Collective effects for long bunches in dual harmonic RF systems

• Published in: Chinese physics C Vol. 32; no. 2; pp. 139 - 145
• Main Author: 安世忠 Klaus Bongardt Rudolf Maier 唐靖宇 张天爵
• Format: Journal Article
• Language: English
• Published: IOP Publishing 01.02.2008; China Institute of Atomic Energy,Beijing 102413,China%IKP,FZ Juelich,52425 Juelieh,Germany%Institute of High Energy Physics,CAS,Beijing 100049,China
• Subjects: 不相干动态; 对偶谐波射频系统; 相干偶极不稳定性; 集体效应; coherent dipole instability; resistive impedance; incoherent motion; halo formation
• ISSN: 1674-1137; 0254-3052; 2058-6132
• DOI: 10.1088/1674-1137/32/2/013

The storage of long bunches for large time intervals needs flattened stationary buckets with a large bucket height. Collective effects from the space charge and resistive impedance are studied by looking at the incoherent particle motion for the matched and mismatched bunches. Increasing the RF amplitude with particle number provides r.m.s wise matching for modest intensities. The incoherent motion of large amplitude particles depends on the details of the RF system. The resulting debunching process is a combination of the too small full RF acceptance together with the mismatch, enhanced by the collective effects. Irregular single particle motion is not associated with the coherent dipole instability. For the stationary phase space distribution of the Hofmann-Pedersen approach and for the dual harmonic RF system, stability limits are presented, which are too low if using realistic input distributions. For single and dual harmonic RF system with d=0.31, the tracking results are shown for intensities, by a factor of 3 above the threshold values. Small resistive impedances lead to coherent oscillations around the equilibrium phase value, as energy loss by resistive impedance is compensated by the energy gain of the RF system.