  The linear properties of the geodesic acoustic modes (GAM) in tokamaks are
investigated by means of the comparison of analytical theory and gyrokinetic
numerical simulations. The dependence on the value of the safety factor,
finite-orbit-width of the ions in relation to the radial mode width,
magnetic-flux-surface shaping, and electron/ion mass ratio are considered.
Nonuniformities in the plasma profiles (such as density, temperature, or safety
factor), electro-magnetic effects, collisions and presence of minority species
are neglected. Also, only linear simulations are considered, focusing on the
local dynamics. We use three different gyrokinetic codes: the lagrangian
(particle-in-cell) code ORB5, the eulerian code GENE and semi-lagrangian code
GYSELA. One of the main aims of this paper is to provide a detailed comparison
of the numerical results and analytical theory, in the regimes where this is
possible. This helps understanding better the behavior of the linear GAM
dynamics in these different regimes, the behavior of the codes, which is
crucial in the view of a future work where more physics is present, and the
regimes of validity of each specific analytical dispersion relation.
