Numerical resolution of the global eigenvalue problem for the gyrokinetic-waterbag model in toroidal geometry

In this paper, we present two codes for the linear stability analysis of the ion temperature gradient instability in toroidal geometry using a gyrokinetic multi-waterbag model for ion dynamics. The first one solves the linearized ion dynamics as an initial value problem, while the second relies on an asymptotic expansion in the so-called ballooning representation allowing us to build a tractable eigenvalue problem. Results from the two codes are presented and compared for equilibria based on modified Cyclone parameters. A good agreement between both codes is found for a class of equilibria with a narrow extent in perpendicular velocity and for which trapped particle orbits are ignored. The local spectrum computed by the eigenvalue is shown to agree remarkably well with previous Cyclone results when trapped particle orbits are included. Lastly we discuss how the equilibrium building procedure for this type of waterbag model requires particular care when dealing with closed equilibrium contours related to the presence of trapped particle orbits.