Importance of centrifugal effects for the internal kink mode stability in toroidally rotating tokamak plasmas

Abstract

Analytical theory and two different magnetohydrodynamical stability codes are used in a study of the effects of toroidal plasma rotation on the stability of the ideal, internal kink mode in tokamaks. The focus of the paper is on the role that the centrifugal effects on the plasma equilibrium play for the stability of this mode, and results from one code where centrifugal effects are self-consistently included ͑CASTOR-FLOW͒ ͓E. Strumberger et al., Nucl. Fusion 45, 1156 ͑2005͔͒ are compared with the results from another code where such effects are not taken into account ͑MISHKA-F͒ ͓I. T. Chapman et al., Phys. Plasmas 13, 062511 ͑2006͔͒. It is found that, even at rather modest flow speeds, the centrifugal effects are very important for the stability of the internal kink mode. While the results from the two codes can be quite similar for certain profiles in the plasma, completely opposite results are obtained for other profiles. A very good agreement between analytical theory and the numerical results are, both for inconsistent and consistent equilibria, found for plasmas with large aspect ratio. From the analytical theory, the distinctly different stability properties of equilibria with and without centrifugal effects included can be traced to the stabilizing effect of the geodesic acoustic mode ͑GAM͒ induced by the plasma rotation. This GAM exists solely as a consequence of the nonuniform plasma density and pressure created by the centrifugal force on the flux surfaces, and a stabilizing coupling of the internal kink instability to this mode cannot therefore take place if the centrifugal effects are not included in the equilibrium. In addition to the GAM stabilization, the effects of the radial profiles of the plasma density and rotation velocity are also found to be significant, and the importance of these effects increases with decreasing aspect ratio.

Generalised zonal modes in stationary axisymmetric plasmas

“…The dispersion relation for the ideal MHD instability, whose effects of toroidal rotation are almost exclusively confined to the inertial enhancement, yields complex frequencies and thus modified growth rates [27]. These physical phenomena have been verified in a detailed study of the internal kink mode [8], where analytic work has carefully identified that centrifugal and coriolis effects effects are physical, and where benchmarking against a full MHD codes in which toroidal rotation was self consistently included in the equilibrium and the linearly perturbed MHD equations.…”

“…In Ref. [8] it was shown that continuum modes oscillating at the Brunt-Väisälä [9] frequency directly impacts the stabilily threshold of the internal kink mode, and that inconsistent treatment of the effect of toroidal rotation on the continuum mode would lead to erroneous results. The mode oscillating at the Brunt-Väisälä frequency is in fact a finite n zonal mode, which arises as one of two roots [10] from a dispersion relation that also defines the geodesic acoustic mode.…”

Stability of localized modes in rotating tokamak plasmas

“…Typically in a tokamak 2 < 0 so that S f is stabilizing. A potential energy term proportional to ρ 2 was found in [17] and [11,51] in relation to ballooning modes and the internal kink mode, respectively.…”

The effects of sheared toroidal rotation on stability limits in tokamak plasmas

“…Whilst treating the rotation only in the stability analysis can be a valid approximation at very sub-Alfvénic rotation velocities, it can also lead to significantly misleading, or even erroneous results [23,24]. The stability of over 6000 equilibria with different pressures, toroidal rotation velocities and profiles has been tested.…”