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Toroidal modeling of interaction between resistive wall mode and plasma flow
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10.1063/1.4793449
/content/aip/journal/pop/20/2/10.1063/1.4793449
http://aip.metastore.ingenta.com/content/aip/journal/pop/20/2/10.1063/1.4793449
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

The plasma boundary shape of the toroidal equilibrium.

Image of FIG. 2.
FIG. 2.

Radial profiles of the equilibrium quantities for (a) the safety factor q, (b) the plasma pressure normalized by , (c) the plasma density normalized to unity at the magnetic axis, and (d) the toroidal rotation frequency of the plasma, normalized by the on-axis Alfvén frequency.

Image of FIG. 3.
FIG. 3.

Linear stability of (a) the ideal external, pressure-driven kink mode and (b) the resistive wall mode in the presence of the plasma flow.

Image of FIG. 4.
FIG. 4.

Evolution of an initially unstable RWM: (a) the amplitude of the perturbed radial field b 1 at the q = 2 surface, (b) the real and imaginary parts of the perturbed radial field b 1 at the q = 2 surface, (c) the radial profile of the plasma rotation frequency, and (d) the plasma rotation frequency at the q = 2 and q = 3 surfaces. The dashed vertical lines in (a), (b), and (d) indicate the moment of time when the non-linear coupling between the mode and the plasma flow is switched on. The dashed vertical lines in (c) indicate the location of the q = 2 and 3 rational surfaces, respectively. The numbered lines in (c) correspond to time: 1– , 2– , 3– , and 4– . Both the electromagnetic and the NTV torques are included in this simulation.

Image of FIG. 5.
FIG. 5.

Time trace of the net toroidal electromagnetic (solid line) and NTV (dashed line) torques acting on the plasma during the non-linear evolution of an initially unstable RWM as described in Fig. 4 .

Image of FIG. 6.
FIG. 6.

Radial profiles of the initial (i.e., before closing the non-linear coupling loop) E × B rotation frequency , the precessional drift frequency of deeply trapped thermal ions at thermal velocity, and the ion-ion collision frequency . ɛ is approximately the inverse aspect ratio.

Image of FIG. 7.
FIG. 7.

Evolution of an initially unstable RWM: (a) the amplitude of the perturbed radial field b 1 at the q = 2 surface, (b) the real and imaginary parts of the perturbed radial field b 1 at the q = 2 surface, (c) the radial profile of the plasma rotation frequency, and (d) the plasma rotation frequency at the q = 2 and q = 3 surfaces. The dashed vertical lines in (a), (b), and (d) indicate the moment of time when the non-linear coupling between the mode and the plasma flow is switched on. The dashed vertical lines in (c) indicate the location of the q = 2 and 3 rational surfaces, respectively. The numbered lines in (c) correspond to time: 1– , 2– , and 3– . Only the electromagnetic is included in this simulation.

Image of FIG. 8.
FIG. 8.

Time traces of the amplitude of the perturbed radial field b 1 at the q = 2 surface, with and without inclusion of the NTV torque in the simulation. The dashed curve corresponds to the exponential growth of the initially unstable linear mode. The dashed vertical line indicates the moment of time when the non-linear coupling between the mode and the plasma flow is switched on.

Image of FIG. 9.
FIG. 9.

Evolution of an initially stable RWM: (a) the amplitude of the perturbed radial field b 1 at the q = 2 surface, (b) the real and imaginary parts of the perturbed radial field b 1 at the q = 2 surface, (c) the plasma rotation frequency at the q = 2 and q = 3 surfaces, and (d) the net toroidal electromagnetic and NTV torques acting on the plasma. The dashed vertical lines in (a), (b), and (c) indicate the moment of time when the non-linear coupling between the mode and the plasma flow is switched on. The initial mode amplitude, normalized by B 0, is .

Image of FIG. 10.
FIG. 10.

Evolution of an initially stable RWM: (a) the amplitude of the perturbed radial field b 1 at the q = 2 surface, (b) the real and imaginary parts of the perturbed radial field b 1 at the q = 2 surface, (c) the radial profile of the plasma rotation frequency, and (d) the plasma rotation frequency at the q = 2 and q = 3 surfaces. The dashed vertical lines in (a), (b), and (d) indicate the moment of time when the non-linear coupling between the mode and the plasma flow is switched on. The dashed vertical lines in (c) indicate the location of the q = 2 and 3 rational surfaces, respectively. The numbered lines in (c) correspond totime: 1– , 2– , and 3– . The initial mode amplitude, normalized by B 0, is . Both the electromagnetic and the NTV torques are included in this simulation.

