Dispersion-Induced Beam Instability in Circular Accelerators.

The envelope instability near the 90° phase advance in periodically focused space charge dominated beams is a well-known phenomenon in linear transport sections or linacs. The corresponding stop band is usually avoided because of the resulting strong mismatch oscillations and beam loss. We show that in circular accelerators or transport sections including bending magnets the instability is modified due to the effect of dispersion. Using the two-dimensional envelope equations extended by the dispersion equation we identify an additional stop band above 120°. For periodic focusing the stop band results from the confluence of an envelope mode with the newly identified coherent dispersion mode. Results from perturbation theory are compared with the full envelope model and particle-in-cell simulation, which all show good agreement. The newly identified mode has several implications and applications for the characterization of intense beams in circular machines.