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A successful method for solving the nonlinear Vlasov equation is the semi-Lagrangian method, in which the phase space density is represented by its values on a fixed Cartesian grid with interpolation to off-grid points. Integration for a time step consists of following orbits backward in time from initial conditions on the grid, with the collective force frozen during the time step. We ask whether it would be more efficient to use scattered data sites rather than grid points, namely sites from a low-discrepancy sequence as used in quasi - Monte Carlo integration. This requires a technique for interpolation of scattered data, and with such a technique in hand one can try either backward or forward orbits. Here we explore the forward choice, with the data sites themselves following forward orbits. We treat a problem well studied by the backward method, longitudinal motion in the SLAC damping rings. Over one or two synchrotron periods results are encouraging, in that the number of data sites can be reduced by a large factor. Over longer times it appears that the sites must be redistributed or changed in number from time to time, because of clustering.
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