Recently it has been pointed out that numerical simulation of some systems containing charged particles with highly relativistic directed motion can by speeded up by orders of magnitude by choice of the proper Lorentz boosted frame. A particularly good example is that of short wavelength free-electron lasers (FELs) in which a high energy (E0>- 250 MeV) electron beam interacts with a static magnetic undulator. In the optimal boost frame with Lorentz factor gamma F, the red-shifted FEL radiation and blue shifted undulator have identical wavelengths and the number of required time-steps (presuming the Courant condition applies) decreases by a factor of g2 F for fullyelectromagnetic simulation. We have adapted the WARP code to apply this method to several FEL problems including coherent spontaneous emission (CSE) from pre-bunched e-beams, and strong exponential gain in a single pass amplifier configuration. We discuss our results and compare with those from the 'standard' FEL simulation approach which adopts the eikonal approximation for propagation ofthe radiation field.
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