Discontinuous Galerkin hybrid particle-in-cell modeling of cyclotron wave growth and damping in inhomogeneous media

Details Discontinuous Galerkin hybrid particle-in-cell modeling of cyclotron wave growth and damping in inhomogeneous media Discontinuous Galerkin hybrid particle-in-cell modeling of cyclotron wave growth and damping in inhomogeneous media

Dec 2011

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011agufmsm13b2054f&link_type=abstract

American Geophysical Union, Fall Meeting 2011, abstract #SM13B-2054

Physics

Plasma Physics

[2753] Magnetospheric Physics / Numerical Modeling, [2772] Magnetospheric Physics / Plasma Waves And Instabilities, [7867] Space Plasma Physics / Wave/Particle Interactions

Scientific paper

We present some recent work towards the development of a hybrid discontinuous Galerkin particle in cell (DG-PIC) code to study wave-particle interactions in strongly inhomogeneous media. The nodal DG method solves Maxwell's field equations on interpolation points defined on finite elements on a fully unstructured grid. The scheme supports arbitrary geometries and has a variable order of accuracy, making it attractive for modeling problems with strong inhomogeneity or complex boundaries. Individual particles are projected onto the stationary DG grid via an arbitrary shape function and coupled into the equations through a nonlinear current term. The particles are in turn moved by the Lorentz force, found by evaluating the DG basis at arbitrary particle locations. As shown by Jacobs et al. [2006], the scheme has exceptional stability properties, including very well-controlled grid heating even when the Debye length is poorly resolved. The geometric flexibility of the scheme, however, makes its efficient parallel implementation challenging, which we discuss in this work. We have implemented a large-scale, parallel DG-PIC scheme in the Petsc framework. We discuss details of the parallel implementation, including grid partitioning, blocking strategies, precomputation, efficient element search, particle cloud projection, and efficient evaluation of the DG basis functions at arbitrary particle locations. We extend the basic DG-PIC scheme into a hybrid scheme by including the cold plasma component and hot plasma components as separate terms. The multicomponent cold plasma tensor is included as an auxiliary first-order differential equation, while the hot particle distribution is sampled using particles. We compare this scheme against known analytical results for electron cyclotron growth and damping of transverse whistler mode waves. The hybrid PIC scheme shows good agreement with full PIC for relatively mild growth or damping rates, consistent with the results expected by numerical evaluation of the dispersion relation for an anisotropic particle distribution integrated over a restricted range of parallel particle velocities (those near resonance with the wave). Finally, we show some preliminary results from the scheme applied to whistler mode wave growth in a hot, anisotropic plasma with an inhomogeneous background magnetic field.

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