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There was a time when physicists where concerned about electron internal structure. The rotating ring model was one of the proposals to explain how a charge density could become stable against electrostatic repulsion, by postulating that the charge is distributed as a ring with angular velocity, which engenders a magnetostatic force that exactly cancels the electrostatic repulsion (actually they don't exactly cancel, they both become equal to the centripetal force)

Now we don't concern ourselves with the electron internal structure anymore, but i wonder if there are other physical circumstances where we can still see a ring of charges to become stable against self-repulsion by this mechanism

One of the problems i see is that it is usually assumed in the analysis that the ring rotates at the speed of light. My question is:

Is possible to stabilize such structure by physical sub-light tangential velocities of the ring?

Edit There have been some research on a related area of nuclear phenomena, namely high spin nuclear deformation (a book reference about such excitations here), a very interesting application of the above ideas is to look out to reduce or eliminate nuclear decay processes in unstable nuclei, by applying a high spin with a strong background magnetic field to such nuclei, something i highlighted in the comments to this answer.

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You use the word "self-magnetostatic", is this to indicate that the magnetic forces counter both the electrostatic repulsion as well as the centripetal acceleration? I'd imagine it's better to refer to this as a "torus" rather than a ring, since the electrostatic force is infinite for a true ring. – Alan Rominger Oct 2 '12 at 18:35
AlanSe, good point. the ring is just the geometrical layout, but the electron charges are still supposed to be placed at discrete intervals in the circle – lurscher Oct 2 '12 at 18:54

My opinion is that stability can only be achieved by continuous feeding of energy to the electron ring, due to the loss of energy from synchrotron radiation. The higher the energy (velocity closer to c) the stronger the effect, that is why designs for circular rings for electron accelerators stopped at LEP energies.

At a Lorentz factor ( = particle energy/rest mass = [104.5 GeV/0.511 MeV]) of over 200,000, LEP still holds the particle accelerator speed record extremely close to the limiting speed of light

The next electron collider ILC will be linear.

Reading the wiki article on accelerators will enlighten you on the subject.

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this argument may well apply when the electrons move classically, but i'm less convinced that this can be dismissed so easily when the electrons behave coherently – lurscher Oct 19 '12 at 1:58
How do you envisage inducing coherence in a ring of electrons necessarily produced incoherently ? – anna v Oct 19 '12 at 3:31
honestly no idea. I hope to get a clearer theoretical picture before looking into the experimental difficulties to test such a thing – lurscher Oct 19 '12 at 5:04
I believe it cannot be done in vacuum with magnets. You are really talking of macroscopic bound states. After all the electron around the proton in hydrogen fulfills your requirements. Macroscopic quantum effects occur in superconductivity, for example. Any theoretical exploration should go that way, imo. – anna v Oct 19 '12 at 5:10

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