Equilibrium profiles, from the DIII-D discharge 125 701 at 2.5 s, used in the modeling, for (a) safety factor , (b) plasma pressure normalized by , (c) plasma density normalized by the central value, and (d) drift frequency profile normalized by the central amplitude. is the normalized poloidal magnetic flux.
Computed perturbed fluid and drift kinetic potential energies for a case with , , and . The eigenfunction of the fluid RWM without flow is used for the kinetic energy evaluation in the perturbative approach.
Computed eigenvalue of the kinetic RWM, following the perturbative approach, for the same case, as shown in Fig. 2.
2D plots of the (a) real and (b) imaginary parts of the kinetic RWM eigenvalue following the perturbative approach, for the case with , . The black dots indicate a stable RWM.
Comparison of the real part of the kinetic RWM eigenvalues, computed using the perturbative approach. Three cases are compared to (a) , [the same as in Fig. 4(a)], (b) , , and (c) , .
The (a) real and (b) imaginary parts of the growth rate of the RWM vs , computed using the self-consistent approach for the DIII-D plasma, with .
The eigenvalue of the kinetic RWM vs for (a) , , and (b) , , following the self-consistent (SC) calculations.
2D plots of the (a) real and (b) imaginary parts of the kinetic RWM eigenvalue following the self-consistent approach, for the case with . The black dots indicate a stable RWM.
Comparison of the real part of the kinetic RWM eigenvalue between (a) perturbative [the same as Fig. 5(a)] and (b) self-consistent approaches. A case with is considered.
Comparison of the poloidal Fourier harmonics of normal displacement vs the plasma minor radius, for (a) no-wall ideal kink mode, (b) fluid RWM, and (c) kinetic RWM from the self-consistent calculations. The other parameters, where applicable, are , , and . An equal-arc coordinate system is used in the MARS-K computations. is the normalized poloidal magnetic flux.
Growth/damping rate of the kinetic RWM vs , following the dispersion relation (3). A typical set of parameters is chosen: , , and . The growth rate of the mode from a perturbed approach [let in Eq. (3)] is also plotted as solid lines. Note that roots 1 and 2 are complex conjugates, hence symbols “” and “×” in the upper panel overlap to form “.”
Eigenvalues of the kinetic RWM vs : (top) real and (bottom) imaginary part of the eigenvalue. Perturbative approach (solid line) assumes . Nonlinear eigenvalue formulation via the kinetic integrals results in three roots (markers). Other parameters are the same as in Fig. 11, except for .
Comparison of the poloidal Fourier harmonics of normal displacement vs the plasma minor radius, obtained from the self-consistent computations for a DIII-D plasma with , , and equal to (a) 0.01%, (b) 0.3%, and (c) 1%.
Geometry of 3D ITER walls used in the RWM modeling by CARMA. Only one section along the toroidal angle is shown. Included in the geometry are the OTS with bypass, wall holes, and tubular extensions.
The stabilizable region in terms of initial vertical magnetic field perturbations at the outboard midplane, following the BAP approach. and are at 90° phase to each other, corresponding to the cos and sin components of the sensor signal. The ELM control is assumed active. An ITER plasma is considered with , for which the passive growth rate of the RWM is .
The toroidal distribution of voltages in the ELM coils at for a perturbation at the border of the BAP region, as shown in Fig. 15. Shown are voltages for (a) upper coils, (b) middle coils, and (c) lower coils.
The toroidal distribution of currents in the ELM coils at for the same perturbation at the border of the BAP region, as shown in Fig. 16. Shown are currents for (a) upper coils, (b) middle coils, and (c) lower coils.
The RWM control simulations (the ELM coil currents) for an ITER equilibrium with , assuming random initial field perturbation amplitude, and with a current limit of 250 A in all coils.
Comparison of the passive growth rates (in ) of the RWM for ITER plasmas, with a 2D vacuum-vessel (VV) model (column 4), a VV model including port holes (column 5) and including the tubular extensions, as shown in Fig. 14 (column 6). MARS-F computations always assume a complete axisymmetric wall (2D).
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