= Solution
<Synchrotron radiation> is emitted by relativistic charges accelerated along curved paths. A <magnetic field> can supply the transverse <acceleration> while doing no work on the charge; the radiated <energy> must ultimately be replenished if the orbit <energy> is to remain constant. <Relativistic beaming> confines much of the radiation to angles of order $1/\gamma$ about the instantaneous <velocity>.
For circular motion of curvature radius $\rho$ and $\gamma\gg1$,
$$
\boxed{\omega_c\simeq\frac{3\gamma^3c}{2\rho},\qquad
P\simeq\frac{q^2c\gamma^4}{6\pi\epsilon_0\rho^2}.}
$$
The exact classical circular-orbit <power> contains an additional factor $\beta^4$. A distant observer sees short pulses as the beamed direction sweeps past, producing a broad high-frequency spectrum. Radiation is predominantly linearly polarized in the orbital plane and becomes elliptically polarized off it. The critical <frequency> is a spectral scale, not a monochromatic emission <frequency> or a hard cutoff.
\Image[/past-exam-of-the-optics-and-electrodynamics-course-of-the-university-of-cambridge/2014/paper-1-oe2014-synchrotron.png]
{title=Original geometric synchrotron-beaming schematic: radiation near the velocity tangent, cone angle of order inverse Lorentz factor and curved electron trajectory}
Storage rings provide intense radiation for <spectroscopy> and <diffraction>, while relativistic electrons in astrophysical <magnetic fields> also produce synchrotron emission. The classical theory relates total <power>, angular beaming and spectrum to the particle's trajectory; sufficiently strong quantum recoil requires corrections.<On the Classical Radiation of Accelerated Electrons by Julian Schwinger>[Physical Review 75, 1912 (1949), primary abstract: total radiation, angular preference and high-frequency spectrum of accelerated energetic electrons]{ref}
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