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An electrostatic self-cleaning panel for solar collectors is described. An electrodynamic screen is formed by inter-digitated, transparent surface electrodes energized by three-phase, low-frequency ac voltages in the range 5 to 200 Hz and 500 to 1000 V. The resulting electrostatic field wave exerts force on the particles and sweeps them laterally across the panel. Particle trajectories are simulated to help ascertain parameters for maximum dust-removal efficiency. The electric field of the electrodynamic screen is found by a Fourier expansion of Laplace's equation solutions for a surface potential that is periodic in space and time. Trajectories are found for particles of various size and charge, and electrode excitations; these are compared qualitatively to experimental observations. One unexpected result is the chaotic behavior of larger particles which jump sporadically back and forth and only slowly migrate in the direction of the impressed electrostatic surface wave.