Three-dimensional envelope instability in periodic focusing channels

Abstract

The space-charge driven envelope instability can be of great danger in high intensity accelerators and was studied using a two-dimensional (2D) envelope model and three-dimensional (3D) macroparticle simulations before. In this paper, we study the instability for a bunched beam using a three-dimensional envelope model in a periodic solenoid and radio-frequency (rf) focusing channel and a periodic quadrupole and rf focusing channel. This study shows that when the transverse zero current phase advance is below 90°, the beam envelope can still become unstable if the longitudinal zero current phase advance is beyond 90°. For the transverse zero current phase advance beyond 90°, the instability stopband width becomes larger with the increase of the longitudinal focusing strength and even shows different structure from the 2D case when the longitudinal zero current phase advance is beyond 90°. Breaking the symmetry of two longitudinal focusing rf cavities and the symmetry between the horizontal focusing and the vertical focusing in the transverse plane in the periodic quadrupole and rf channel makes the instability stopband broader. This suggests that a more symmetric accelerator lattice design might help reduce the range of the envelope instability in parameter space.

Multi-Particle Simulation Techniques

“…But in a circular accelerator, violating the symplectic condition may result in undesired numerical errors in the long-term tracking simulation. Recently, symplectic multi-particle model was proposed for self-consistent space-charge simulations [31,32].…”

Intensity limitations due to space charge for bunch compression in synchrotrons

“…This is different from the case of a high current linac, where a symmetrical three-dimensional set of envelope equations is often used (for example, see Refs. [12,20]). Second, even for fast bunch rotation, the synchrotron frequency is much smaller than the transverse one, which means space charge is increasing "adiabatically" for the transverse motion.…”

“…[25]) with a fourth order single particle space charge resonance has more recently been studied in straight lattices and for short bunches [20,[26][27][28].…”

Six-dimensional matching of intense beam with linear accelerating structure

“…To this end, the related problem of deviation away from matched 3D beam envelopes and associated resonance envelope behavior has been explored in Refs. [18][19][20].…”