ICAP 2002 Abstracts and Posters

Vlasov simulation of beams

Abstract

Most numerical simulations of beams are performed nowadays using the Particle-In-Cell method, which consists in integrating the trajectories of a reduced set of macro-particles and gathering the charge and current densities on a grid of the physical space for the computation of the self fiels. This technique has been very successful and will still be in the future for many applications. However, it has the drawback of generating numerical noise which decreases only in $1/\sqrt N$ when the number of particles $N$ is increased. This can be a problem in cases where precises features are investigated.

To remedy this problem, methods discretizing the Vlasov equation on a mesh of phase space have been proposed: The semi-lagrangian method, consisting in computing the distribution function at each grid point by following the characteristic curves. To compute the origin of the characteristic a high order interpolation method is needed. And also finite volume type methods based on the computation of the average of the Vlasov equation solution on each cell of phase space grid by a conservative method. Another option is to use spectral methods (Fourier-Fourier or Fourier- Hermite).

In this talk we shall give an overview of the numerical Vlasov methods which have been used and focus on recent developments of these methods, in particular their implementation on unstructured meshes and the first step towards a self adaptive method being able to adaptively refine the discretization mesh based on wavelet techniques.

Eric Sonnendrucker, Nicolas Besse, Francis Filbet, Ioana Paun, Michael Gutnic

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