Simulating CNT plasmas

Figure 1: Results of a VMEC fixed-boundary simulation of the CNT plasma. In this image, the plasma boundary is shown color-coded according to the strength of the magnetic field. For reference, the interlocked coils partially responsible for creating the magnetic field are also shown.

To enhance our understanding of the plasmas we observe in CNT, we have begun using the VMEC code to simulate the plasmas. Using certain measured steady-state plasma properties (e.g., pressure) as inputs, VMEC solves the equilibrium magnetohydrodynamic (MHD) equations to reconstruct other plasma properties that would be more difficult to measure directly (e.g., local current density).

Simulating CNT plasmas with VMEC presents some challenges owing to (1) fine structure in CNT's magnetic confinement volume and (2) CNT's low aspect ratio (the ratio of the major radius to the minor radius; toroids with a low aspect ratio are "thicker"). The low aspect ratio necessitates a large spatial volume to be simulated, and the fine structure requires high resolution within that volume. These two requirements are computationally demanding and result lengthy simulations that sometimes do not descend successfully.

To date, some successful simulations have been attained by sacrificing some spatial resolution. The simulations have been carried out in two ways: one (fixed-boundary) in which the plasma boundary is prescribed based on our own calculations of the vacuum magnetic field, and the other (free-boundary) in which VMEC figures out the boundary itself. As can be seen in Fig. 2, fixed-boundary simulations have permitted greater spatial resolution and therefore a more accurate depiction of the shape of CNT's confinement volume. For hotter, denser plasmas, however, free-boundary simulations will be necessary because the plasma geometry will likely deform significantly from the magnetic confinement volume in a vacuum.

Figure 2: Two cross-sections of the CNT plasma volume, comparing the precision of the plasma boundaries of the free- and fixed-boundary simulations. The outermost black curve represents the "true" boundary of the CNT plasma in the case of low temperature and density ("vacuum" conditions), the red curves represent the plasma edges determined in the highest-resoultion free-boundary simulation, and the blue curves represent the plasma edges corresponding to the highest-resolution fixed-boundary simulation.
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