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Emittance-dominated long bunches in dual harmonic RF system

Chinese Physics C 2008年第1期32卷 60-66页

作者：安世忠 Klaus Bongardt Rudolf Maier 唐靖宇张天爵 China Institute of Atomic Energy ikp fz juelich 52425 JuelichGermany Institute of High Energy Physics CAS

The storage of long bunches for long time intervals needs flattened stationary buckets with a large bucket height. The longitudinal motion of the initially mismatched beam has been studied for both the single and dual harmonic RF systems. The RF amplitude is determined to be r.m.s wise matched. The bucket height of the single harmonic system is too small even for shorter bunch with only 20% increased energy spread. The Halo formation and even debunching can be seen after a few synchrotron periods for single particles with large amplitude. In the case of small energy spread for a cooled beam, Coulomb interaction cannot be ignored. The external voltage has to be increased to keep the r.m.s bunch length unchanged. The new voltage ratio R（N） simplifies physics for the emittance-dominated bunches with modest particle number N. For the single harmonic system, substantial amount of debunching occurs without increasing the external voltage, but very little if the RF amplitude is doubled. Results from the ORBIT tracking code are presented for the 1 GeV bunch in the HESR synchrotron, part of the GSI FAIR project.

关键词： bucket height mismatch space charge effect debunching

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Collective effects for long bunches in dual harmonic RF systems

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Chinese Physics C 2008年第2期32卷 139-145页

作者：安世忠 Klaus Bongardt Rudolf Maier 唐靖宇张天爵 China Institute of Atomic Energy Beijing 102413 China ikp fz juelich 52425 JuelichGermany Institute of High Energy Physics CAS Beijing 100049China

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.

关键词： resistive impedance incoherent motion halo formation coherent dipole instability

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