An electron bunch circulates in the storage ring of a colliding beam accelerator. The current is 500 mA, the speed of the electrons is 0.99 of the speed of light. What is the power of synchrotron emission?

Answer

97 W.

Explanation

The power of the synchrotron radiation may be found from the fourmua
`P=(mu_(u)q^(2)a^(2))/(12pic)`
where a is the acceleration and a the charge of the bunch. Since a = `omega6(2) r` and the current is I = q/T = `q omega //2pi`, where T is the period of circular motion it follows that q= `2pi I //omega`. Substituting into the expression for the power, we obtain
`P=4pi^(2)mu_(0)I^(2)omega^(2)r^(2)//(12pic)`
But `omega r = v` is the velocity of the electron, therefore
`P=pimu_(0)I^(2)v^(2)//3c`