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FREQUENCY DEPENDENCE OF THE POLARIZABILITY AND SUSCEPTIBILITY OF A CIRCULAR HOLE IN A THICK CONDUCTING WALL

FREQUENCY DEPENDENCE OF THE POLARIZABILITY AND SUSCEPTIBILITY OF A CIRCULAR HOLE IN A THICK CONDUCTING WALL,Wen-Hao Cheng,Alexei V. Fedotov,Robert L.

FREQUENCY DEPENDENCE OF THE POLARIZABILITY AND SUSCEPTIBILITY OF A CIRCULAR HOLE IN A THICK CONDUCTING WALL  
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We calculate a generalized polarizability and susceptibility of a circular hole in a thick metallic plate as a function of hole di- mensions and wavelength. In particular, we construct a varia- tional form which allows us to obtain accurate numerical results with a minimum of computational effort. Numerical results are obtained for a variety of hole dimensions relative to the wave- length. In addition, analytic results are obtained and shown to be accurate to second order in the ratio of the hole dimension to the wavelength for a vanishingly thin wall. I. INTRODUCTION The penetration of electric and magnetic fields through a hole in a metallic wall plays an important role in many devices. In an accelerator, such holes in the beam pipe serve to allow access for pumping, devices for beam current and beam position measure- ment, coupling between cavities, etc. In much of the early work the hole dimensions were considered to be very small compared to the wavelength. The purpose of this paper is to extend the cal- culation to include the effects of finite wavelength, although we still confine our attention to wavelengths no smaller than the hole dimensions. We redefine the conventional static treatment of polarizabil- ity and susceptibility in terms of the cavity detuning, defining a new generalized polarizability and susceptibility. In this way, we include the frequency dependence of the polarizability and sus- ceptibility as well as the contributions of higher multipole mo- ments of the hole. But these generalized polarizability and sus- ceptibilites should only be seen as intermediate vehicles to relate the coupling integrals of interest to the detuning of the cavity by the hole. We will obtain an expression for the detuning of the modes of the symmetric cavity structure due to the presence of the hole. The symmetric cavity structure consists of two identi- cal cavities, each of the length and radius . Clearly the modes will be either symmetric or antisymmetric in the axial coordi- nate. Our analysis will be limited to the modes near the TM , TM and TE modes of the unperturbed pillbox.
Published in 1996.
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