Theory of Cerenkov and transition radiation from layered structures

A scattering theoretical approach is used to describe the generation of bot h transition and Cerenkov radiation due to the passage of fast electrons th rough layered, in general absorptive, dielectrics. It leads to a considerab le improvement over the coherent summation method usually employed. Reflect ion of the produced radiation from the layer interfaces is now properly tak en into account and absorption of radiation, if present, is automatically t aken care of. The usual restriction that the energy of the produced photons must be small relative to the initial electron energy is lifted. In contra st to existing theories the production of Cerenkov radiation, if it takes p lace, is included as well. Our expressions for radiation production feature the eigenmodes of the Helmholtz equation fur the dielectric and we discuss how the latter can be obtained by means of a transfer matrix formalism. A numerical evaluation shows that under the appropriate conditions our result s are in agreement with those from the coherent summation formalism. Finall y, we present numerical results that give an impression of the relative yie lds for transition and Cerenkov radiation.