Explicit expression for the photon number emission in synchrotron radiation
An explicit and remarkably simple one-dimensional integral expression is derived for the mean number $ $ of photons emitted per revolution in synchrotron radiation. The familiar high-energy expression $5πα/\sqrt{3(1-β^2)}$, printed repeatedly in the literature, is found to be inaccurate and only truly asymptotic with relative errors of 160%, 82% for $β=0.8$, 0.9, respectively. A new improved high-energy expression for $ $ is given.