deceleration

I sometimes feel stuck in accelerator physics. I am running computer codes, reading papers and thinking about particles in storage rings that have been accelerated up to high energies. The machine I am working on for example, has electrons with energies of 3 GeV. This corresponds to a relativistic factor gamma of around 6000. Its a strange phenomenon to work at these extremes. Its not very grounded. There is not a feeling that you really understand things.
One of the aspects I've studied have been off-momentum dynamics. Whether particles with slightly different energies or momenta will still stay stable. Particles scattering for example causes a change in their energy and this can cause the particles to be lost.
As I finally start thinking about the relevant equations for off-energy particles, I imagine the deceleration process, the returning of these electrons to rest.
Even electrons themselves are hard to picture, and the whole field has an air of unreality to it.
I guess it says I've been too much of a theorist.