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Eigenmode characteristics of the double tearing mode in the presence of shear flows
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10.1063/1.4793445
/content/aip/journal/pop/20/2/10.1063/1.4793445
http://aip.metastore.ingenta.com/content/aip/journal/pop/20/2/10.1063/1.4793445
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Equilibrium magnetic field with (solid curves) and shear flow profiles with (dashed curves).

Image of FIG. 2.
FIG. 2.

Dependence of the linear growth rate on the flow amplitude for m = 1 mode.

Image of FIG. 3.
FIG. 3.

Contour plots of the magnetic flux for undistorted (a) and distorted (b) island structure. The markers X and O stand for the X-point and O-point of the magnetic islands. (a) and (b) .

Image of FIG. 4.
FIG. 4.

Evolution of the potential energy for , , and .

Image of FIG. 5.
FIG. 5.

Linear growth rates (a) and real frequencies (b) of the eigen modes as a function of the flow amplitude. Zoomed views for the region are shown in (c) and (d). The parameters are the same as in Fig. 2 . The dotted-dashed lines are straight lines for reference.

Image of FIG. 6.
FIG. 6.

Contour plots of the island structures (upper panel) and the perturbed magnetic fluxes (middle panel) as well as the eigen functions of m = 1 mode (lower panel) for the two DTMs corresponding to the cases A–E marked in Fig. 5 for different flow amplitudes.

Image of FIG. 7.
FIG. 7.

Radial profiles of the phase angle of perturbed magnetic flux for different flow amplitudes , , and . (a) even DTM, (b) odd DTM. The dotted-dashed lines are straight lines for reference.

Image of FIG. 8.
FIG. 8.

Difference between the phase angles at two sides out of the current sheets, , as a function of flow amplitude.

Image of FIG. 9.
FIG. 9.

Growth rates as a function of for the even and odd DTMs with equilibrium flow profile and .

Image of FIG. 10.
FIG. 10.

Time evolution of the potential energy of the DTMs with different initial perturbations: (a) only the eigen function with or , (b)mixed eigen function of the both. The analytical expression of Eq. (14) is also plotted for comparison.

Image of FIG. 11.
FIG. 11.

Radial structures of the perturbed currents ( ) and the Alfvén resonance condition of the DTM with negative frequency for different flow amplitudes (a) , (b) , and (c) .

Image of FIG. 12.
FIG. 12.

Plasma flow patterns (arrows) overlapped by the island structure (curves) for different flow amplitudes (a) , (b) , and (c) corresponding to the cases in Fig. 11 .

Image of FIG. 13.
FIG. 13.

Real part of the instability parameter, , for the STM-type DTM as a function of flow amplitude in the region .

Image of FIG. 14.
FIG. 14.

Growth rates (a) and real frequencies (b) of the DTMs with the equilibrium flow profile .

Image of FIG. 15.
FIG. 15.

Comparison of the growth rates of the KHI for different models. Case 1: the ideal piecewise continuous profile of shear flow (solid). Case 2: asymptotic limit ( ) of Eq. (5) with constant B 0 (long dashed). Case 3: with double current sheet configuration (dotted-dashed). Case 4: with constant B 0 (short dashed).

Image of FIG. 16.
FIG. 16.

Eigen functions of the KHIs under double current sheet configuration (case 3, thick curves) and constant magnetic field (case 4, thin curves) with .

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/content/aip/journal/pop/20/2/10.1063/1.4793445
2013-02-21
2014-04-17
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Eigenmode characteristics of the double tearing mode in the presence of shear flows
http://aip.metastore.ingenta.com/content/aip/journal/pop/20/2/10.1063/1.4793445
10.1063/1.4793445
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