Electron accelerators and storage rings are usually above 1 or 2 GeV. They are usually used for synchrotron radiation sources, external electron beams, or sometimes colliding beams. There are several facilities in the U. S.; Brookhaven, Argonne. Jefferson, Lawrence Berkeley, Cornell, Madison, to name a few. In addition to the longitudinal energy, the beams have transverse energy. This comes about because the electrons in the bunches, often about 1 nanoCoulomb (nC), are all mutually repelled by Coulomb forces, and therefore oscillate back and forth transversely, focused by the quadrupoles (strong focusing). The transverse aperture of the machine has an aperture limit, called the acceptance. The beam has a transverse size, called the emittance (units = mm-mrad). If the transverse emittance exceeds the acceptance, electrons are lost (hit the aperture). Similarly, in the longitudinal (energy) coordinate, electrons oscillate back and forth in the stable RF "bucket", and if the longitudinal emittance (units=eV-sec) exceeds the longitudinal acceptance, they are lost. Electrons continuously radiate away lots of energy (synchrotron radiation) and need to replace that energy every turn in RF cavities. An electron with above average energy takes longer to go around the ring ("above transition") and gets less acceleration the next time around (phase stability).
Bob S
