  Synchrotron emission from runaway electrons may be used to diagnose plasma
conditions during a tokamak disruption, but solving this inverse problem
requires rapid simulation of the electron distribution function and associated
synchrotron emission as a function of plasma parameters. Here we detail a
framework for this forward calculation, beginning with an efficient numerical
method for solving the Fokker-Planck equation in the presence of an electric
field of arbitrary strength. The approach is continuum (Eulerian), and we
employ a relativistic collision operator, valid for arbitrary energies. Both
primary and secondary runaway electron generation are included. For cases in
which primary generation dominates, a time-independent formulation of the
problem is described, requiring only the solution of a single sparse linear
system. In the limit of dominant secondary generation, we present the first
numerical verification of an analytic model for the distribution function. The
numerical electron distribution function in the presence of both primary and
secondary generation is then used for calculating the synchrotron emission
spectrum of the runaways. It is found that the average synchrotron spectra
emitted from realistic distribution functions are not well approximated by the
emission of a single electron at the maximum energy.
