Abstract
The twofluid, lowcollisionality equilibrium model [Ishida et al., Phys. Plasmas17, 122507 (2010)] was applied to reconstruct the highperformance National Spherical Torus eXperiment (NSTX) [Bell et al., Phys. Plasmas17, 082507 (2010)]. Profiles of the electron and ion temperatures, the toroidalflow, the density, and the magnetic field pitch angle of the reconstructed equilibrium fit well the measured profiles of NSTX shot 132484 at 0.7 s. The reconstructed equilibrium shows that (1) the global twofluid effect is fairly large; (2) the perpendicular flow of both species differs significantly from the ExB drift; (3) local gradient scale lengths can be smaller than the ion inertial length especially on the outboard side; (4) the electrostatic potential varies along a given magnetic flux by as much as several percent of the electron temperature in the core region.
We would like to thank Dr. Stanley M. Kaye, Dr. Ronald E. Bell, Dr. Benoit P. LeBlanc, and Dr. Howard Y. Yuh for providing the NSTX data and the TRANSP results shown in Figs. 1–6 and Table III and their useful comments. One of the authors (A.I.) acknowledges the encouragement of Dr. Y.K. Martin Peng.
I. INTRODUCTION
II. MODEL AND METHOD OF SURFACE FUNCTION SELECTION
A. Full twofluid model
B. Method for constructing the surface functions
C. Contrasts with onefluid and HallMHD models
III. RECONSTRUCTION OF NSTX EQUILIBRIA
IV. PROPERTIES OF RECONSTRUCTED EQUILIBRIA
V. DISCUSSION
Key Topics
 Toroidal plasma confinement
 30.0
 Magnetic fields
 20.0
 Plasma temperature
 17.0
 Current density
 9.0
 Plasma flows
 9.0
H05H1/02
Figures
Comparison of electron temperature profiles. Black diamonds show the electron temperatures T_{e} (keV) at (a) 0.7 s and (b) 0.916 s of NSTX #132484. The red lines show the reconstructed electron temperatures T_{e} at the symmetry plane. The black dotted lines show the results computed by the TRANSP code.
Comparison of electron temperature profiles. Black diamonds show the electron temperatures T_{e} (keV) at (a) 0.7 s and (b) 0.916 s of NSTX #132484. The red lines show the reconstructed electron temperatures T_{e} at the symmetry plane. The black dotted lines show the results computed by the TRANSP code.
Comparison of ion temperature profiles. Black diamonds show the ion temperatures T_{i} (keV) at (a) 0.7 s and (b) 0.916 s of NSTX #132484. The red lines show the reconstructed bulk ion temperatures T_{i} at the symmetry plane. The black dotted lines show the results computed by the TRANSP code.
Comparison of ion temperature profiles. Black diamonds show the ion temperatures T_{i} (keV) at (a) 0.7 s and (b) 0.916 s of NSTX #132484. The red lines show the reconstructed bulk ion temperatures T_{i} at the symmetry plane. The black dotted lines show the results computed by the TRANSP code.
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 poloidalflow contribution, last term of Eq. (23). The black dotted lines show the results computed by the TRANSP code.
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 poloidalflow contribution, last term of Eq. (23). The black dotted lines show the results computed by the TRANSP code.
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 u_{iz} in the outboard region indicates that the bulk ion poloidal rotation is in the ion diamagnetic drift direction.
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 u_{iz} in the outboard region indicates that the bulk ion poloidal rotation is in the ion diamagnetic drift direction.
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.
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.
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.
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.
Safety factor q for the reconstructed equilibria for (a) 0.7 s and (b) 0.916 s.
Safety factor q for the reconstructed equilibria for (a) 0.7 s and (b) 0.916 s.
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.
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.
Radial electric field profiles of the reconstructed equilibria for (a) 0.7 s and (b) 0.916 s E_{r}_pi (dotted red line), E_{r}_tz (blue line), E_{r}_zt (green line), and E_{r}_centri (purple line) show the first, second, third, and fourth terms of Eq. (38) in the unit of kV/m. E_{r}_centri is too small to see. The red lines show the net electric field E_{r}.
Radial electric field profiles of the reconstructed equilibria for (a) 0.7 s and (b) 0.916 s E_{r}_pi (dotted red line), E_{r}_tz (blue line), E_{r}_zt (green line), and E_{r}_centri (purple line) show the first, second, third, and fourth terms of Eq. (38) in the unit of kV/m. E_{r}_centri is too small to see. The red lines show the net electric field E_{r}.
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.
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.
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.
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.
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 B_{z} 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.
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 B_{z} 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.
Poloidal magnetic flux (black line) and ion surface variable Y_{i} (red line) defined by Eq. (10) at the symmetry plane in dimensionless unit. Scale of the vertical axis is 0.147 Wb per unit.
Poloidal magnetic flux (black line) and ion surface variable Y_{i} (red line) defined by Eq. (10) at the symmetry plane in dimensionless unit. Scale of the vertical axis is 0.147 Wb per unit.
(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.
(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.
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 onefluid model. Scale of the vertical axis is 111.7 kHz per unit.
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 onefluid model. Scale of the vertical axis is 111.7 kHz per unit.
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 percent.
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 percent.
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).
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
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.
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.
Various values of the reconstructed equilibria.
Various values of the reconstructed equilibria.
Discharge parameters of NSTX shot 132484.
Discharge parameters of NSTX shot 132484.
Article metrics loading...
Full text loading...
Most read this month
Most cited this month










Electron, photon, and ion beams from the relativistic interaction of Petawatt laser pulses with solid targets
Stephen P. Hatchett, Curtis G. Brown, Thomas E. Cowan, Eugene A. Henry, Joy S. Johnson, Michael H. Key, Jeffrey A. Koch, A. Bruce Langdon, Barbara F. Lasinski, Richard W. Lee, Andrew J. Mackinnon, Deanna M. Pennington, Michael D. Perry, Thomas W. Phillips, Markus Roth, T. Craig Sangster, Mike S. Singh, Richard A. Snavely, Mark A. Stoyer, Scott C. Wilks and Kazuhito Yasuike

Commenting has been disabled for this content