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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:



  • $P$ 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.

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up vote 1 down vote accepted

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, $\gamma^2 = 1/(1-v^2/c^2)$.

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And what is the ultrarelativistic acceleration? $\omega^2r$? – peterh May 26 '14 at 19:18
good question: – diffeomorphism May 26 '14 at 19:42
For circular motion $a = v^2/r = \omega^2 r$. – Robin Ekman May 26 '14 at 20:08
This is not taking into account magnetic field or the particles charge (both important factors), this formula does not look correct to me... – Killercam Jan 8 '15 at 12:42

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