= Solution
\b[<Synchrotron radiation> is radiation from relativistic charges undergoing transverse <acceleration>], for example electrons bent by a <magnetic field>. <Relativistic aberration> concentrates the radiation within an angle of order $1/\gamma$ about the instantaneous velocity. An observer sees short pulses as this cone sweeps past; <synchrotron pulse compression> produces a broad spectrum extending far above the orbital <frequency>.
For an ultrarelativistic circular trajectory of curvature radius $\rho$, the characteristic scales are
$$
\boxed{\omega_c\simeq\frac{3\gamma^3c}{2\rho},\qquad\Delta t_{\rm pulse}\sim\frac{\rho}{\gamma^3c}.}
$$
<Synchrotron Radiation in the Geant4 Physics Reference Manual by Geant4 Collaboration>[Critical energy and critical mode number]{ref} The <synchrotron critical frequency> sets the spectral turnover; it is not a sharp upper cutoff. The transverse-acceleration <Lienard formula> gives
$$
P=\frac{q^2\gamma^4v^4}{6\pi\epsilon_0c^3\rho^2}\simeq\frac{q^2c\gamma^4}{6\pi\epsilon_0\rho^2}.
$$
The strong energy dependence is a major loss mechanism in electron storage rings. Radiation observed in the orbital plane is linearly polarized in that plane; away from it the two components generally produce <elliptical polarization>, with opposite handedness on opposite sides. Accelerator light sources exploit its brightness, broad tunable spectrum and pulsed timing. At low speeds the relativistic beaming and high-frequency extension disappear, approaching ordinary cyclotron radiation.<Synchrotron Radiation by Richard Fitzpatrick>[Relativistic radiation cone, pulse compression and synchrotron spectrum]{ref}
\Image[/past-exam-of-the-optics-and-electrodynamics-course-of-the-university-of-cambridge/2016/paper-1-synchrotron-beaming.png]
{title=Radiation is concentrated around the instantaneous tangent to a relativistic circular orbit}
{source=paper-1-synchrotron-beaming.py}
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