The electromagnetic geodesic acoustic modes in a tokamak plasma with a poloidal electric field

In a tokamak plasma, a poloidal electric field may be induced, e.g., by the auxiliary heating using cyclotron waves or by biasing electrodes, etc. The electromagnetic geodesic acoustic mode in the presence of a poloidal electric field is studied in this work. The dispersion relation is derived and analyzed for the normal standard geodesic acoustic modes. The frequencies of the electromagnetic geodesic acoustic modes decrease with the increasing poloidal electric field, and as a result, the damping rate increases if the ion beta is not too small. In the zero beta limit, the frequencies of the electrostatic geodesic acoustic modes will increase with the increasing poloidal electric field if there is a potential well on the low field side. There appears an m = 1 magnetic component whose amplitude is proportional to the strength of the poloidal electric field.