A major concern for the tokamak as well as the stellarator is the excitation of instabilities by fast particles – either from neutral beam injection, RF heating, or fusion reactions. It is important to establish whether the plasma remains stable when such particles are present, and the greatest threat to stability appears to come from the shear Alfvén wave (modified by the magnetic geometry).

A rigorous description of shear Alfvén waves destabilized by fast particles is given by self-consistent gyrokinetic theory. This description automatically includes all non-ideal-MHD effects such as Landau and radiative damping, as well as all non-perturbative effects (energetic particle modes).

An analytic solution of the gyrokinetic Vlasov-Maxwell system appears to be impossible in most cases if a realistic tokamak or stellarator geometry is considered. That is why it is necessary to develop a numerical approach to this problem. The particle-in-cell (PIC) method is a well-established approach to the numerical solution of the gyrokinetic equations. This method can be used to solve these equations globally in a realistic magnetic geometry. In our group we have developed two electromagnetic particle-in-cell codes which can be used to study the shear Alfvén wave and fast-particle physics.

The GYGLES code is a linear δf PIC code which can be used in tokamak or pinch geometry. This code is flexible and easy to run, and can be used for testing new numerical schemes, but it is also possible to perform realistic (although linear) simulations in tokamaks (see figure).

EUTERPE is a nonlinear electromagnetic δf PIC code, which can be used in arbitrary magnetic geometry (pinch, tokamak or stellarator). EUTERPE has been benchmarked successfully with GYGLES in tokamak geometry.

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