Equilibria and Synchrotron Stability in Two Energy Storage Rings

In a dual energy storage ring, the electron beam passes through two loops at markedly different energies E_{L}, and E_{H}, i.e., energies for low energy loop and high energy loop respectively. These loops use a common beamline where a superconducting linac at first accelerates the beam from EL to EH and then decelerates the beam from EH to EL in the next pass. There are two basic solutions to the equilibrium problems possible, i.e., ’Storage Ring’ (SR) equilibrium and ’Energy Recovery Linac’ (ERL) equilibrium. SR equilibrium mode more resembles the usual single loop storage ring with strong synchrotron motion and ERL equilibrium mode is the case where RF in two beam passes nearly cancels. Calculations based on linear transfer matrix formalism show that longitudinal stability exists for both SR mode and ERL mode in two energy storage rings.