A method of determining the deQing requirement of indi-vidual cavity higher-order modes (HOM) for a multi-cavity RF system is presented and applied to the APS ring. Since HOM resonator frequency values are to some degree uncertain, the HOM frequencies should be regarded as random variables in predicting the stability of the coupled bunch beam modes. A Monte Carlo simulation provides a histogram of the growth rates from which one obtains an estimate of the probability of instability. The damping of each HOM type is determined such that the damping effort is economized, i.e. no single HOM dom-inates the specified growth rate histogram
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