Cross-Separatrix Simulations of Turbulent Transport in the Field-Reversed Configuration

Numerical Model Developments of A New Code (ANC) for Fully-kinetic Ion Simulation of Turbulence in C-2W D. P. Fulton1, C. K. Lau1, J. Bao2, Z. Lin2, T. Tajima1,2, and the TAE Team1
1 TAE Technologies, Inc., 19631 Pauling, Foothill Ranch, CA 92610 2 University of California, Irvine, CA 92697 A New Code (ANC)
Title Filler
Advanced beam-driven field- reversed configuration (FRC)
n C-2W “Norman” (see poster by H. Gota)
n Goal: explore plasma confinement in extended (higher
temperature) parameter regime.
n Successor to C-2U, which achieved 5 ms sustainment AND shots > 10 ms limited only by stored-in-house electrical energy.
CAD schematic of the C-2W “Norman” device at TAE Technologies. The “Norman” upgrade represents a significant upgrade in beam injection and stored energy in order to investigation of confinement at higher plasma temperatures.
n Macroscopic stability of beam-driven FRCs motivates computational modeling of turbulence. This turbulence model must capture several physics features not resolved by existing models: large ion Larmor radius compared to plasma size, cross-separatrix coupling, kinetic electron effects, high-beta.
n Simulation Strategy and Vision
n Develop high-fidelity turbulent transport model, using two codes: established high-performance kinetic suite GTC, and FRC-specific ANC.
n Verify the model implementation against both analytic cases and with cross-code comparison.
n Validate the model against C-2U, C-2W. Is the formulation faithful to real experiments?
n Calibrate a faster ad-hoc tool that may be used in real time.
n Predictively compute particle and energy fluxes, that may be used to initialize macroscopic transport and stability codes, e.g. Q2D,FPIC
Physical scales of complimentary ANC and FPIC simulation codes, for computing FRC microturbulent transport and stability, respectively.
n Flux-based Density Advance
n Past method: particle density calculated from direct
scatter to mesh
n New method: flow density calculated from particle velocity scatter, density calculated via continuity equation and flow, time-advanced by RK4
n This avoids numerical discrepancies in delta-f (weight) equation that can arise due to fast time-scales of electrons
n Possible Code Validation Efforts:
n New extensive diagnostic suite on C-2W (see poster by M. Thompson) makes it possible to generate per-shot equilibria, allowing validation of simulation model against a single shot.
n Potential to compare against electrostatic and magnetic fluctuation data from Cross-Polarization Scattering/ Doppler Back Scattering (see poster by L. Schmitz)
and against line integrated density from FIR (see poster by R. Smith).
n Future Development of ANC Transport Model:
􏰀 Sheath boundary conditions on open field lines 􏰀 Equilibrium rotation for delta-f scheme
􏰀 Full-f particle distribution evolution 􏰀 Sources/sinks
􏰀 Non-zero toroidal equilibrium magnetic field 􏰀 Electromagnetic field solver
Title Filler
n Code Description Summary:
n A New Code (ANC) is a first-principles, integrated PIC code, based on GTC, but designed specifically for FRC magnetic geometry, to capture large-orbit ion dynamics, and cross-separatrix transport.
n Model Features:
n Fully-kinetic or gyro-kinetic ions (Vlasov equation). n Gyro-kinetic or Boltzmann electrons.
n Electrostatic field solver (Poisson equation).
n Perturbative (delta-f) model.
n Hybrid message passing/shared memory parallelization scheme, enabling performance on Leadership Computing Facility supercomputers.
Strong scaling of ANC on the Theta supercomputer at Argonne Leadership Computing Facility.
n Fully-kinetic Ion Model
n Hybrid Boris/4th order Runge Kutta push implemented
for particle equations of motion:
􏰀 FK position-velocity update by Boris-leapfrog
􏰀 FK particle weight update by RK4 (weight and position at same time steps)
􏰀 Identical energy/momentum convergence to Boris scheme in linear simulation.
n Field Solver Formulation
n Perpendicular Poisson equation implemented on fixed grid via finite element (with assumed quadratic interpolant) and PETSc.
n For adiabatic electrons and long wavelength approximation, Poisson solver reduced to fast algebraic solver.
n Field Aligned Mesh
n Magnetic field-aligned grid allows filtering of parallel vs. perpendicular mode components, and alleviates numerical resolution problems.
n Mesh generation: sampling is uniform in sqrt(magnetic flux) and field-line length at separatrix; perpendicular mesh points are found via ray tracing
n Jacobian numerically sampled
n Particle scattered to different field-lines (Psi direction) first, then along field-line (S direction)àeffectively elongated particle shape along field-line direction
Field-aligned mesh shown in real space (left) and flux (right) coordinates.
n Can be extended through formation to end divertors. n New mesh has been verified. (see below)
Recent publications
n D. P. Fulton et al, Phys. Plasmas 23, 012509 (2016).
n D. P. Fulton et al, Phys. Plasmas 23, 056111 (2016). n L. Schmitz et al, Nature Comm. 7, 13860 (2016).
n C. K. Lau et al, Phys. Plasmas 24, 082512 (2017). n C. K. Lau, UC, Irvine, Doctoral Thesis (2017)
n Other publications/presentations by TAE available at: https://tae.com/research-library
schematic of hybrid Boris/RK push
(RK2 used for illustration)
timestep
| • | • | •
i i+1⁄2 i+1 i+11⁄2 i+2 i+21⁄2
Acknowledgements
Simulations in 2018 were performed using resources at the Argonne Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract No. DE-AC02-06CH11357, and the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported under Contract No. DE-AC02-05CH11231. Ongoing work (2019) is underway using ALCF resources awarded through the DOE INCITE program.