Charged particles emiting radiation

Question

I tried to find the reason by couldn't get the right answer. I wished to know that if both proton and electron have same acceleration, do they radiate same amount/amplitude of EM radiation. Also, since quarks have electric charge, do they radiate photons along with gluons (which I have not heard much about)?

Answer 1

Proton and electron have exactly the same charge so they would radiate the same amount of EM radiation as per Larmor Formula. Relativistic generalization of it could be calculated through Liénard–Wiechert potential, but it is still going to be independent of the mass.

Quarks are charged particles with a charges equal to the fraction of the electron charge ($\frac{1}{3}$, $\frac{2}{3}$, $\cdots$), and thus are obliged to interact with Electromagnetic field too.

---

This answer might be useful too.

Answer 2

Charged particles emit synchrotron radiation in the special case of moving perpendicularly to a magnetic field, and this radiation depends on mass.

The LEP electron synchrotron has a rated energy of 50 GeV and a radius of 4300 meters. This gives a relativistic gamma of about 98,000 compared to a gamma of 54 for a 50 GeV proton (see relativistic kinetic energy calculation). At that energy, the velocity is essentially c, so the synchrotron radiation power for a single electron can be calculated as follows:

Two-tenths of a microwatt may not sound like much loss, but per electron it is enormous! At this energy the proton velocity would also be essentially c, so the synchrotron radiation loss for the two particles scales like their gammas. So the loss rate for the electron is (97833/54)^4 or over 10^13 times the loss for a proton of the same energy in the same synchrotron.

So for circular accelerators the energy loss of an electron is much greater than for a proton, and that is why the future plans after LEP are talking of a linear collider, (also here page8).

By contrast the radiation in linear, one dimensional acceleration is smaller in its dependence on the mass of the particle :

Note the smaller power dependence. Thus ligher particles radiate more, but heavier one do also.

Quarks are not free , and radiation is expressed in Feynman diagrams and yes, there are electromagnetic interactions of quarks, but the strong ones dominate due to their strength. If you are discussing within the bound state of a proton or a neutron, that is taken into account with the lattice QCD models used.(example: Electromagnetic Splittings and Light Quark Masses in Lattice QCD A. Duncan, E. Eichten, and H. Thacker Phys. Rev. Lett. 76, 3894 (1996) )

I have toclarify that in this discussion I am talking about radiated energy, which is the important factor in constructing accelerators. And radiated energy depends on the mass of the particle. At the energies of accelerators the velocities are fractions of the velocity of light.