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A new method to quantify fluctuations in the initial state of heavy ion collisions is presented. The initial state energy distribution is decomposed with a set of orthogonal basis functions which include both angular and radial variation. The resulting two dimensional Fourier coefficients provide additional information about the nature of the initial state fluctuations compared to a purely angular decomposition. We apply this method to ensembles of initial states generated by both Glauber and Color Glass Condensate Monte-Carlo codes. In addition initial state configurations with varying amounts of fluctuations generated by a dynamic transport approach are analysed to test the sensitivity of the procedure. The results allow for a full characterization of the initial state structures that is useful to discriminate the different initial state models currently in use.

Classification of initial state granularity via 2D Fourier expansion