The Short-Range Resistive Wall Wakefields

In an sccelerstor when the bunch length becomes comparable to a characteristic distance ss, one which depends on the radius and the conductivity of the besm tube and in typical structures is on the order of lena of microns, the usud furmulas for the resistive wall wakefield do not apply. In this report we derive the short-range resistive wdl wakefields of an ultra-relativistic point prrtick in a metallic. cylindrical tube, both for s model in which the wall conductivity is taken to be independenl d frequency and for one in which s hcgwncy dependence is included. On this scale the rakefield is found (0 be dominsted by a dsmped, high frequency resonator component. For the case of constant conductivity the -snt frequency is given by w = fic/ss and the Q-fsctor equds A/2. We provide s physicsl model to explain these results. For the case of s frequency dependent conductivity the resonator parameters depend also on the relaxation time of the metal r. For cr/ss 2 0.5 the frequency w w m, with W, the plasma frequency of the free electrons in the metal and b the tube radius, and the I/e damping time becomes 4~. Finally. we cslculate the wsketield and Ias fsctor of a short Caussiau bunch.