Synchrotron emission from a relativistic loss-cone distribution with application to the ELMO Bumpy-Torus Experiment

Analytic expressions for the power emitted per unit volume per solid angle per unit frequency at perpendicular propagation as synchrotron radiation from a relativistic loss-cone distribution of electrons are derived and compared with exact numerical results. These expressions are useful for understanding how the radiation scales and for inferring properties of the plasma from measurements of the radiation. As an example, it is shown that the temperature and loss-cone angle of the electron distribution in the ELMO Bumpy Torus (EBT) ring can be determined in a straightforward fashion from the ratio of radiation in the two polarizations at two frequencies. Also, it is demonstrated that the loss-cone angle can be determined from the frequency at which this emission ratio is a minimum, even if the emission ratio itself cannot be measured very accurately.