Self-consistent study of space-charge-driven coupling resonances

• Main Authors: I. Hofmann, G. Franchetti
• Format: Article
• Language: English
• Published: American Physical Society 2006-05-01
• Series: Physical Review Special Topics. Accelerators and Beams
• Online Access: http://doi.org/10.1103/PhysRevSTAB.9.054202

In this paper we present a comprehensive analysis of the self-consistent, collective behavior associated with the space-charge-driven (Montague) coupling resonance near 2Q_{x}-2Q_{y}=0, including the effect of linear coupling. Based on analytical work and particle-in-cell simulation in the 2D coasting beam limit, we derive scaling laws for stop-band widths and growth rates, which may be applied to circular machines as well as to linear accelerators. For slow crossing of the stop bands, we find a strong directional dependence. In the case of crossing from below—assuming that the rising tune pertains to the direction, in which the initial emittance is the larger one—the emittance exchange is a smooth and fully reversible process. For crossing from above, we encounter a discontinuous behavior, which disappears largely, if an external linear coupling is applied.