Page 10 - Feasibility study of microwave electron heating on the C-2 field-reversed configuration device

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Phys. Plasmas 23, 012509 (2016)
FIG. 6. Mode structure and field geometry of kfqi 1⁄4 5:42 instability in the FRC SOL versus poloidal angle. From top to bottom, panels show electro- static potential, field line curvature, magnitude of the magnetic field line, and the radial gradient of the magnetic field.
Overall change in energy and momentum is less than 1% for both species.
The mode structure of the instability is shown in Fig. 6. The mode is characterized by m1⁄40, 1, 2, 3 mode number components. This structure is common to all of the scanned single-n modes in the SOL. The curvature, magnitude of the magnetic field, and the radial gradient of the magnetic field are also shown in Fig. 6. Small-scale fluctuations in the magnetic curvature are due to numerical differencing on the discrete grid. Geometrically, the scrape-off layer region has weaker curvature than the core but a much stronger magnetic field gradient.
Numerical convergence tests have been carried out in the SOL. Mode frequencies converge with only a single par- ticle per cell. Across the entire particle-per-cell convergence scan, the variation in x is less than 5% and variation in c is less than 0.1%. The implementation of the partial torus do- main allows a significant number of particles per wavelength even in simulations using only one particle per cell. Linear growth rate, c, converges around a time step size, DtðR0 =Cs Þ 1⁄4 0:005, while x shows little variation over the scan. The frequency converges at 64 poloidal grid points, while the growth-rate converges around 128 grid points.
V. DISCUSSION
In this study, a formulation for gyrokinetic particle sim- ulation of a field reversed configuration is presented. A map- ping algorithm to produce Boozer magnetic coordinates has been developed and verified, along with an extension of Boozer coordinates into the scrape-off layer region. A for- mulation for an efficient linear Poisson solver with particle gyroaveraging is also established. All of these new features have been implemented in the GTC, and linear instabilities in an FRC geometry have been simulated.
Initial results from GTC represent, to date, the only first- principles gyrokinetic simulation of an FRC in realistic
geometry. Simulation in the scrape-off layer also represents the first inclusion of open field line geometry in the GTC for- mulation. Initial simulation parameters and results are pre- sented. Pressure gradient driven driftwave modes are observed and effects of collisionality are considered. One no- table caveat is that electromagnetic effects are expected to be important in high-b FRC plasmas, but are excluded in this study. Electromagnetic effects, already included in the GTC framework, will be investigated in FRCs in the future.
Interestingly, in the FRC core, ion scale instability is found to be suppressed, likely by large ion Larmour radius. Electron scale turbulence is also strongly stabilized, but details of possible electron scale modes are still under evaluation. In the scrape off layer, both ion and electron scale linear drift- waves are present and unstable. Remarkably, considering the electrostatic limitation of the computational model, linear instability thresholds in both the core and SOL have good qual- itative agreement with experimental turbulence fluctuation measurements made with Doppler backscattering in the C-2 FRC experiment.68 More detailed theoretical analysis of the physics in both the FRC core and SOL will be discussed in a forthcoming publication.66 Comparisons against experimental data will be reevaluated as the computational model is refined.
The ultimate goal of first principles FRC simulations is to understand the transport scaling in the FRC plasma, towards the goal of creating a fusion reactor. Understanding the coupling between the core and SOL regions of the FRC is a critical piece of the transport scaling picture. Immediate efforts in the future are towards developing coupled core- SOL simulations. Other priorities include electromagnetic simulations and a Vlasov ion pusher, which has already been implemented in GTC, to accurately capture large ion Larmour radius effects.
ACKNOWLEDGMENTS
The authors would like to thank Lothar Schmitz, Toshiki Tajima, and Michl Binderbauer at Tri Alpha Energy, Inc., for ongoing insights and collaboration in the development of these simulations. We are also grateful for the ground breaking contributions of the late Norman Rostoker. This work was supported by Tri Alpha Energy through the Norman Rostoker Fellowship and Grant No. TAE-200441 and by the DOE SciDAC GSEP center. This research used resources of the Oak Ridge Leadership Computing Facility at Oak Ridge National Laboratory (DOE Contract No. DE-AC05-00OR22725), and the National Energy Research Scientific Computing Center (DOE Contract No. DE-AC02-05CH11231).
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