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An algorithm for calculating the spectral intensity of radiation due to thecoherent addition of many particles with arbitrary trajectories is described.Direct numerical integration of the Lienard-Wiechert potentials, in thefar-field, for extremely high photon energies and many particles is madecomputationally feasible by a mixed analytic and numerical method. Exactintegrals of spectral intensity are made between discretely sampledtrajectories, by assuming the space-time four-vector is a quadratic function ofproper time. The integral Fourier transform of the trajectory with respect totime, the modulus squared of which comprises the spectral intensity, can thenbe formed by piecewise summation of exact integrals between discrete points.Because of this, the calculation is not restricted by discrete samplingbandwidth theory, and hence for smooth trajectories, time-steps many orderslarger than the inverse of the frequency of interest can be taken.

Algorithm for calculating spectral intensity due to charged particles in arbitrary motion