Jackson Paper

We consider an electron moving in a constant magnetic field (z direction). The trajectory is described by a an angular frequency $\omega_0 = \frac{\beta c}{\rho}$

(1)
\begin{align} x= \rho sin\omega t \end{align}
(2)
\begin{align} y=\rho (1-cos\omega t) \end{align}
(3)
$$z=0$$

The calculation follows in equation in equation 33 that gives the radiated intensity per unit solid angle, per unit frequency.