The Short-Range Resistive Wall Wakefields

In this paper we find the short range resistive wall wakefields of a point particle in a cylindrical tube, both for a dc model of conductivity and for an ac model. The distance scale SO depends on the radius of the tube and on the conductivity of the metal walls, and in typical structures is on the order of tens of microns. For both ac and dc models the short range wakefield is found to be well approximated by a simple, high frequency resonator wakefield. For the dc model of conductivity the frequency of the resonance is given by w/c = fi/ so and the Q-factor equals a/2. We provide a physical model to explain these results. For the ac model of conduc- tivity the resonance frequency depends also on the relaxation time of the metal 7. For large cr/so the frequency becomes w/c = dm, with oP the plasma frequency of the metal and b the tube radius, and the Q-factor becomes large. Finally we obtain the wakefields of a short Gaussian bunch, and then calculate the loss factor. From our results we find that, even for short bunches, the loss factor for the ac model is only slightly larger than that for the dc model.