I understand the principle of synchrotron radiation in saying that , when a charged particle gyrates around some magnetic field line it emits energy in the form of photons.
However I can't understand why electrons dominate the process over the much heavier protons and ions? Can someone explain this to me?
It's basically a consequence of the Larmor formula for the power radiated by an accelerated charged particle. This can be written as $$ P = \frac{q^2 a^2}{6 \pi \epsilon_0 c^3},$$ where $q$ is the charge and $a$ is its (time-averaged) acceleration.
When charged particles are accelerated by electromagnetic fields the force depends only on the charge and not the mass; therefore the acceleration will be inversely proportional to the mass. Since $q$ for an electron and proton are of the same magnitude but the proton is 1836 times more massive, then accelerated protons will emit 1836$^2$ less radiative power.
