Multibunch Instability Investigations for a Tau-Charm Factory Page: 3 of 13
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In practice, it is difficult to achieve a high luminosity without having a high average beam current
in the rings. Because the multibunch growth rates scale linearly with average current, the
resulting rates tend to be very high. It might be imagined that, for sufficient bunch separation
and low enough Q values for the higher-order cavity modes, the wake fields have time to die
away between successive bunches, thus reducing the bunch-to-bunch coupling. For most cases
of interest, however, it is hard to reduce the Q values sufficiently to achieve this condition.
Because the details of higher-order modes of the RF cavities are only a guess at present, the
results contained herein should not be interpreted quantitatively. However, experience has
shown that the magnitudes of multibunch growth rates estimated as is done here are in reasonable
agreement with observed growth rates under comparable conditions.2 Thus, although the
particular modes that grow will depend on details of the impedance that are not well known at
this time, the predicted growth rates are expected to reflect the requirements of a feedback system
with good accuracy.
OVERVIEW OF CALCULATIONS
ZAP performs calculations of multibunch instabilities in the frequency domain, and thus is
restricted to the case of equally spaced bunches in the ring. In the case of a high-luminosity
collider, of course, this is the standard operating configuration, so ZAP is well suited to such
studies. Each higher-order longitudinal and transverse mode of the RF cavity is represented by
three parameters, a resonant frequency (fR), a shunt impedance (Rs or Rt), and a quality factor
(Q). Because the growth times depend on the angular frequency shift, we typically use this value
to represent the higher-order modes, i.e., we quote (R = 2fR. Thus the longitudinal
impedance is represented by
Z o) = .4R J
1 + iQ - I
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Zisman, Michael S. Multibunch Instability Investigations for a Tau-Charm Factory, article, May 1, 1989; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc841446/m1/3/: accessed January 20, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.