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Three-dimensional magnetohydrodynamic simulations of the Helicity Injected Torus with Steady Inductive drivea)
a)Paper PI1B 4, Bull. Am. Phys. Soc. 49, 287 (2004).
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Image of FIG. 1.
FIG. 1.

A cross section of HIT-SI showing one injector, and a schematic of the flux in that plane. Flux linking the injector shown also links one side of the spheromak, and the loop voltage on these field lines drives high spheromak edge currents.

Image of FIG. 2.
FIG. 2.

(a) A cut-away view of HIT-SI showing the location of the injector openings in the spheromak region. (b) A cut-away view of the simulated spheromak region. Where the injector openings would be are normal magnetic field boundary conditions, whose relative amplitudes are indicated on the two annular regions. The amplitudes oscillate sinusoidally, with the two injectors 90° out-of-phase.

Image of FIG. 3.
FIG. 3.

(Color). An injector annulus. The color indicates the magnitude of . The pink arrows are the radial electric fields that produce the “gap voltage.” A brief simulation with these boundary conditions produces the fields indicated by the black arrows, which connect the fields that are entering and exiting the simulated region on either side. The electric fields producing the voltage along these field lines are not shown.

Image of FIG. 4.
FIG. 4.

The grid for the SIHI simulations. The first two grid lines are at a uniform distance of 1 mm apart everywhere around the boundary. This is much smaller than the grid spacing elsewhere, as seen in the magnified region.

Image of FIG. 5.
FIG. 5.

(Color). Magnetic and kinetic energy spectra for the 1 mm edge-layer case, simulation, with all Fourier components plotted.

Image of FIG. 6.
FIG. 6.

(Color). Magnetic and kinetic energy spectra for the 1 cm edge layer, simulation, with all Fourier components plotted.

Image of FIG. 7.
FIG. 7.

(Color). (a) An flux tube that forms in the core of the 1 mm edge layer, simulation at 0.87 ms. Field lines outside this region are stochastic. (b) A cross section of (a) showing the islands.

Image of FIG. 8.
FIG. 8.

(Color). (a) A core of good flux surfaces at 1.23 ms surrounded by an rational surface, with one flux tube on this surface shown. Field lines outside the rational surface are stochastic. (b) A cross section of (a).

Image of FIG. 9.
FIG. 9.

(Color). Magnetic and kinetic energy spectra for the higher simulation. Beginning at 1.0 ms, three different scenarios are simulated, and each is plotted. In one, the injectors are maintained at their present amplitude, and the magnetic energy reaches a steady peak amplitude shortly thereafter. In the second, the injectors begin to ramp down at this point, and the magnetic energy soon begins to decay. In the third, the injectors are ramped up to 1.5 times their previous amplitude over the course of 0.2 ms, and held flat until nearly 2.0 ms.

Image of FIG. 10.
FIG. 10.

The ratio of (equilibrium) magnetic energy to (injector) magnetic energy. The dashed lines indicate the average value over one-half cycle for at its peak (gray) and at the end of the simulation (black).

Image of FIG. 11.
FIG. 11.

The spheromak toroidal current and toroidal flux and their ratio (times ) for and 897. The ratio gives a global value for the spheromak which is smaller than the spheromak eigenvalue of .

Image of FIG. 12.
FIG. 12.

(Color). Driven field lines at . The green lines follow a short path from one injector opening to the other that lies close to the inner radius on one side and close to the outer radius on the other. These field lines link the single blue field line, which follows a much longer path, making many toroidal transits around the core. Field lines of intermediate lengths also exist, but are not shown.


Generic image for table
Table I.

Parameters for the low simulations.

Generic image for table
Table II.

Parameters for the high simulation.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Three-dimensional magnetohydrodynamic simulations of the Helicity Injected Torus with Steady Inductive drivea)