We know that a charged particle moving at uniform speed does not radiate. However, when travelling sufficiently fast in a medium, the build up of wavefronts cause a shockwave to form, which we observe as Cherenkov radiation. As the name suggests, the waves in the Cherenkov radiation radiate away to infinity.
Everytime the particle 'enters a new position in space', its electromagnetic influence propagates outwards in a wave-like manner. At subluminal speeds, there is no radiation field.
At superluminal speeds, I'd expect the picture to be similar, except that the wavefronts build up along a line forming a shock wave. Since Maxwell's theory is a linear one, I am inclined to think that this shockwave, being a superposition of 'circular waves', is non radiative. Yet we have the phenomenon of radiation. This seems a bit contradictory.
Am I thinking about this correctly, or is it plain wrong to think of drawing this analogy for electromagnetic wave to acoustic waves?