Beamstrahlung from colliding electron-positron beams with negligible disruption

We present radiative energy loss formulas for beamstrahlung from colliding electron-positron beams which experience negligible disruption, as determined by numerical simulation. Our computer code uses the correct quantum mechanical photon number spectrum for synchrotron radiation emitted by relativistic electrons to simulate with macroparticles the discrete nature of photon emission. For Gaussian beams with small average electron energy loss, we determine energy loss formulas valid for all radiation regimes from classical to extreme quantum mechanical which depend on only two beam parameters, a quantum radiation parameter ϒ0 and a beam energy per unit length, Γ0.