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Waterbags and gyrokineticwaterbagsFigure 1: Density perturbation of the plasma obtained as a sum over all the contours. This test case deals with the development of an iontemperaturegradient instability driving the plasma to a turbulent state. From Coulette & Besse (2013b). We have developed semilagrangian and discontinuousGalerkin schemes for reduced models of waterbagtype (gyrowaterbag, waterbag{Poisson, Maxwell, quasineutral}) which are multifluid models of one to three space dimensions and are similar to hyperbolic systems of conservation laws (Besse & Bertrand 2009; Coulette & Besse 2013a, 2013b). To do this, we have used efficient parallel numerical schemes to run the codes on a large number of processors, which is essential because of the high dimensionality of kinetic models. Figure 1 provides an example of a simulation of the 3D gyrowaterbag model in cylindrical geometry [GMWB3DSLCS code (Besse & Bertrand, 2009; Coulette & Besse 2013a, 2013b) with 12 3Dcontours of the 4D phasespace]. It illustrates the development of an iontemperaturegradient instability in cylindrical geometry driving the plasma to a turbulent state and depicts the density perturbation of the plasma which is obtained as a sum over all the contours. As an additional example, Figure 2 and 3 below show respectively, in toroidal geometry, the initial conditions of a simulation and the expected eigenmodes of the gyrowaterbag model. We next plan to develop a Lagrangian gyrokineticwaterbag code for the toroidal geometric configuration, based on the tesselation approach currently developped in 6D for cold dark matter dynamics. The method would consist in following the lagrangian evolution of 3Dmanifolds in a 4D dimensional phasespace. References
