Linear gyrokinetic particle-in-cell simulations of Alfvén instabilities in tokamaks

The linear dynamics of Alfvén modes in tokamaks is investigated here by means of the global gyrokinetic particle-in-cell code ORB5, within the NEMORB project. The model equations are shown and the local shear Alfvén wave dispersion relation is derived, recovering the continuous spectrum in the incompressible ideal MHD limit. A verification and benchmark analysis is performed for continuum modes in a cylinder and for toroidicity-induced Alfvén Eigenmodes. Modes in a reversed-shear equilibrium are also investigated, and the dependence of the spatial structure in the poloidal plane on the equilibrium parameters is described. In particular, a phase-shift in the poloidal angle is found to be present for modes whose frequency touches the continuum, whereas a radial symmetry is found to be characteristic of modes in the continuum gap.