Page 10 - Electrostatic quasi-neutral formulation of global cross-separatrix particle simulation in field-reversed configuration geometry

Physics of Plasmas ARTICLE
FIG. 8. The 3D electrostatic potential during linear growth is shown. The top (a) shows full ðR; Z; fÞ view where the gray region shows the extent of the simulation domain, and the purple shell represents the separatrix surface marking the separa- tion of the core and SOL regions. The cut on the left side of (a) is shown in the 2D slice on the bottom right (b). A zoomed in view on the bottom left (c) shows the short wavelength mode structure where the dashed line represents the separatrix.
FIG. 9. The 3D electrostatic potential after nonlinear saturation is shown. The top (a) shows full ðR; Z; fÞ view where the gray region shows the extent of the simula- tion domain, and the purple shell represents the separatrix surface marking the sep- aration of the core and SOL regions. The cut on the left side of (a) is shown in the 2D slice on the bottom right (b). A zoomed in view on the bottom left (c) shows the turbulent eddies where the dashed line in purple represents the separatrix.
Previous results from GTC and ANC represent, to date, the only first principles gyrokinetic turbulence simulations7–9 in realistic FRC geometry. The non-local simulation domain spanning across the sepa- ratrix represented an extension from the earlier local linear gyrokinetic simulations. The initial FRC blended model simulation results pre- sented in this paper are another step in the progress toward more real- istic FRC turbulence simulations. The effects of fully kinetic ion orbits and non-adiabatic electron response are observed. Magnetic perturba- tions, which can affect the field-line structure of the FRC, are not yet included in this model.
In agreement with past work, no linear ion-scale instabilities develop in the FRC core, likely suppressed by the large ion orbits (finite Larmor radius effect). Overall fluctuation levels are also much lower than in the SOL, though details of inward spread are still under consideration. In the SOL, a linear instability develops at short wave- lengths, eventually leading to an inverse spectral cascade to longer wavelengths as well as an inward spread from SOL to core. These pre- liminary results are consistent with previous findings.
The goal of these first principles FRC simulations is understand
transport scaling for the realization of a fusion reactor based on the
FRC concept. This is the motivation for the inclusion of the non-
adiabatic electron response, which enables the calculation of particle
diffusivity and electron thermal conductivity. Electron heat flux due to
e e2e2e;0E
takes into account the effect of the collisionless fluctuations. This heat
flux can then be used to calculate the conductivity from Fick’s law
^~^
ve 1⁄4 ~qe 􏰀 w=ðne;0rTe;0 􏰀 wÞ. Finally, from the conductivity, the
perpendicular core energy confinement time can be estimated by
sE;e 1⁄4 R2S=hvei, where RS is the separatrix radius and hvei is the con-
ductivity averaged over the post-saturation duration, in the toroidal
direction, and in the field-line direction. Despite lacking several effects
known to exist in the experiment, perpendicular energy confinement
time in the core is estimated to be 􏰈1 ms in the preliminary FRC sim-
ulations shown in this paper, a surprisingly reasonable estimate when
22,23
reevaluated as further effects are included.
Validating the fluctuation spectra and transport calculations
against the current experiments is a necessary step before transport scaling can be understood. Immediate efforts in the future are toward ongoing FRC blended model simulations based on reconstructed experimental equilibria. These ongoing simulations also feature the effect of equilibrium electric field, an important experimentally avail- able tool. Other future physics development priorities include parallel sheath boundary conditions and electromagnetic effects. In addition, with the upcoming exascale computing platforms in mind, upgrades for GPU acceleration using OpenACC directives are ongoing.
ACKNOWLEDGMENTS
The authors would like to thank the TAE team at TAE Technologies, Inc., for equilibrium data as well as ongoing insights and for the continued development of this simulation model. Initial development began at University of California, Irvine with the
27, 082504-10
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the self-consistent fluctuations can be calculated within the simulation
^Ð123^
via ~q 􏰀w 􏰂 df ð m j~vj 􏰁 T Þð~v 􏰀wÞdv, noting that this only
It should be noted that the simu- lations shown have not incorporated beam ions and equilibrium elec- tric fields, both of which can significantly modify the properties of possible instabilities and the saturated level. These estimates will be
compared with the experiments.
Phys. Plasmas 27, 082504 (2020); doi: 10.1063/5.0012439 Published under license by AIP Publishing