 Solution

For a ring whose total bending angle $2\pi$ is supplied by dipoles with the computed radius, the single-electron energy loss per turn isA stored current $I$ corresponds to $I/|e|$ electron turns per second: the number of stored electrons times the revolution rate. ThereforeThis is the whole beam's radiated power, not the power accepted by one beamline. If the specified radius describes only one dipole and the other bends are different, the radiation integral is needed instead:The numerical result uses the standard equal-radius-bend assumption; the ring circumference, including straight sections, is not required. The RF system must replenish this loss to maintain stored beam energy.