Presence Of Toroidal Flow Research Articles

Stability of compressible reduced magnetohydrodynamic equilibria—Analogy with magnetorotational instability

Stability analyses for equilibria of the compressible reduced magnetohydrodynamics (CRMHD) model are carried out by means of the Energy-Casimir (EC) method. Stability results are compared with those obtained for ideal magnetohydrodynamics (MHD) from the classical δW criterion. An identification of the terms in the second variation of the free energy functional for CRMHD with those of δW is made: two destabilizing effects present for CRMHD turn out to correspond to the kink and interchange instabilities in usual MHD, while the stabilizing roles of field line bending and compressibility are also identified in the reduced model. Also, using the EC method, stability conditions in the presence of toroidal flow are obtained. A formal analogy between CRMHD and a reduced incompressible model for magnetized rotating disks, due to Julien and Knobloch [EAS Pub. Series, 21, 81 (2006)], is discovered. In light of this analogy, energy stability analysis shows that the condition for magnetorotational instability (MRI) for the latter model corresponds to the condition for interchange instability in CRMHD, with the Coriolis term and shear velocity playing the roles of the curvature term and pressure gradient, respectively. Using the EC method, stability conditions for the rotating disk model, for a large class of equilibria with possible non-uniform magnetic fields, are obtained. In particular, this shows it is possible for the MRI system to undergo, in addition to the MRI, another instability that is analogous to the kink instability. For vanishing magnetic field, the Rayleigh hydrodynamical stability condition is recovered.

Beta limits for the N=1 mode in rotating-toroidal-resistive plasmas surrounded by a resistive wall

The stability analysis of a high-β toroidal tokamak plasma is carried out in the presence of toroidal flow, finite plasma resistivity, and a surrounding shell of finite electrical resistivity. The beta limits for the n=1 mode are set by the resistive-wall-tearing mode (RWTM), the ideal-wall-tearing mode (IWTM), and the ideal-plasma-resistive-wall mode (IPRWM). Slow plasma rotation suppresses the RWTM while the IPRWM is not directly affected by slow plasma flow. For small plasma resistivity, the IPRWM is stabilized by fast flow only. For large plasma resistivity, the IPRWM only exists in a plasma rotating faster than the typical tearing mode growth rate, and its instability threshold is a complicated function of the wall position and rotation frequency. Very fast rotation can destabilize the ideal kink through centrifugal effects. Furthermore, for b/a (wall radius/plasma radius) below a critical value, a stationary plasma is stable to the n=1 ideal kink and tearing mode for large values of β.

Effect of toroidal flow on the stability of a diffuse high-beta tokamak

The effect of toroidal flow on the stability of a diffuse current model tokamak to external kink modes is examined. For a high-β tokamak it is shown that, to leading order in the inverse aspect ratio, the effect of toroidal flow is simply to modify the kinetic pressure by adding to it the flow pressure. Then the limit on the plasma beta in the presence of toroidal flow can be obtained from the results for a static plasma. It is shown that, for a given safety factor profile and shape of the plasma boundary, the maximum plasma beta for stability to external kink modes is always lower in the presence of flow compared to a static configuration. This is true for any arbitrary profile of the toroidal flow velocity.