= Solution
A shorter radiation flash has a broader <Fourier transform>. From <1/c/iii>, its characteristic angular-frequency bandwidth is
$$
\boxed{\Delta\omega\sim\Delta t_{\rm arr}^{-1}\sim\frac{c}{R}\gamma^3.}
$$
At fixed bending radius this scales as $\gamma^3$ as $v\to c$. The standard synchrotron critical angular <frequency> makes the same scaling explicit:
$$
\boxed{\omega_c=\frac{3c}{2R}\gamma^3.}
$$
A periodically circulating <electron> produces harmonics of its revolution <frequency>. The very large harmonic range, of order $\gamma^3$, forms the familiar effectively continuous broad synchrotron spectrum at ordinary detector resolution. The result concerns the intrinsic spectrum of the radiation, not merely the slow envelope imposed by a long incoherent bunch. Ordinary <frequency> is $\nu=\omega/(2\pi)$; mixing cycles per second with radians per second would introduce a spurious factor of $2\pi$ into photon-energy estimates.<Synchrotron Radiation in the Geant4 Physics Reference Manual by Geant4 Collaboration>[critical-energy formula and validity discussion, critical harmonic number $3\gamma^3/2$]{ref}
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