Abstract: Characteristics of the fundamental and harmonic emission from free-electron lasers (FELs) is examined in the spontaneous emission regime. The radiation at both odd and even harmonic frequencies is treated for electron beams with finite emittance and energy spread. For wigglers with many wiggle periods, calculation of the SE by integrating an ensemble of electrons along their exact trajectories becomes exceedingly cumbersome. Therefore, a different technique is used in which the far-field radiation pattern of a single electron is manipulated in transform space to include the effects of emittance. The effects of energy spread can be included by a weighted sum over the energy distribution. The program execution time for wigglers of arbitrary length is negligible. The transverse radiation patterns including the transverse frequency dependences, are given. How this radiation is modeled in FEL simulation codes is discussed.!8
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