A spectral function method applied to the calculation of the wake function for the NLCTA

The equivalent circuit representation of the dipole modes of the SLAC damped detuned structure (DDS) which is being fabricated at LAC has been analyzed by three different methods. The first two are based upon a modal analysis: in the first, damped modes are found by a first order perturbation in the cell to damping manifold coupling strength; while in the second, preferred when the coupling strength is large (as is the case for the SLAC structure) they are determined exactly (a time consuming procedure). The third method, which the authors report here, expresses the wake as a modal sum for modes whose frequencies place them outside the propagation bands of the manifolds (a minor contribution) plus a Fourier like integral of a spectral function over the propagation band of the manifolds (the major contribution). They will present comparisons to previous calculations, assessment of appropriate domains of applicability, and applications to the SLAC structure with matched and mismatched manifold terminations.