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Integration of vacuum potential energy into ideal magnetohydrodynamic stability calculations for flux-core-spheromak configurations
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10.1063/1.2754632
/content/aip/journal/pop/14/8/10.1063/1.2754632
http://aip.metastore.ingenta.com/content/aip/journal/pop/14/8/10.1063/1.2754632
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

(Color online) Magnetic coordinates cross section for (a) a CKF configuration, composed of ST, SP, and two SC, showing the origin and the “separatrix” angle that labels the lower regular X-point, (b) a FCS configuration, composed of ST and SP, showing the angles labeling the lower singular X-point, labeling the lower regular X-point, and that marks the position of the lower plasma-electrode interface.

Image of FIG. 2.
FIG. 2.

PROTO-SPHERA equilibrium; full curves represent the magnetic surfaces through the separatrix and the axis of symmetry , where the Boozer coordinates are singular. Dotted curves represent: the last mesh surface inside the ST ; the first mesh surface inside the SP ; and the last mesh surface near the symmetry axis .

Image of FIG. 3.
FIG. 3.

(Color online) Vacuum 2D finite-element mesh used for PROTO-SPHERA with ideal conducting shells within the vacuum vessel.

Image of FIG. 4.
FIG. 4.

(Color online) Mesh of Boozer coordinates ( radial, poloidal) for PROTO-SPHERA with conducting shells and conductors of the Screw-Pinch current. The shadings mark the smaller vacuum regions involved in the calculation of the vacuum energy contribution from the last mesh surface .

Image of FIG. 5.
FIG. 5.

(Color online) PROTO-SPHERA: (a) flux surfaces (red), values of Boozer poloidal angle (blue), and directions of contour integrations; (b) path for calculation of vacuum energy on , in the intermediate range and illustration of the action of reduced Green’s functions and ; (c) path for calculation of vacuum energy on , in the two disconnected ranges of poloidal Boozer angles and , and illustration of the action of reduced Green’s functions and .

Image of FIG. 6.
FIG. 6.

(Color online) TS-3 flux-core-spheromak configuration, composed of ST and SP, with and : (a) Boozer coordinates cross section, showing the angles labeling the lower regular X-point and and that mark the position of the two plasma-electrode interfaces; (b) vacuum 2D finite element mesh (shaded), with conducting shells marked in green.

Image of FIG. 7.
FIG. 7.

(Color online) Displacement arrow plots for the largest eigenvalue mode with for TS-3 with , , and . The left-hand side plots are calculated by STABLE, with the condition ; the right-hand side plots are calculated by STABLECN.

Image of FIG. 8.
FIG. 8.

(Color online) Displacement arrow plots for the largest eigenvalue mode with for TS-3 with , , and , all upon a poloidal cross section. The left-hand side plots are calculated by STABLE, with the condition ; the right-hand side plots are calculated by STABLECN.

Image of FIG. 9.
FIG. 9.

(Color online) Displacement arrow plots for the largest eigenvalue mode with for TS-3 with , , and . The left-hand side plots are calculated by STABLE, with the condition ; the right-hand side plots are calculated by STABLECN.

Image of FIG. 10.
FIG. 10.

(Color online) Displacement arrow plots for the largest eigenvalue mode with for TS-3 with , , and , all upon a poloidal cross section. The left-hand side plots are calculated by STABLE, with the condition ; the right-hand side plots are calculated by STABLECN.

Image of FIG. 11.
FIG. 11.

(Color online) Comparison of for free-boundary stability results (without any ideal conducting shell near the plasma) between the compressible stability code STABLE (squares) and the ERATO code (Ref. 21) (line), for the Solovev equilibrium with and . The toroidal mode numbers are and , respectively. All the results from STABLE are obtained with a spectrum of poloidal mode numbers in the range and a few cases with (diamonds).

Image of FIG. 12.
FIG. 12.

(Color online) Comparison of for free-boundary stability results (with an ideal conducting shell at ) between the compressible stability code STABLE (dots) and the Kerner and PEST codes (Ref. 21) (line), for the Solovev equilibrium with and . The toroidal mode number is . All the results from STABLE are obtained with a spectrum of poloidal mode numbers in the range .

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2007-08-28
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Integration of vacuum potential energy into ideal magnetohydrodynamic stability calculations for flux-core-spheromak configurations
http://aip.metastore.ingenta.com/content/aip/journal/pop/14/8/10.1063/1.2754632
10.1063/1.2754632
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