An Interesting Poster to look at from the Tri Alpha Energy Team in California

GTC is a first-principles simulation code which has been extensively used for microturbulence, energetic particles, magneto- hydrodynamics (MHD), neoclassical effects, and RF heating/current drive
 Realistic C-2 equilibrium
 Wedge Poisson solver
 Core & SOL are separate (Boozer coordinates)
agree with analytically calculated dispersion relations
 Antenna frequency sweeps in simulations of driftwave 𝜔∗
in realistic FRC equilibrium finds agreement between analytic eigenfrequency and resonant frequency from simulation:
𝜔resonant ~ 0.96 𝜔analytic
𝑓antennaΩp
Divergence-free B-field representation
Global simulation of field-reversed configuration using fully kinetic ion and drift kinetic electron Calvin K. Lau1, Daniel Fulton2, Jian Bao1, Animesh Kuley1, Zhihong Lin1, Michl Binderbauer2, Toshiki Tajima1,2, Lothar Schmitz2,3
Motivations
 Advanced beam-driven FRCs at TAE have lifetimes of milliseconds (transport-limited regimes)
 Local GTC simulations of realistic C-2 equilibrium find  Unstable ion-to-electron scale modes in scrape-off layer (SOL)  Core is robustly stable
 Does turbulence spread from SOL explain observed fluctuations?
 cross-separatrix ANC simulations to explore coupling effects GTC local simulations
1UNIVERSITY OF CALIFORNIA, IRVINE, Irvine, CA 92697, 2TRI ALPHA ENERGY, INC., Rancho Santa Margarita, CA 92688, 3UNIVERSITY OF CALIFORNIA, LOS ANGELES, Los Angeles, CA 90095 First ANC cross-separatrix simulations of electrostatic driftwaves
ANC global simulations
 Radially local 𝐤𝐫 ≪ 𝟏 No instability found in realistic C-2 core
 No instability found* for 𝐤𝛇𝛒𝐞 ≤ 𝟎. 𝟑, 𝛈 = 𝟏, 𝛋 ≤ 𝟓
 Consistent with experimental measurements of low
amplitude of core fluctuations
 Stabilized by
 Ion finite larmour radius effects (FLR)
 Magnetic well (radially increasing B-field)
 Electron parallel dynamics (shown via artificial elongation of core, or by slowing down electrons via artificial increase of electron mass)
Fully kinetic ions are also underway Implemented: full-kinetic ion in GTC, transferred to ANC
Verified: Boris push & Runge-Kutta for integrating ion cyclotron orbit in realistic FRC geometry using cylindrical coordinates
 Next: self-consistent simulation with full-kinetic ions
 Electron bounce motion resonates with mode
FRC equilibrium
 Equal density and temperature gradients
(𝜂𝑖 = 𝜂𝑒) are set just outside of the separatrix (inverse density scale length and density profiles are plotted in the R-Z plane below)
 Ion temperatures are 5x hotter than electron temperature
R/ Ln
n/ n0
 ANC’s magnetic
field represented |B0| through
derivatives of the
poloidal flux
function b
 𝛁 ⋅ 𝐁 = 𝟎 is strictly enforced
References
 D. P. Fulton et al, Phys. Plasmas 23, 012509 (2016)  D. P. Fulton et al, Phys. Plasmas 23, 056111 (2016)  http://www.trialphaenergy.com/research-library/
This work is supported by the Norman Rostoker Fellowship. Also, see posters by Lothar Schmitz and Daniel Fulton!
Z [m]
Z [m]
 Using equal density gradients and temperature gradients (𝜂𝑖 = 𝜂𝑒 )
 Frequency in electron diamagnetic & curvature drift direction
 Studied effects: particle resonances, Ti/Te, 𝜂𝑒, 𝜂𝑖 , FLR, 𝛻B, collisions*
 First ANC linear simulations of electrostatic driftwaves with coupled core and scrape-off layer (SOL) with gyro-kinetic ions and drift-kinetic electrons, toroidal mode number n= 50 (full-kinetic ion simulations to come)
 Perturbed electrostatic potential plotted on the R-Z plane  Shaded blue region corresponds to cyan line (Z=-1.125 [m])
 Top: perturbed potential (normalized per time-step) with gray line representing separatrix
 Bottom left: radial profile of perturbed potential with gray line representing separatrix
 Bottom right: time history of perturbed potential at R=0.32[m] shows exponential growth
 Inward propagation can be seen in the radial-time plot of the potential as well as different time snapshots of the radial profile or toroidal plane
 Numerical convergence tests, parameter scans, and nonlinear simulations to follow
GTC local simulations find ion-to-electron-scale driftwave instability in SOL
 Realistic C-2 equilibrium  Core & SOL are coupled
(cylindrical coordinates)  Fully kinetic ions
(verification in progress)
ANC is a first-principles, integrated simulation code being developed with the experience of GTC developers for FRC turbulence simulations capable of coupling the core and scrape-off layer regions.
 Plotted lines show 𝜔 𝐸 , 𝜇𝐵0 = 𝜔
𝑏,𝑒 𝑇 𝐸 𝑟
 SOL thresholds are consistent with experiment
Simulation
R/ Ln
𝜇B0/ E Experiment
෠
ANC benchmarks
 Simulations of ITG 𝑘 𝐶 and driftwave 𝜔∗ ∥ 𝑠 𝑒
have been performed in a uniform straight B-field, simulation results
𝑒
R [m]
𝛾R/ Cs
E/ T e
𝜙 [AU]