Moments in Particle-in-Cell Simulations

The moment equations that form the basis of the BEDLAM simulation code can also be used as a check on Particle-In-Cell (PIC) simulations. Moments can be computed as sums over the macroparticles used in the PIC simulations. These moments should satisfy the moment equations if the simulation is valid. A check has been done to sixth order for two cases: the RFQRZP code, which simulated a radio-frequency quadrupole (RFQ) linac, and the BEAMTRACE code, which simulated the final focusing system in a heavy ion fusion facility. We observed how well the moment equations were satisfied for various values of the independent-variable step size and the number of macroparticles. Generally, we found that the PIC codes satisfied the moment equations very well. Because our modified PIC codes were able to compute moments that satisfied the correct moment equations, we were able to use our modified version of RFQRZP, which we called RFQMOM, to work on another problem. Every moment simulation code has to include some truncation approximation. The error of this approximation can be determined by RFQMOM before actually writing the moment code. As an example, we investigated the accuracy of the truncation approximation that is used in the BEDLAM code.