Moment-Preserving and Mesh-Adaptive Reweighting Method for Rare-Event Sampling in Monte-Carlo Algorithms

We present novel roulette schemes for rare-event sampling that are both structure-preserving and unbiased. The boundaries where Monte Carlo markers are split and deleted are placed automatically and adapted during runtime. Extending existing codes with the new schemes is possible without severe changes because the equation of motion for the markers is not altered. These schemes can also be applied in the presence of nonlinear and nonlocal coupling between markers. As an illustrative application, we have implemented this method in the ASCOT-RFOF code, used to simulate fast-ion generation by radio-frequency waves in fusion plasmas. In this application, with this method the Monte-Carlo noise level for typical fast-ion energies can be reduced at least of one order of magnitude without increasing the computational effort.