Mode coupling effects on resistive wall instabilities

The stability of a perfectly conducting fluid layer flowing along a magnetic field, parallel to a finitely conducting thin wall is examined. Finite layer width and compressibility of the fluid are shown to significantly lower the flow velocity required for instability to set in. The effect of axial flow on the stability of a cylindrical pinch surrounded by a resistive wall is examined. Flow is shown to have a destabilizing effect.

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“…A similar result has been obtained before. 17 This result has a simple physical explanation. The dispersion relation Eq.…”

Section: ͑90͒mentioning

confidence: 82%

“…However, some recent studies, 8,17 show that there are parameter regimes where plasma flow and a resistive wall can have a destabilizing effect. In order to isolate this destabilizing effect a very simple configuration was studied in Ref.…”

Section: Discussionmentioning

confidence: 97%

Flow driven resistive wall instability

1999

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“…This behavior is explained by the mode-coupling picture of Ref. 17 and is even more noticeable for ideal plasma resistive wall modes. 1,17 Larger X is stabilizing for the full MHD model and the expanding stable region develops a tail toward negative G and K. This general behavior of stabilization as X increases is consistent with the observation in Ref.…”

Section: Results With Plasma Rotation and Complex Gain G Imentioning

confidence: 77%

“…1,2,5, 7,8,[11][12][13]17,18,20,23,26,28 Studies have also been performed for reversed field pinches (RFPs). 4, 39,40 Earlier studies in tokamak geometry 3, 6,9,10,14,30,38 investigated sensing either the radial or the poloidal component of the magnetic field, concluding that it is better to sense the poloidal component, and that the latter measurement is of more use if it is inside the wall.…”

Section: Introductionmentioning

confidence: 99%

Control of linear modes in cylindrical resistive magnetohydrodynamics with a resistive wall, plasma rotation, and complex gain

Brennan

Finn

2014

Physics of Plasmas

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Feedback stabilization of magnetohydrodynamic (MHD) modes in a tokamak is studied in a cylindrical model with a resistive wall, plasma resistivity, viscosity, and toroidal rotation. The control is based on a linear combination of the normal and tangential components of the magnetic field just inside the resistive wall. The feedback includes complex gain, for both the normal and for the tangential components, and it is known that the imaginary part of the feedback for the former is equivalent to plasma rotation [J. M. Finn and L. Chacon, Phys. Plasmas 11, 1866 (2004)]. The work includes (1) analysis with a reduced resistive MHD model for a tokamak with finite b and with stepfunction current density and pressure profiles, and (2) computations with a full compressible visco-resistive MHD model with smooth decreasing profiles of current density and pressure. The equilibria are stable for b ¼ 0 and the marginal stability values b rp,rw < b rp,iw < b ip,rw < b ip,iw (resistive plasma, resistive wall; resistive plasma, ideal wall; ideal plasma, resistive wall; and ideal plasma, ideal wall) are computed for both models. The main results are: (a) imaginary gain with normal sensors or plasma rotation stabilizes below b rp,iw because rotation suppresses the diffusion of flux from the plasma out through the wall and, more surprisingly, (b) rotation or imaginary gain with normal sensors destabilizes above b rp,iw because it prevents the feedback flux from entering the plasma through the resistive wall to form a virtual wall. A method of using complex gain G i to optimize in the presence of rotation in this regime with b > b rp,iw is presented. The effect of imaginary gain with tangential sensors is more complicated but essentially destabilizes above and below b rp,iw . V C 2014 AIP Publishing LLC. [http://dx.

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“…On the other hand, in the parameter range for which the resistive plasma form of the mode ͑''tearing''͒ is wall stabilized, it appears to be possible to stabilize the mode over a large parameter range with slow rotation frequencies, of the order of the nominal tearing growth rate. [31][32][33][34][35] These results suggest that rotational stabilization of the resistive wall mode is too delicate and requires too much rotation above the ideal plasma threshold ͑with wall at infinity͒, but that actual devices might be operated at parameters for which the resistive plasma form of the mode is wall stabilized. Since the external kink is a resonant mode ͑i.e., has mode rational surfaces in the plasma but is not an internal mode͒ more recent studies have found that it can be stabilized by slow ͑tearing rate͒ rotation, above the ideal plasma ␤ limit with the wall at infinity in the range of parameters for which the resistive plasma form of the mode is also wall stabilized.…”

Section: Introductionmentioning

confidence: 91%

Nonlinear tearing modes in the presence of resistive wall and rotation

Finn

Sovinec

1998

Physics of Plasmas

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Nonlinear simulations of tearing modes with a resistive wall and plasma rotation in a two-dimensional (2-D) incompressible slab are presented. The regimes of interest include cases (1) in which a tearing mode is unstable even for a perfectly conducting wall; (2) in which a resistive wall tearing mode is unstable but may be stabilized by rotation. In (1), the mode can lead to a wall locking process, in which both the flow and the mode’s phase velocity are slowed, allowing flux diffusion through the wall and a wider island. There is a bifurcation with hysteresis between locked and unlocked states. If the decay of total momentum is large, the range with multiple states is smaller. In (2) resistive wall modes grow and lock for all parameters with linear instability. And even if rotation gives linear stability, there is nonlinear instability. The bifurcation diagram is similar to that for case (1), but in which the zero island width state takes the place of the unlocked state. Results are shown for case (2) giving the critical field error to drive nonlinear instability and begin locking.

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Mode coupling effects on resistive wall instabilities

Cited by 24 publications

References 13 publications

Flow driven resistive wall instability

Flow driven resistive wall instability

Control of linear modes in cylindrical resistive magnetohydrodynamics with a resistive wall, plasma rotation, and complex gain

Nonlinear tearing modes in the presence of resistive wall and rotation

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