Image of FIG. 11.
FIG. 11.

Evolution of an initially stable RWM: (a) the amplitude of the perturbed radial field b 1 at the q = 2 surface, (b) the real and imaginary parts of the perturbed radial field b 1 at the q = 2 surface, (c) the radial profile of the change of the plasma rotation frequency, and (d) the plasma rotation frequency at the q = 2 and q = 3 surfaces. The dashed vertical lines in (a), (b), and (d) indicate the moment of time when the non-linear coupling between the mode and the plasma flow is switched on. The dashed vertical lines in (c) indicate the location of the q = 2 and 3 rational surfaces, respectively. The initial mode amplitude, normalized by B 0, is . Only the electromagnetic torque is included in this simulation.

Image of FIG. 12.
FIG. 12.

Time traces of the net toroidal electromagnetic (solid line) and NTV (dashed line) torques acting on the plasma, during the non-linear evolution of an initially stable RWM, with the initial mode amplitude : (a) both electromagnetic and NTV torques are included in the toroidal torque balance and (b) only the electromagnetic torque is included.

Image of FIG. 13.
FIG. 13.

Evolution of an initially stable RWM: (a) the amplitude of the perturbed radial field b 1 at the q = 2 surface, (b) the real and imaginary parts of the perturbed radial field b 1 at the q = 2 surface, (c) the radial profile of the plasma rotation frequency, and (d) the plasma rotation frequency at the q = 2 and q = 3 surfaces. The dashed vertical lines in (a), (b), and (d) indicate the moment of time when the non-linear coupling between the mode and the plasma flow is switched on. The dashed vertical lines in (c) indicate the location of the q = 2 and 3 rational surfaces, respectively. The numbered lines in (c) correspond to time: 1– , 2– , 3– , and 4– . The initial mode amplitude, normalized by B 0, is . Both the electromagnetic and the NTV torques are included in this simulation.

Image of FIG. 14.
FIG. 14.

Evolution of an initially stable RWM: (a) the amplitude of the perturbed radial field b 1 at the q = 2 surface, (b) the real and imaginary parts of the perturbed radial field b 1 at the q = 2 surface, (c) the radial profile of the plasma rotation frequency, and (d) the plasma rotation frequency at the q = 2 and q = 3 surfaces. The dashed vertical lines in (a), (b), and (d) indicate the moment of time when the non-linear coupling between the mode and the plasma flow is switched on. The dashed vertical lines in (c) indicate the location of the q = 2 and 3 rational surfaces, respectively. The numbered lines in (c) correspond to time: 1– , 2– , and 3– . The initial mode amplitude, normalized by B 0, is . Only, the electromagnetic torque is included in this simulation.

Image of FIG. 15.
FIG. 15.

Time traces of the amplitude of the perturbed radial field b 1 at the q = 2 surface, with and without inclusion of the NTV torque in the simulations for an initially stable RWM, with the initial mode amplitude at (a) and (b) . The dashed curves correspond to the exponential decay of the initially stable linear mode. The dashed vertical lines indicate the moment of time when the non-linear coupling between the mode and the plasma flow is switched on.

Image of FIG. 16.
FIG. 16.

Time traces of (a) the amplitude of the perturbed radial field b 1 at the q = 2 surface, and (b) the plasma rotation frequency at the q = 2 and q = 3 surfaces, with various choices of the initial mode amplitude. The dashed curves in (a) correspond to the exponential decay of the initially stable linear mode. The dashed vertical lines indicate the moment of time when the non-linear coupling between the mode and the plasma flow is switched on. Both the electromagnetic and the NTV torques are included in the simulations.

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/content/aip/journal/pop/20/2/10.1063/1.4793449
2013-02-21
2014-04-16
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Toroidal modeling of interaction between resistive wall mode and plasma flow
http://aip.metastore.ingenta.com/content/aip/journal/pop/20/2/10.1063/1.4793449
10.1063/1.4793449
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