical pipe - art. no. 026503

The longitudinal space charge and resistive wall impedances have been inves tigated in a smooth cylindrical beam pipe. At any point from the beam axis, we obtained an expression for the total impedance, which at the beam surfa ce r=a for infinite pipe wall conductivity gives the expression for the tot al impedance that was derived by Zotter and Kheifets in studying the impeda nce of uniform beams in concentric cylindrical wall chambers, when a single cylindrical chamber is considered [B. W. Zotter and S. A. Kheifets, Impeda nces and Wakes in High-Energy Particle Accelerators (World Scientific, Sing apore, 1998), Chap. 6]. A fitting formula for the space-charge impedance at the beam surface (r=a), which is valid for arbitrary wavelengths, is given . Rather than calculating the impedance with the field on the axis [Joseph J. Bisognano, Fifth European Particle Accelerator Conference (EPAC96), edit ed by S. Myers, A. Pacheco, R. Pascual, Ch. Petit-Jean-Genaz, and J. Poole (Institute of Physics, Bristol, 1996), Vol. 1, p. 328], the fitting formula is obtained by averaging over the transverse beam distribution. We also gi ve another approach for the calculation of the resistive wall impedance usi ng the flux of the Poynting vector at the pipe wall and then compare it wit h the expression obtained from the volume integral over the beam distributi on.