Abstract
Selfconsistent computations are carried out to study the stability of the resistive wall mode(RWM) in DIIID [J. L. Luxon, Nucl. Fusion42, 614 (2002)] plasmas with slow plasma rotation, using the hybrid kineticmagnetohydrodynamic code MARSK [Y. Q. Liu et al., Phys. Plasmas15, 112503 (2008)]. Based on kinetic resonances between the mode and the thermal particle toroidal precession drifts, the selfconsistent modeling predicts less stabilization of the mode compared to perturbative approaches, and with the DIIID experiments. A simple analytic model is proposed to explain the MARSK results, which also gives a qualitative interpretation of the recent experimental results observed in JT60U [S. Takeji et al., Nucl. Fusion42, 5 (2002)]. Our present analysis does not include the kinetic contribution from hot ions, which may give additional damping on the mode. The effect of particle collision is not included either. Using the CARMA code [R. Albanese et al., IEEE Trans. Magn.44, 1654 (2008)], a stability and control analysis is performed for the RWM in ITER [R. Aymar et al., Plasma Phys. Controlled Fusion44, 519 (2002)] steady state advanced plasmas, taking into account the influence of threedimensional conducting structures.
This work was partly funded by the Engineering and Physical Sciences Research Council (United Kingdom) and by the European Communities under the contract of Association between EURATOM and UKAEA. The views and opinions expressed herein do not necessarily reflect those of the European Commission. Work was partly conducted within the framework of the European Fusion Development Agreement. Work also supported by the U.S. Department of Energy under Grant No. DEFG03956ER54309.
I. INTRODUCTION
II. MODELING RESULTS FOR DIIID PLASMAS
A. DIIID equilibrium used in computations
B. Computation results using perturbative approach
C. Computation results using selfconsistent approach
D. Discussion
III. A SIMPLE ANALYTIC MODEL
IV. RWMMODELING FOR ITER WITH 3D CONDUCTORS
A. 3D geometry of ITER walls
B. Passive growth rates of the RWM
C. Feedback results
V. SUMMARY AND DISCUSSION
Key Topics
 Resistive wall mode
 86.0
 Eigenvalues
 17.0
 Toroidal plasma confinement
 13.0
 Magnetohydrodynamics
 11.0
 Plasma pressure
 11.0
Figures
Equilibrium profiles, from the DIIID 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.
Equilibrium profiles, from the DIIID 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 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.
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.
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) , .
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 selfconsistent approach for the DIIID plasma, with .
The (a) real and (b) imaginary parts of the growth rate of the RWM vs , computed using the selfconsistent approach for the DIIID plasma, with .
The eigenvalue of the kinetic RWM vs for (a) , , and (b) , , following the selfconsistent (SC) calculations.
The eigenvalue of the kinetic RWM vs for (a) , , and (b) , , following the selfconsistent (SC) calculations.
2D plots of the (a) real and (b) imaginary parts of the kinetic RWM eigenvalue following the selfconsistent approach, for the case with . The black dots indicate a stable RWM.
2D plots of the (a) real and (b) imaginary parts of the kinetic RWM eigenvalue following the selfconsistent 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) selfconsistent approaches. A case with is considered.
Comparison of the real part of the kinetic RWM eigenvalue between (a) perturbative [the same as Fig. 5(a)] and (b) selfconsistent approaches. A case with is considered.
Comparison of the poloidal Fourier harmonics of normal displacement vs the plasma minor radius, for (a) nowall ideal kink mode, (b) fluid RWM, and (c) kinetic RWM from the selfconsistent calculations. The other parameters, where applicable, are , , and . An equalarc coordinate system is used in the MARSK computations. is the normalized poloidal magnetic flux.
Comparison of the poloidal Fourier harmonics of normal displacement vs the plasma minor radius, for (a) nowall ideal kink mode, (b) fluid RWM, and (c) kinetic RWM from the selfconsistent calculations. The other parameters, where applicable, are , , and . An equalarc coordinate system is used in the MARSK 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 “.”
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 .
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 selfconsistent computations for a DIIID plasma with , , and equal to (a) 0.01%, (b) 0.3%, and (c) 1%.
Comparison of the poloidal Fourier harmonics of normal displacement vs the plasma minor radius, obtained from the selfconsistent computations for a DIIID 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.
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 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 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 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.
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.
Tables
Comparison of the passive growth rates (in ) of the RWM for ITER plasmas, with a 2D vacuumvessel (VV) model (column 4), a VV model including port holes (column 5) and including the tubular extensions, as shown in Fig. 14 (column 6). MARSF computations always assume a complete axisymmetric wall (2D).
Comparison of the passive growth rates (in ) of the RWM for ITER plasmas, with a 2D vacuumvessel (VV) model (column 4), a VV model including port holes (column 5) and including the tubular extensions, as shown in Fig. 14 (column 6). MARSF computations always assume a complete axisymmetric wall (2D).
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