When the distribution function of plasma particles stays close to some analytically known function, statistical noise inherent to Monte Carlo simulations can be greatly reduced by introducing this function as a control variate in the computation of the velocity moments. Such a method, even though it can be naturally applied to nonlinear simulations, has originally emerged from linearised simulations and is usually called the delta f particle-in-cell (PIC) method. In the past, the method has been extended to also handle collisions. This resulted in a two weight scheme which is known to produce a pronounced weight growth problem which rapidly makes it inefficient as a control variate method for variance reduction. In this work we analyse the weight growth problem within a simple example, which allows us to overcome its pathological behaviour. We also introduce a new split algorithm based on switching the control variate for PIC simulations with collisions. A key element of our algorithm is a new weight smoothing operator which enables us to obtain a significant noise reduction both in the presence of collisions and in the deep nonlinear phase of PIC simulations.     «

When the distribution function of plasma particles stays close to some analytically known function, statistical noise inherent to Monte Carlo simulations can be greatly reduced by introducing this function as a control variate in the computation of the velocity moments. Such a method, even though it can be naturally applied to nonlinear simulations, has originally emerged from linearised simulations and is usually called the delta f particle-in-cell (PIC) method. In the past, the method has bee...     »