Cross-separatrix Coupling in Nonlinear Global Electrostatic Turbulent Transport in C-2U
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High-performance beam-driven field- reversed configuration (FRC)
Title Filler
n  Code Description:
A New Code (ANC)
Title Filler
n  Poisson solver verifications of field aligned mesh   Confinement vessel only:
  Field aligned mesh can be extended through formation section to end divertors
n  Future Development of ANC Transport Model   Sheath boundary conditions on open field lines (co-
developed with GTC).
  Equilibrium rotation for delta-f particle evolution   Electromagnetic field solver
  Full-f particle distribution evolution
See Also
n  C-2U
n Campaign timeline:   March 2015- 
March 2016
n  Achieved 5 ms   sustainment in   June 2015,   AND 
shots >10 ms,  limited only by   stored in-house   electrical energy. 
neutral-beam injectors
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 Physics 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  Cylindrical coordinates (spanning separatrix).
n Parallelization and Programming Model:
n Fully-kinetic Ion Model
n Hybrid Boris/4th order Runge Kutta push
DC   magnets
confinement vessel
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.
schematic of hybrid   Boris/RK push  
(RK2 used for illustration)
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timestep i i+1⁄2 i+1 i+11⁄2 i+2 i+21⁄2
Perpendicular Poisson equation implemented on fixed grid via finite differences and PETSc
  For adiabatic electrons and   long wavelength approximation,   Poisson solver reduced to  
fast algebraic solver 
scrape-off layer (SOL)
n  C-2W “Norman”(see poster by H. Gota) n Commissioning and first plasma: Spring 2017
n Goal: explore plasma confinement in extended (higher temperature) parameter regime. 
n  Macroscopic stability of beam-   driven FRCs motivates turbulent   transport model
n Must capture several physics features not resolved by existing models: high-beta, large ion Larmor radius compared to plasma size, cross- separatrix coupling, kinetic electron effects. 
n  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   (see poster by S. Dettrick)
n  n 
Hybrid message passing/threading scheme.
Group decomposition of particles by MPI task, particle loop parallelization by OpenMP.
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Fully-kinetic Ion Simulation of Global Electrostatic Turbulent Transport in C-2U
D. P. Fulton1, C. K. Lau2, J. Bao2, Z. Lin2, T. Tajima1, and the TAE Team1
1 TAE Technologies, Inc., 19631 Pauling, Foothill Ranch, CA 92610 2 University of California, Irvine, CA 92697
more questions? email me at
mirror plug
FRC (core)
plasma gun
Spectral decomposition of electrostatic Poisson solver into toroidal modes, by MPI task. Laplace matrix inversion by PETSc. Loop level OpenMP parallelization.
Tested on Intel Haswell (NERSC Cori I, OLCF Titan) and Xeon Phi (NERSC Cori II, ALCF Theta) 
n Magnetic field-aligned grid allows filtering of parallel vs. perpendicular mode components, and alleviates numerical resolution problems.
n Key Differences of ANC from GTC n  FRC specific
n  Smaller code base
n  More modularity
n  Fortran 2003/2008 (versus Fortran 95)
!more nimble development cycle
n  Recent publications
   D. P. Fulton et al, Phys. Plasmas 23, 012509 (2016).    D. P. Fulton et al, Phys. Plasmas 23, 056111 (2016).    L. Schmitz et al, Nature Comm. 7, 13860 (2016).
   C. K. Lau et al, Phys. Plasmas 24, 082512 (2017).
n  Other publications/presentations by TAE
Simulations 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.
mesh generation
  Mesh generation in core: sampling is uniform in magnetic flux and geometric angle about O-point
  Mesh generation in SOL: uniform in flux, matches at separatrix, then uniform in axial position
  Jacobian numerically sampled   Interp between radial neighbors for
finite differences across separatrix
neighbor sampling across separatrix
Adjacent posters at APS DPP 2017
   C.K. Lau – ANC simulation with gyrokinetic ions
   J. Bao – GTC simulation of FRC
   S. Dettrick – Whole Device Modeling of FRC
   L. Schmitz – experimental measurement of FRC turbulence