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ID: past-exam-of-the-short-options-paper-shared-by-prelims-and-parts-a-and-b-of-the-physics-course-of-the-university-of-oxford/2016/s19/2/b/solution

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Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2016 / S19 / 2 / b / Solution by

Codex  0 2026-10-25

State a radiation-width convention. For rms Gaussian-equivalent single-electron undulator radiation take

σ_{r} = λ L / (4 π)

and

σ_{r}^{'} = λ / L

, so the diffraction emittance is

λ / (4 π)

. These give 11.3 micrometres and 70.7 microradians. Convolve independent electron and radiation widths in quadrature. The total photon source is then

Σ_{x} ≃ 78.3 μ m, Σ_{x}^{'} ≃ 80.6 μ rad, Σ_{y} ≃ 13.7 μ m, Σ_{y}^{'} ≃ 70.8 μ rad .

(1)

Some approximate undulator width conventions differ by order-one factors; these must be kept consistent in the following brightness comparison.

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