particle physics - Conceptually speaking, why does synchrotron radiation arise?

First, a bit of background. I'm a chemist who works with synchrotron-based techniques, but I'm focussed on materials analysis rather than synchrotron physics.

I'm struggling to work out where synchrotron radiation (SR) actually comes from. Why does subjecting an electron to radial acceleration cause it to emit photons? I understand, with Bremsstrahlung radiation that the energy from the decelerating particle has to go somewhere. My first thought was that SR may arise from a similar effect, as my understanding is that you do work when you radially accelerate a particle. I reasoned that, since the magnitude of its velocity remains constant, and the magnitude of the kinetic energy (KE) remains constant, SR must result from conservation of energy (i.e. the work done in the radial acceleration is converted into SR). However, I've since read that emission of SR causes the electrons in the storage ring to lose energy. And, this energy must be resupplied by the inclusion of RF cavities in the ring. This would suggest that SR comes from the KE of the electron, not from the work of the magnet on the electron. (On reflection, I can't see how a permanent magnet could "do work".)

So why is SR emitted?

(Please bear in mind, that as a chemist, I have next to no knowledge of relativity, electrodynamics, Maxwell's equations, etc. I'm really just looking for a conceptual understanding. I don't mind a mathematical answer if you can give one without assuming knowledge of such physics. But, I imagine that's unlikely.)

Edit: Any good textbook recommendations would be helpful too. All the books I've read either gloss over the issue or use physics that goes over my head.

Answer

Conceptually the idea is based on a simple principle: conservation of linear momentum.

Every time a charged particle has to be accelerated, a photon has to be involved. If you want to linearly accelerate a charged particle, you have to shoot photons at its back. If you want to stop a charged particle (decelerate), it has to emit photons in the forward direction: at every emission the charged particle recoils back and slows down.

The circular motion is not much different. The acceleration in this case points towards the center of the circle (centripetal), so the charged particle has to emit a photon outwards, tangentially to the circle, every time it needs to curve. You can imagine it's trajectory not as a perfect circle but as a almost regular polygon with many sides. This means that in circular accelerators the charged particles have to be constantly resupplied with energy.

Now, about the energy transfer from the accelerator to the charged particle, you are perfectly right when you say that a fixed magnetic field doesn't transfer energy, but fortunately any other kind of EM field does. In particular I'd like to quote this page on wikipedia:

While a classical cyclotron uses both a constant guiding magnetic field and a constant-frequency electromagnetic field [...], its successor, the isochronous cyclotron, works by local variations of the guiding magnetic field, adapting the increasing relativistic mass of particles during acceleration.

As you can see, the magnetic field is variable and this means that there is also an electric field that can accelerate the charged particles.