Theory of wakefields in a dielectric-lined waveguide

Abstract

Excitation of wakefields from a short charge bunch moving parallel to the axis of a dielectric-lined cylindrical waveguide is analyzed. This situation amounts to generation of Cerenkov radiation in a transversely bounded system. Wakefields are expanded into an orthonormal set of hybrid electric-magnetic eigenfunctions for this waveguide geometry. The orthonormalization relations for this system are obtained, evidently for the first time, both for a stationary source and for a localized moving source such as a charge bunch; it is shown that these orthonormalization relations differ. Forces arising from wakefields are found, valid within and behind a distributed bunch. Deviation of bunch distribution from axisymmetry leads to generation of dipole modes of significant amplitude that may lead to instability. Poynting's theorem is examined for this system, and it is shown that convected Coulomb field energy must be subtracted from the Poynting flux to obtain the radiation power. This power, which balances drag on the bunch as calculated directly from the fields, is shown to flow in a direction opposite to that of the charge bunch. The results are easily generalized to bunches of arbitrary length and charge distribution, and to a train of such bunches. Numerical examples are presented for monopole, dipole, and quadrupole wakefield forces, and sample electric field patterns are shown to assist in understanding the unusual nature of this type of Cerenkov radiation. For a 2-nC rectangular drive bunch of length 0. 20 mm, moving along the axis of an alumina-lined waveguide (varepsilon=9.50) with inner and outer radii of 0.50 and 5.0 mm, a peak accelerating gradient behind the bunch of 155 MeV/m is predicted. This relatively high magnitude of accelerating gradient suggests that a simple uniform dielectric pipe could be the basis for the structure of a future high-gradient electron/positron linear accelerator, once low-emittance, kiloampere, subpicosecond electron bunches are available in the laboratory.