[SLAC] [SLAC Pubs and Reports]

SLAC-R-554
New Diagnostics and Cures for Coupled-Bunch Instabilities

Abstract

Electromagnetic interaction between a charged particle beam and its surroundings causes collective instabilities, which must be controlled if the new light sources and colliders are to meet their design goals. Control requires a combination of passive damping and fast active feedback on an unprecedented technological scale. Efficient instability diagnosis techniques are also needed for machines with large numbers of bunches. This thesis describes new methods of measuring and analyzing coupled-bunch instabilities in circular accelerators, and demonstrates the existence of a new cure.

A new technique is demonstrated for simultaneous measurement of growth rates, damping rates and coherent tune shifts of all unstable coupled-bunch eigenmodes from a single 10-25-ms transient snapshot of beam motion. The technique has been used to locate and quantify beam impedance resonances at PEP-II, ALS and SPEAR. This method is faster than existing spectral scan methods by at least an order of magnitude, and has the added advantage of revealing coupled-bunch dynamics in the linear small-signal regime. A method is also presented for estimating beam impedance from multi-bunch fill shape and synchronous phase measurements.

Phase space tracking of multi-bunch instabilities is introduced as a “complete instability diagnostic.” Digitised multi-bunch data is analyzed offline, to estimate the phase space trajectories of bunches and modes. Availability of phase space trajectories is shown to open up a variety of possibilities, including measurement of reactive impedance, and diagnosis of the fast beam-ion instability.

Knowledge gained from longitudinal measurements (all made using a digital longitudinal feedback system) has been used to optimise cavity temperatures, tuner positions and feedback parameters, and also to identify sources of beam noise at the three machines.

A matrix-based method is presented for analyzing the beneficial effect of bunch-to-bunch tune variation on instability growth rates. The method is applicable to the calculation of instability eigenvalues in machines with more than one unstable coupled-bunch mode. This technique is useful in studying machines like PEP-II and KEK-B, which do not lend themselves to tune spread analysis by conventional methods.

A similar mathematical formalism is used to understand the dynamics of azimuthally asymmetric beams. Simple formulae are derived for asymmetry-induced growth rate reduction. 'Optimal' fill shapes based on these ideas have been experimentally verified at the ALS and SPEAR, where the longitudinal instability threshold has been raised by factors of six and two, respectively. Thus we have a new, zero-cost, easily implementable cure for coupled-bunch instabilities.

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Notes

The present version of SLAC-R-554 was revised in August 2001 from the original version published at SLAC in February 2000.

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