 Solution

ID: past-exam-of-the-symmetry-and-relativity-course-of-the-university-of-oxford/2015/1/c/v/solution

Using the conventional critical scale rather than guessing a precise Fourier-width coefficient,

E_{c} = ℏ ω_{c} = \frac{3ℏ c γ ^{3}}{2 R} = 1.07 \times 1 0^{2} eV, λ_{c} = \frac{h c}{E _{c}} ≃ 11.6 nm .

This is extreme ultraviolet and the very soft X-ray boundary, with a broad spectrum extending on either side; it is not a hard, multi-keV X-ray source at the stated large bending radius. The characteristic energy is not a sharp upper cutoff. For orientation, the standard angle-integrated spectral power per unit frequency peaks near

0.29 E_{c} ≃ 31

eV, also in the extreme ultraviolet; a particular angular acceptance weights that spectrum differently.

The crucial scale follows from both the

3

GeV energy and the

561

m radius. Using only the fact that synchrotron sources can make X-rays, or replacing the bending radius by a much smaller unstated value, would misidentify the characteristic photon energies here. The critical-energy convention and the broadband character are described by the primary radiation model.^[ref]

 New to topics? Read the docs here!