Page 5 - Gyrokinetic simulation of driftwave instability in field-reversed configuration

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FIG. 4. Sample dispersion relation in the SOL region, for a drive strength, R0=L 1⁄4 4. Real frequency is shown by the blue solid line, and linear growth rate is shown by the red dashed line.
The dispersion relation for a typical SOL mode, with a driving gradient R0=L 4, is shown in Fig. 4. Notably, the sign of the mode frequency is consistent with both the elec- tron diamagnetic frequency as well as the ion grad-B fre- quency. As expected, the growth rate trends upwards as the gradient strength, R0=L, is increased.
The corresponding mode structure for the SOL instabil-
ity, for an intermediate scale length mode (kfqs 1⁄4 5:48), is
shown in Fig. 5. The qs length normalization is similar to qi
In this paper, electrostatic gyrokinetic simulations of driftwave turbulence in FRC geometry have been performed. Notably, for ion scale lengths (kf qi 1Þ, no instabilities exist in simulation in the FRC core region. A number of mecha- nisms may contribute to this observed stability. These candi- dates for core stabilization are under investigation and include finite Larmour radius, magnetic field gradient, and other effects of the magnetic geometry.
Driftwave turbulence is still marginal in the SOL, but possible to drive with realistic temperature and density gra- dients. A typical dispersion relation in the SOL indicates increased growth with stronger drive and indicates electron diamagnetic response or ion grad-B response as energy chan- nels for instability. Further analysis of particle phase space resonances is underway and will help complete the physical picture of the instabilities in the SOL.29 Realistically, mod- elled input equilibrium suggests that the peak driving gra- dients occur in the SOL region, just outside the magnetic separatrix.
These simulation results are consistent with the recent experimental data taken from the C-2 experiment.13 Doppler backscattering measurements of density fluctuations indicate a unique inverted turbulence spectrum with ion-scale lengths inside the separatrix. Measured fluctuation amplitude outside the separatrix is significantly higher, although still quiescent in the C-2 HPF operating regime, and displays a more- typical exponential turbulence spectrum.
Despite this consistency, GTC simulation results are not directly comparable to turbulent fluctuation measurements. Linear growth rates in simulation do not translate directly to nonlinear fluctuation amplitudes. Different nonlinear satura- tion mechanisms may come into play for separate linear modes, resulting in saturation levels independent of growth rate. A fully nonlinear simulation is necessary to capture these saturation mechanisms and directly compare simula- tion to experiment. These and other limitations of the simula- tion model are caveats to the results presented here, and provide a roadmap for future investigation and code development.
VI. FUTURE WORK
Towards the goal of predictive transport simulations of an FRC-based fusion reactor, a number of additional physics features need to be included in a working simulation model. One of the major challenges is to address the nature of cou- pling between the core, separatrix, and SOL regions of the advanced beam-driven FRC. The magnetic coordinates used in GTC and in other highly optimized PIC codes are singular at the magnetic separatrix, making simulation at this location numerically intractable. To address the separatrix problem, development of A New Code (ANC), which leverages GTC physics but uses a cylindrical coordinate grid, is well under- way. Currently, the ANC model is perturbative (df) and includes a drift kinetic ion species and adiabatic electrons, which are parallelized in groups. A fully 3D field solver is parallelized and spectrally decomposed in the azimuthal coordinates. The same realistic numerical equilibria used to
but includes electron temperature as well as ion temperature
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
and is defined qs 1⁄4 miðTi þ TeÞ=ðeBÞ. The mode ampli- tude in the top panel displays mixed kk 1⁄4 0 and low finite-kk contributions. Although the field line has bad-curvature everywhere (second panel), the length scale of the magnetic field gradient (fourth panel) is comparable or larger every- where in the simulation domain, so the drift terms have an overall stabilizing effect.
FIG. 5. Sample mode structure in the SOL region. From top to bottom, am- plitude of electrostatic potential, field line curvature, magnetic field magni- tude, and normalized magnetic field gradient are shown versus poloidal angle, h. In the SOL, poloidal angle corresponds well with axial position in the machine. Reprinted with permission from Phys. Plasmas 23, 012509 (2016). Copyright 2016 AIP Publishing LLC.
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V. DISCUSSION