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The optimal distribution of the bunch pattern around the RHIC circumference is studied to decrease the electron density for a fixed total beam current. In the search for a bunch pattern that minimizes this density, we show that, for typical parameters, the bunch-to-bunch evolution of the electron cloud density can be represented by a cubic map. Furthermore, we discuss the use of linear bunch-to-bunch maps for small electron cloud densities. The linear coefficients evaluate the electron cloud stability for a given set of physical parameters (bunch charge, SEY, et cetera). Thus, the use of (linearized) maps frees up the slow but detailed simulation codes to explore parameter space, when studying the increase (to a saturated value) or disappearance of the electron cloud under alternative bunch patterns.

Use of maps in the exploration of electron cloud parameter space