# Gyrokinetic simulations of plasmas

In gyrokinetic theory the six dimensional phase space of kinetic theory is reduced to a five dimensional one what leads to a considerable reduction in complexity. This reduction is possible under the assumptions that e.g. the time scale of fluctuations is much longer than the gyration time and that the fluctuations are small. Roughly speaking: in gyrokinetic theory the gyrating particle is replaced by a pseudo particle which is a charged ring. This theory is especially suited to describe microinstabilities and the resulting turbulence.

The gyrokinetic equations can be solved numerically by various methods. One possibility are Monte-Carlo particle methods.  This approach is used in the particle-in-cell code EUTERPE. It solves the gyrokinetic equations for up to three species (ions, electrons and fast particles/impurities) globally for the full volume of a stellarator device. The necessary stellarator equilibria are calculated with the VMEC code.

The code allows linear and nonlinear simulations of electrostatic and electromagnetic perturbations. Also a pitch angle scattering operator can be employed to include collisional effects. EUTERPE can thus be used to simulate ITG/TEM instabilities, turbulence, MHD instabilities and neoclassical transport.

Numerically the code uses a control-variate technique ($\delta f$) to reduce the noise inherent to particle methods. The field equations for the electric potential and the parallel vector potential are discretized using B-splines. The resulting equations are then solved using parallel iterative methods. The combination of domain decomposition and domain cloning leads to a very good parallel scalability of the code.

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