Synchrotron radiation spectrum for an intense relativistic E layer

The synchrotron radiation spectrum is calculated for an intense relativistic nonneutral E layer including self-field effects. The analysis is carried out for the class of thin E-layer equilibria described self-consistently by equilibrium distribution functions of the form fe0 (x, p) = R0F(H)δ(Pθ − P0), where H is the energy, is the canonical angular momentum, and R0 and p0 are constants. Since individual electrons execute radial betatron oscillations about a helix with mean radius R0, the single-particle emission spectrum is modified from the conventional Schott-Trubnikov result. To determine the spectrum of radiation emitted by all electrons in the E layer, the single-particle emission spectrum is averaged over the distribution function fe0 (x, p) that self-consistently generates the E layer equilibrium.