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A central hyperplane arrangement in C^2 with multiplicity is called a `locusconfiguration' if it satisfies a series of `locus equations' on eachhyperplane. Following Chalykh, Feigin and Veselov [CFV99], we demonstrate thatthe first locus equation for each hyperplane corresponds to a force-balancingequation on a related interacting particle system on C^*: the chargedtrigonometric Calogero-Moser system. When the particles lie on S^1 in C^*,there is a unique equilibrium for this system. For certain classes of particleweight, this is enough to show that all the locus equations are satisfied,producing explicit examples of real locus configurations. This in turn producesnew examples of Schr\"odinger operators with Baker-Akhiezer functions.

2D Locus Configurations and the Charged Trigonometric Calogero-Moser System