Radiated power bending magnet

An electron charge moving on a circular trajectory undergoes a centripetal acceleration if viewed on edge the charge appears to undergo oscillatory motion akin to a dipole. 

In the non-relativistic case the radiated power, Q, is given by the Larmor (1897) formula 

In a SR source the electron moves at a speed close to c so that for a radius of curvature, q, the relativistic generalisation of the Larmor formula is 

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Figure 3.2 Comparison of the emitted power from two different synchrotron storage ring NSLS at 0.8 GeV, and SOLEIL at 2.75 GeV, with that of a blackbody at 2000 K. For SR, bending magnet radiation is considered, with collection angles of 40 mrad x 40 mrad (horizontal x vertical).

Figure 2.7. Schematic diagram of a synchrotron illustrating x-ray radiation output from bending magnets. Electrons must be periodically injected into the ring to replenish losses that occur during normal operation. Unlike in conventional x-ray sources, where both the long-and short-term stability of the incident photon beam are controlled by the stability of the power supply, the x-ray photon flux in a synchrotron changes with time it decreases gradually due to electron losses, and then periodically and sharply increases when electrons are injected into the ring.

Bending magnet. The radiation spectrum emitted from a bending magnet (Fig. 1) is a smooth function of energy characterized by a critical or half-power energy given by... 

Most properties of synchrotron radiation may be derived starting from classical electrodynamics, where an oscillating dipole is subjected to a Lorentz transformation. Assuming that relativistic electrons move on curved trajectories in a bending magnet of the radius R, the radiated power... 

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