By using a Vlasov-Poisson solver, where phase space is discretized, we can solve highly nonlinear problems such as the beam-plasma
instability. We can also tackle this problem using a PIC code. But just how many particles to use per Debye length so as to have enough
statistics and not be undersampling is not a priori clear. Nor is it the practice of PIC code runner to remove as much of the noise from
subsampled simulations as possible every step of the way (actively), every few steps (partially) or afterwards as a post processing step
(passively).
We will show techniques to do just that which rely on a good understanding of the noise properties of the simulations, together with
wavelet techniques. Typically, it is Poisson noise that one is dealing with. We will show results from numerical experiments which demonstrate how this denoising in phase space works and how reliable it is in making few particle per Debye length simulations approach the accuracy of many more particles per Debye length simulations. Using undecimated
wavelets and correct statistical procedures in phase space, including multiscale interpolations onto uniform grids in order to solve the
Poisson equation, are crucial for the success of these methods. It is our hope that these techniques will be easily adaptable to
astrophysical simulations such as those that treat the cosmological N-body problem or the Galaxy formation problem, among others. The
plasma physics treated here examples should serve as a guide and as advertisement for the potential realization of that project.
Work in conjunction with K. Won of PRI, J. L. Starck of Saclay, CEA, France and Viktor Decyk of UCLA.
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