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Spherical torus equilibria reconstructed by a two-fluid, low-collisionality model
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10.1063/1.4762846
/content/aip/journal/pop/19/10/10.1063/1.4762846
http://aip.metastore.ingenta.com/content/aip/journal/pop/19/10/10.1063/1.4762846

Figures

Image of FIG. 1.
FIG. 1.

Comparison of electron temperature profiles. Black diamonds show the electron temperatures Te (keV) at (a) 0.7 s and (b) 0.916 s of NSTX #132484. The red lines show the reconstructed electron temperatures Te at the symmetry plane. The black dotted lines show the results computed by the TRANSP code.

Image of FIG. 2.
FIG. 2.

Comparison of ion temperature profiles. Black diamonds show the ion temperatures Ti (keV) at (a) 0.7 s and (b) 0.916 s of NSTX #132484. The red lines show the reconstructed bulk ion temperatures Ti at the symmetry plane. The black dotted lines show the results computed by the TRANSP code.

Image of FIG. 3.
FIG. 3.

Comparison of ion toroidal flow profiles. Black diamonds show the toroidal flow velocities (km/s) at (a) 0.7 s and (b) 0.916 s of NSTX #132484. The red lines show the reconstructed bulk ion toroidal flow velocities at the symmetry plane. The cyan lines show the contribution from the first term of Eq. (23). The difference between the red and cyan lines shows the poloidal-flow contribution, last term of Eq. (23). The black dotted lines show the results computed by the TRANSP code.

Image of FIG. 4.
FIG. 4.

Comparison of ion poloidal flow profiles. Black diamonds show the measured impurity ion (carbon) poloidal flow velocities (km/s) at (a) 0.7 s and (b) 0.916 s of NSTX #132484. The red lines show the reconstructed bulk ion (deuterim) poloidal flow velocities at the symmetry plane. Vertical lines (cyan) mark the magnetic axis. Negative uiz in the outboard region indicates that the bulk ion poloidal rotation is in the ion diamagnetic drift direction.

Image of FIG. 5.
FIG. 5.

Comparison of electron density profiles. Black diamonds show the electron densities n () at (a) 0.7 s and (b) 0.916 s of NSTX #132484. The red lines show the reconstructed electron densities n at the symmetry plane. The cyan lines show defined by Eq. (21). Thus difference between the cyan and red lines is due to the effect of flow (See Eq. (20)). The black dotted lines show the results computed by the TRANSP code.

Image of FIG. 6.
FIG. 6.

Comparison of magnetic field pitch angle profiles. Black diamonds show the magnetic field pitch angles (degree) at (a) 0.696 s and (b) 0.918 s of NSTX #132484. The red lines show the reconstructed magnetic field pitch angles at the symmetry plane. The black dotted lines show the results computed by the TRANSP code.

Image of FIG. 7.
FIG. 7.

Safety factor q for the reconstructed equilibria for (a) 0.7 s and (b) 0.916 s.

Image of FIG. 8.
FIG. 8.

Toroidal current density profiles for the reconstructed equilibria for (a) 0.7 s and (b) 0.916 s: ion current density , electron current density , and toroidal current density . Scale of the vertical axes is per unit.

Image of FIG. 9.
FIG. 9.

Radial electric field profiles of the reconstructed equilibria for (a) 0.7 s and (b) 0.916 s Er_pi (dotted red line), Er_tz (blue line), Er_zt (green line), and Er_centri (purple line) show the first, second, third, and fourth terms of Eq. (38) in the unit of kV/m. Er_centri is too small to see. The red lines show the net electric field Er.

Image of FIG. 10.
FIG. 10.

Flow velocities perpendicular to the magnetic field for ions (, blue) and electrons (, green) compared with the E × B drift velocity (red) of the reconstructed equilibria for (a) 0.7 s and (b) 0.916 s.

Image of FIG. 11.
FIG. 11.

The red lines (blue lines) show the local ratio of the ion inertial length to the ion pressure gradient scale length (toroidal velocity gradient scale length) of the reconstructed equilibria for (a) 0.7 s and (b) 0.916 s.

Image of FIG. 12.
FIG. 12.

Magnetic field profiles at the symmetry plane. The blue line shows the toroidal magnetic field which is in counter direction to the plasma current. The dotted red line shows the vacuum magnetic field and the green line the axial component of magnetic field Bz in dimensionless unit. The magnetic axis is at R 0 = 106.5 cm. Clearly, near the edge. Scale of the vertical axis is 0.070T per unit.

Image of FIG. 13.
FIG. 13.

Poloidal magnetic flux (black line) and ion surface variable Yi (red line) defined by Eq. (10) at the symmetry plane in dimensionless unit. Scale of the vertical axis is 0.147 Wb per unit.

Image of FIG. 14.
FIG. 14.

(a) Electron density n and (b) total pressure Pt versus normalized flux , where is the value of at the magnetic axis in dimensionless unit. Subscript “in” (“out”) indicates each profile in the inboard (outboard) region. The density n is not a magnetic surface function. As a result, the total pressure (sum of the ion and electron pressures) Pt is not a magnetic surface function. The total pressure peak position is 2.3 cm outward from the magnetic axis. The scale of the vertical axis in (a) is per unit and in (b) is per unit.

Image of FIG. 15.
FIG. 15.

versus normalized flux . See the caption of Fig. 14 for symbols. Toroidal velocity divided by major radius, , is not a magnetic flux function even though polodal velocity is much less than toroidal velocity. This clearly differs from the one-fluid model. Scale of the vertical axis is 111.7 kHz per unit.

Image of FIG. 16.
FIG. 16.

Ratio of electrostatic potential difference to electron temperature versus normalized flux . The potential difference is defined by Eq. (39). In the core region, can be several per-cent.

Image of FIG. 17.
FIG. 17.

Reconstructed 2D spherical torus equilibrium. The contours of magnetic flux function (separatrix, red line), 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 are shown. and −0.074 at the inner and outer boundaries (blue line).

Tables

Generic image for table
Table I.

Input parameters and surface function coefficients of reconstructed equilibria for NSTX shot 132484 at 0.7 s and 0.916 s. The additional numbers in parentheses are at 0.916 s; otherwise the other numbers are the same for 0.7 s and 0.916 s.

Generic image for table
Table II.

Various values of the reconstructed equilibria.

Generic image for table
Table III.

Discharge parameters of NSTX shot 132484.

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/content/aip/journal/pop/19/10/10.1063/1.4762846
2012-10-25
2014-04-17
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Spherical torus equilibria reconstructed by a two-fluid, low-collisionality model
http://aip.metastore.ingenta.com/content/aip/journal/pop/19/10/10.1063/1.4762846
10.1063/1.4762846
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