= Bunch-length broadening of synchrotron radiation
{title2=$\Delta t_b\sim L_b/u$}
In a fixed tangent viewing geometry, an <electron> bunch of longitudinal <length> $L_b$ passes the same radiating point over approximately $L_b/u$. Different <electrons> then emit from nearly the same point at different times. The incoherent pulse envelope is the <convolution> of the single-<electron> intensity profile with the bunch's passage-time distribution, assuming equal particle trajectories and a linear detector. Its width generally has scale at least $\max\{L_b/u,r/(c\gamma^3)\}$. A bunch short compared with the orbit need not be short compared with the intrinsic single-<electron> pulse.
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