Rotation and Kinetic Modifications of the Tokamak Ideal-Wall Pressure Limit

The impact of toroidal rotation, energetic ions, and drift-kinetic effects on the tokamak ideal wall mode stability limit is considered theoretically and compared to experiment for the first time. It is shown that high toroidal rotation can be an important destabilizing mechanism primarily through the angular velocity shear; non-Maxwellian fast ions can also be destabilizing, and drift-kinetic damping can potentially offset these destabilization mechanisms. These results are obtained using the unique parameter regime accessible in the spherical torus NSTX of high toroidal rotation speed relative to the thermal and Alfvén speeds and high kinetic pressure relative to the magnetic pressure. Inclusion of rotation and kinetic effects significantly improves agreement between measured and predicted ideal stability characteristics and may provide new insight into tearing mode triggering.

Figure 1

Radial profiles of (a) total, thermal, and fast-ion $\beta$, and (b) safety factor $q$ and normalized ${\mathrm{\Omega }}_{\varphi }$ and ${\omega }_E$ frequencies.

Figure 2

Time evolution of: (a) mode amplitude, (b) ${\beta }_N$ values, (c) mode frequency, and (d) plasma rotation frequency.

Figure 3

(a) mars-k $\gamma$ vs ${\beta }_N$, (b) experimental ${\beta }_N(\mathrm{t})$, and (c) comparison of measured and predicted effective $\gamma$.

Figure 4

(a) mars-k mode displacement, (b) equilibrium, and (c) fluctuating line-integrated SXR emission from simulation/fit (black lines) and measurement (squares), (d) measured and (e) simulated line-integrated SXR fluctuation signal versus ${\psi }_n^{0.5}$ and time spanning two mode oscillation periods.

Figure 5

Time evolution of: (a) mode frequency, and (b) ${\beta }_N$, radial profiles of: (c) $\beta$, (d) $q$ and normalized ${\mathrm{\Omega }}_{\varphi },{\omega }_E$.

Figure 6

(a) Fluid and kinetic IWM $\gamma$ vs ${\beta }_N$ and ${\mathrm{\Omega }}_{\varphi }$, and (b) predicted and measured mode frequency vs ${\beta }_N$.

Figure 7

Kinetic, $J_{\parallel }$, and rotation $\mathrm{Re}(\delta \widehat{W})$ terms normalized by the sum of positive-definite (i.e., stabilizing) fluid terms.