Soft X-ray Emission Excited by Electron Beams in a Superlattice

Abstract

Fast moving electrons emit FM waves when passing through a spatially periodic medium (resonant transition radiation).1,2 The wavelength λ of the radiation emitted at an angle θ with respect to the electron trajectory is determined by the formula n ¯ ( λ ) cos θ = β − 1 − r λ / ℓ , where β = v/c is dimensionless speed at the electron, n ¯ ( λ ) is averaged refractive index of the system, r is an integer, and ℓ is the period of spatial modulation. It is conventionally assumed that ultra-relativistic beams (e.g., up to 50 GeV3) are required to attain this kind of emission. We show4 that if the period ℓ is much shorter than a “mean” plasma wavelength of the medium λp, (which can be done by using solid-state superlattices with the spatial period 50–200Å), the critical kinetic energy required to get a radiation, turns out to be extremely low. One can show that when parameter Q = rλp/ℓ ≫ 1, this energy is (eU)cr ≃ mc2/2Q2, which is less than 10 KeV for all conventional materials if ℓ ≃ 100 Å. One can get a significant radiation in the range 10Å–300Å using non-relativistic beams with energies 70–300 KeV. The spontaneous radiation from the system has a conical structure with the emission wavelength changing with angle.