Abstract
A numerical study is carried out, based on a simple toroidal tokamak equilibrium, to demonstrate the radial redistribution of the electromagnetic torque density, as a result of a rotating resistive plasma (linear) response to a static resonant magnetic perturbation field. The computed electromagnetic torque peaks at several radial locations even in the presence of a single rational surface, due to resonances between the rotating response, in the plasma frame, and both Alfvén and sound continuum waves. These peaks tend to merge together to form a rather global torque distribution, when the plasma resistivity is large. The continuum resonance induced net electromagnetic torque remains finite even in the limit of an ideal plasma.
This work was funded by the RCUK Energy Programme under Grant No. EP/I501045 and the European Communities under the contract of Association between EURATOM and CCFE. The views and opinions expressed herein do not necessarily reflect those of the European Commission.
I. INTRODUCTION
II. FORMULATIONS
A. MARSF formulation for computing plasma response
B. Resonance conditions with continuum waves
C. Evaluation of electromagnetic torque
III. NUMERICAL RESULTS
A. Equilibrium
B. Resonance induced torque density distribution
C. Global distribution of electromagnetic torque density
D. Finite torque in the ideal plasma limit
IV. CONCLUSION
Key Topics
 Torque
 70.0
 Acoustic resonance
 44.0
 Toroidal plasma confinement
 26.0
 Parity
 18.0
 Electrical resistivity
 13.0
H05H1/02
Figures
The radial profile of the safety factor q for the chosen large aspect ratio toroidal equilibrium. The dashed lines indicate the position of the q = 2 rational surface.
The radial profile of the safety factor q for the chosen large aspect ratio toroidal equilibrium. The dashed lines indicate the position of the q = 2 rational surface.
(a) The radial profiles of the (uniform) plasma rotation frequency , the analytic expressions for the Alfvén frequency , and the sound frequency plotted as functions of the safety factor q. (b) The radial distribution of the computed electromagnetic torque density, with the peak amplitude normalized to unity. The Lundquist number of the plasma is S = 10^{9}.
(a) The radial profiles of the (uniform) plasma rotation frequency , the analytic expressions for the Alfvén frequency , and the sound frequency plotted as functions of the safety factor q. (b) The radial distribution of the computed electromagnetic torque density, with the peak amplitude normalized to unity. The Lundquist number of the plasma is S = 10^{9}.
The detailed radial distribution of the computed electromagnetic torque density as shown in Fig. 2(b), near each resonant surface at (a) q = 1.9128, (b) q = 1.9940 and 2.0060, (c) q = 2.1979, and (d) q = 2.3420. The symbols “ + ” indicate the packed radial mesh.
The detailed radial distribution of the computed electromagnetic torque density as shown in Fig. 2(b), near each resonant surface at (a) q = 1.9128, (b) q = 1.9940 and 2.0060, (c) q = 2.1979, and (d) q = 2.3420. The symbols “ + ” indicate the packed radial mesh.
Radial profiles of the poloidal Fourier harmonics of the computed plasma current perturbations, for (a) radial, (b) poloidal, (c) toroidal, and (d) parallel components, respectively.
Radial profiles of the poloidal Fourier harmonics of the computed plasma current perturbations, for (a) radial, (b) poloidal, (c) toroidal, and (d) parallel components, respectively.
Radial profiles of the poloidal Fourier harmonics of the computed plasma current perturbations near the first resonant surface q = 1.9128, for (a) radial, (b) poloidal, (c) toroidal, and (d) parallel components, respectively.
Radial profiles of the poloidal Fourier harmonics of the computed plasma current perturbations near the first resonant surface q = 1.9128, for (a) radial, (b) poloidal, (c) toroidal, and (d) parallel components, respectively.
Radial profiles of the poloidal Fourier harmonics of the computed plasma current perturbations near the fourth resonant surface q = 2.1979, for (a) radial, (b) poloidal, (c) toroidal, and (d) parallel components, respectively.
Radial profiles of the poloidal Fourier harmonics of the computed plasma current perturbations near the fourth resonant surface q = 2.1979, for (a) radial, (b) poloidal, (c) toroidal, and (d) parallel components, respectively.
Radial profiles of the poloidal Fourier harmonics of the computed plasma current perturbations near the second and third resonant surfaces q = 1.9940 and 2.0060, for (a) radial, (b) poloidal, (c) toroidal, and (d) parallel components, respectively.
Radial profiles of the poloidal Fourier harmonics of the computed plasma current perturbations near the second and third resonant surfaces q = 1.9940 and 2.0060, for (a) radial, (b) poloidal, (c) toroidal, and (d) parallel components, respectively.
The integrated electromagnetic torque density across the plasma minor radius with (a) the full profile and (b) the detailed profile near resonant surfaces. The dashed lines indicate the amount of net torque gained while integrating across each resonant surface.
The integrated electromagnetic torque density across the plasma minor radius with (a) the full profile and (b) the detailed profile near resonant surfaces. The dashed lines indicate the amount of net torque gained while integrating across each resonant surface.
Radial profiles of the computed electromagnetic torque density with different values of the Lundquist number S = 10^{6}, 10^{7}, 10^{9}, for (a) plasma rotation frequency and (b) .
Radial profiles of the computed electromagnetic torque density with different values of the Lundquist number S = 10^{6}, 10^{7}, 10^{9}, for (a) plasma rotation frequency and (b) .
The computed net electromagnetic torque, acting on the plasma column, versus the magnetic Lundquist number S, for (a) plasma rotation frequency and (b) . Both the volumetric integration (“o”) and the vacuum surface integration (“ + ”) methods are applied to compute the net torque in (a).
The computed net electromagnetic torque, acting on the plasma column, versus the magnetic Lundquist number S, for (a) plasma rotation frequency and (b) . Both the volumetric integration (“o”) and the vacuum surface integration (“ + ”) methods are applied to compute the net torque in (a).
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