Photon number emission in synchrotron radiation: Systematics for high-energy particles

A recent derivation of an explicit elementary expression for the mean number $<N>$ of photons emitted per revolution in synchrotron radiation allows a systematic high-energy analysis leading to the result $<N>\simeq 5πα/\sqrt{3(1-β^2)}+a_0α+πα\sqrt{1-β^2}/10\sqrt{3}$ where $a_0$ is a constant, with relative errors of 2.2%, 0.64%, 0.017%, in comparison to the well-known formula tabulated in the literature of 160%, 82%, 17% for $β=0.8$, 0.9, 0.99, respectively.

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