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TY - CONF AU - Lindberg, R.R. ED - Yamazaki, Yoshishige ED - Raubenheimer, Tor ED - McCausey, Amy ED - Schaa, Volker RW TI - A Fast Method to Evaluate Transverse Coupled-Bunch Stability at Non-Zero Chromaticity J2 - Proc. of NAPAC2019, Lansing, MI, USA, 01-06 September 2019 CY - Lansing, MI, USA T2 - North American Particle Accelerator Conference T3 - 4 LA - english AB - We present a dispersion relation that gives the complex growth rate for coupled-bunch instabilities at arbitrary chromaticity in terms of its value at zero chromaticity. We compare predictions of the theory to elegant tracking simulations, and show that there are two distinct regimes to stability depending upon whether the zero chromaticity growth rate is smaller or larger than the chromatic tune shift over the bunch. We derive an approximate expression that is easily solved numerically, and furthermore indicate how the formalism can be extended to describe arbitrary longitudinal potentials. PB - JACoW Publishing CP - Geneva, Switzerland SP - 387 EP - 390 KW - synchrotron KW - wakefield KW - dipole KW - betatron KW - simulation DA - 2019/10 PY - 2019 SN - 2673-7000 SN - 978-3-95450-223-3 DO - doi:10.18429/JACoW-NAPAC2019-TUPLM09 UR - http://jacow.org/napac2019/papers/tuplm09.pdf ER -