Full wave theory of photon acceleration in a cavity

We describe the interaction of electromagnetic radiation in a lossless cavity with a moving electron density perturbation, using the linear mode coupling theory. We calculate analytically and numerically the full spectral content of the radiation inside the cavity when the perturbation is associated with an electron-beam or with an ionization front. It is shown that the spectrum of the electromagnetic wave is much broader than it is usually assumed by other theories. The results are compared with the predictions of the Hamiltonian theory of photon acceleration.