| Paper | Title | Page |
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| WEPLT146 | Mismatch Oscillations in High-current Accelerators | 2176 |
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Strong space charge challenges the designers of modern accelerators such as those used in Heavy Ion Inertial Fusion. Simple, accurate design tools are useful for predicting beam behavior, such as phase advances and envelope oscillation periods, given the beam emittance and charge and the lattice parameters. Along with the KV beam model, the smooth approximation [*] is often used. It is simple but not very accurate in many cases. Although Struckmieir and Reiser [**] showed that the stable envelope oscillations of unbalanced beams could be obtained accurately, they used a hybrid approach where the phase advances σ0 and σ were already known precisely. When starting instead with basic quantities–quadrupole dimensions, field strength, beam line charge and emittance–the smooth approximation formulas give substantial errors (10% or more). We previously described an integration method [***] for matched beams that yields fairly simple third-order formulas for σ0, σ, beam radius and ripple. Here we extend the method to include small-amplitude mismatch oscillations. We derive a simple modification of the smooth approximation formulas and show that it improves the accuracy of the predicted envelope frequencies significantly–for example, by a factor of five when σ0 is 83 degrees.
* M. Reiser, Particle Accelerators 8, 167 (1978) ** J. Struckmeier and M. Reiser, Particle Accelerators 14, 227 (1984)*** O. A. Anderson, Particle Accelerators 52, 133 (1996) |