Easy formula for ultrarelativistic bremsstrahlung?

Question

I am very curious if an easy calculable formula for the bremstrahlung radiation of deeply relativistic, charged particles exists, if they are moving on circular orbit:

$P(E,m_0,Q,r)=?$

...where

• $P$ is the power of the Bremstrahlung radiation;
• $E$ is the total kinetic energy of the particles (we are in deeply relativistic case, thus $E\gg{m_0}c^2$);
• $m_0$ is the total rest mass of the particles;
• $Q$ is the total charge of the particles;
• and $r$ is the radius of the orbit.

If a such clean, trivial formula doesn't exist, a link were also okay, where it can be found.

Answer 1

The radiation from an ultrarelativistic ($v \approx c$) particle on a circular path is called synchotron radiation. The total power radiated from such a particle is $$P = \frac{e^2 a^2}{6\pi \epsilon_0 c}\gamma^4$$ where $a$ is the acceleration and $\gamma$ is the Lorentz factor, $\gamma^2 = 1/(1-v^2/c^2)$.