Characterizing an Improved Broad Band Impedance*

A phenomenological model of broadband impedance containing two free parameters has been recently proposed. This paper attempts to assign physical charaterizations to these free parameters by relating them to the geometric dimensions of a stand-alone cavity structure. Contributed paper at the Broadband Impedance Measurements and ModelZing Workshop SLAC, Stanford, USA February 28 March 2, 2000 ‘Work supported by Department of Energy contract DE-AC03-76SFOO515. One problem with the usual broad band resonator impedance model is that it behaves as a pure capacitance at high frequencies, i.e. Z(w) N i/w. This is not the correct behavior because at high frequencies, we expect a cavity to be described by the diffraction model, for which Z(w) N (1 + i)w-‘i2. To overcome this problem, it has been suggested that an improved longitudinal broad band impedance model can be parametrized as[l, 21 z(w) = (1 -:WwLT)S,2 (1) Compared with the usual broad band resonator model, the impedance model (1) allows for the correct behavior at high frequencies. The attempt of this note is to connect the free parameters L and T in Eq.( 1) to the geometric dimensions of a cavity, shown in Fig.1. We are aware that, depending on the various relative sizes of g, b, and d, the resulting model will have varying degrees of accuracy. However, we intend to proceed in a simplistic and straightforward manner.