Geodesic acoustic modes and zonal flows in rotating large-aspect-ratio tokamak plasmas

Abstract

The effect of equilibrium plasma rotation (toroidal and poloidal) on lowfrequency, electrostatic modes-the geodesic acoustic modes (GAMs) and the zonal flows (ZFs)-in large aspect ratio tokamaks is studied within the framework of ideal MHD. It is shown that the plasma rotation results in a frequency up-shift of the ordinary GAM. The new branch of continuum modes induced by the poloidal rotation is found. This mode originates from the opposite sign Doppler shift of frequency due to poloidal rotation for m = ±1 poloidal side-band harmonics of the perturbed mass density, pressure and parallel velocity. In the case of slow poloidal rotation ( P c s /qR 0 ) its frequency is close to the sound frequency c s /qR 0 ( P is the poloidal angular velocity, c s is the speed of sound, q is the safety factor and R 0 is the major radius of tokamak). The mode can be called the rotation-induced acoustic mode. This mode disappears in the case of purely toroidal plasma rotation. The frequency of the new mode in the case of relatively slow poloidal rotation ( P c s /qR 0 ) is lower than the frequency of the ordinary GAM modified by plasma rotation. In the case of larger poloidal angular velocities P ( P 2c s /qR 0 ) the mode becomes unstable and is identified as the unstable ZF. With a further increase in the poloidal angular velocity at constant toroidal angular velocity the instability is suppressed, and the mode turns again into a marginally stable, oscillating mode.

Heat flux effects on the dispersion relation for geodesic modes in rotating plasmas

“…which is clearly different from equation (53) of reference [3], in which the simple algebraic equation p = c 2 s ρ (adiabatic case) was used to write the RHS simply as B 0 · ∇ c 2 s ρ /ρ 0 .…”

“…For that purpose, we will follow the approach of Ilgisonis et al [3]. The complete set of unperturbed one-fluid ideal MHD equations, using the assumption of isothermal magnetic surfaces and a Gaussian system of units, reads…”

“…The term in brackets can be transformed the same way as in Appendix A of the paper by Ilgisonis et al [3],…”

“…(17). The procedure is exactly the same of Ilgisonis et al, [3]. We have performed all the calculations but here we will just quote the final result without the whole reproduction (that can be found in Appendix B of [3]).…”

“…We are left with the following four equations (they correspond to equations (16)-(19) of [3], with the difference that in this work we consider isothermal surfaces instead of isentropic ones):…”