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For given computational resources, the accuracy of plasma simulations usingparticles is mainly held back by the noise due to limited statistical samplingin the reconstruction of the particle distribution function. A method based onwavelet analysis is proposed and tested to reduce this noise. The method, knownas wavelet based density estimation (WBDE), was previously introduced in thestatistical literature to estimate probability densities given a finite numberof independent measurements. Its novel application to plasma simulations can beviewed as a natural extension of the finite size particles (FSP) approach, withthe advantage of estimating more accurately distribution functions that havelocalized sharp features. The proposed method preserves the moments of theparticle distribution function to a good level of accuracy, has no constraintson the dimensionality of the system, does not require an a priori selection ofa global smoothing scale, and its able to adapt locally to the smoothness ofthe density based on the given discrete particle data. Most importantly, thecomputational cost of the denoising stage is of the same order as one time stepof a FSP simulation. The method is compared with a recently proposed properorthogonal decomposition based method, and it is tested with three particledata sets that involve different levels of collisionality and interaction withexternal and self-consistent fields.

Wavelet-based density estimation for noise reduction in plasma simulations using particles