Solution

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/2017/s19/2/b/solution

Doubling the number of identical-angle bends halves each angle. The minimum emittance scales as , so it becomes . At unchanged energy and unchanged individual magnet length, the bending radius doubles and field halves, giving T and .
At fixed stored current the loss per turn, proportional to , halves: twice as many equal-length bends each have one quarter of the original contribution. Total radiation power therefore halves. The spectrum softens by the factor-two critical-energy change. The characteristic high-energy vertical opening angle remains of order at fixed energy, while each magnet's horizontal sweep halves. At a fixed absolute photon energy the normalized spectral position changes, so a claim that every angular distribution is identical would be too strong. Lower emittance also reduces the electron source size/divergence subject to the optical functions.

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