Saturation of the ion induced transverse blow-up instability
In a recent paper, T. Raubenheimer and F. Zimmermann described a new, fast transverse instability caused by the interaction of a train of bunches with the residual gas. Ions produced by transversely offset bunches in the head of a train induce oscillations of the tail of the train. The ions may be cleared out by a gap after one revolution, but the memory remains in the train. Amplitude of oscillations keeps growing exponentially as exp s{top}s{sub c}, until the amplitude of a bunch centroid is on the order of the transverse rms {sigma} of a bunch. The rise time s{sub c}, of the oscillations of a bunch centroid for the PEP-II HER was found to be a fraction of a millisecond, even taking into account the spread of ion frequencies.Computer simulations confirm the exponential growth. However, the results of the simulations show that the exponential regime holds only for a short period of time and then changes to a much slower growth. Initial growth is rapid; it would be difficult to observe it directly in experiments. From a practical point of view, the important questions are, what is the amplitude at which a transition to slow growth takes place and, secondly, what is the growth rate after that transition compared to the rate, which could be handled with a reasonable feedback system. The exponential regime is limited by nonlinearity of the beam-ion interaction. As a result, exponential growth at large amplitudes is replaced by a linear dependence of the amplitude on time. The transition from exponential growth to a linear regime depends on the initial conditions: exponential growth is noticeable only for very small initial amplitudes. An estimate of the growth rate at large amplitude is obtained and compared with computer simulations.
- Research Organization:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)
- Sponsoring Organization:
- USDOE, Washington, DC (United States)
- DOE Contract Number:
- AC03-76SF00515
- OSTI ID:
- 219419
- Report Number(s):
- SLAC-PUB-6959; CONF-9506279-11; ON: DE96009151; TRN: 96:010625
- Resource Relation:
- Conference: CEIBA95: international workshop on collective effects and impedance for B-factories, Tsukuba (Japan), 12-17 Jun 1995; Other Information: PBD: Jan 1996
- Country of Publication:
- United States
- Language:
- English
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