Rigid motion of C-2W FRC plasma

Blended Kinetic Simulations of Transport in C-2W
Calvin K. Lau1, Zhihong Lin2, Toshiki Tajima1,2, Sean Dettrick1, Lothar Schmitz1,3, and the TAE Team1
1 TAE Technologies, Inc., 19631 Pauling, Foothill Ranch, CA 92610 2 UNIVERSITY OF CALIFORNIA, IRVINE, Irvine, CA 92697 3UNIVERSITY OF CALIFORNIA, LOS ANGELES, Los Angeles, CA 90095
more questions? email me at clau@tae.com
APS-DPP 2020 / Online / November 9-13, 2020
n Goal: understand confinement in current devices; predict confinement in future devices
n Tool: first-principles electrostatic particle-in-cell code (ANC)
n capable of cross-separatrix simulations of multiple toroidal modes n must sufficiently capture necessary physics for relevance
n sufficient model à can interpret measurements
n Previously: simulations interpret experimental results[1,2]
n Nonlinear inverse cascade, fluctuation spread from SOL to
stable core via nonlocal gyroradius effectsàrecovers
experimentally measured spectra
n coreà no inherent instability found, fluctuations originate
from SOL leading to larger deviation in fluctuation level n missing feature: kinetic electron effects not included è
Fig (ABOVE): Electrostatic fluctuations from simulation (lines, shaded region) compared with density fluctuations from experiment (markers). The shaded region denotes the deviation during simulation times (after saturation) which this analysis was done. The fluctuation spectra are qualitatively consistent and quantitatively comparable.
self-consistent electron heat transport not calculated
n What’s new? model updated to correctly represent previously omitted fully kinetic effects
n Core remains linearly stable despite additional complexities in model
n Electron heat transport calculation ~10x classical levels, consistent w/ Q2D model
n Preliminary simulations including fast ions underway and instability arises only in SOL
nCapabilities enabled by new model
n magnetic null included in simulation domain
n blended kinetic deuterons
n blended kinetic electron response w/ partial adiabatic
approx. for faster electrons
n electron heat transport now can be calculated self-
consistently from simulation
Fig (RIGHT): Electrostatic potential during linear growth from simulation with drift- Lorentz deuterons from three views (a) 3-D perspective, (b) slice near mid- plane,(c)zoomed in focus on b.
n Instability develops only in SOL
n Qualitatively consistent with previous sims
n Unconventional short wavelength ion temperature gradient
(SWITG), excited at high toroidal mode numbers (𝑘2𝜌3 > ~10) n Mode rotates in ion diamagnetic (electron grad-B) drift direction
n Largest fluctuations in SOL after inclusion of large orbit ions à consistent w/ past work
n Less inward spread than previous sims w/gyrokinetic model n ~100x lower amplitude fluctuations in core vs SOL à lower
transport in core vs SOL
n Average electron conductivity in core ~10x classical levels
𝑒𝜙/𝑇!
(consistent w/ Q2D and Q1D simulation results[5])
post saturation
𝑒𝜙/𝑇!
during linear growth
During linear growth During saturation
resonance condition resonance condition
Fig (ABOVE, RIGHT): Electrostatic potential after saturation of mode. Fluctuations have spread into the core, but at much lower amplitude than SOL (colorbar is symmetric-log to allow for core fluctuations to be visible). (LEFT) Kinetic electron response 𝛿𝑓!/𝑓 isplottedagainsttheresonancecondition
𝜔 − 𝑘"𝑣# . The peak corresponds to when mode frequency roughly equal to drift frequency (dashed line).
n Previous gyrokinetic model limited
■ did not describe figure-8 or betatron orbits, only
gyro-orbits
■ magnetic null region was not described
n Previous adiabatic approx. for electrons limited
■ particle flux was not allowed
■ electron heat flux was not self-consistently described
n New particle model blending full Lorentz and drift- kinetic orbits [3,4]
n avoids gyrokinetics
n retains capability of large time-steps for low
frequency scales
n Same model used for both ions and electrons, capable
of capturing high and low frequency physics and allows for self-consistent electron heat transport calculations
n To remove high frequency oscillations beyond low-
Basic parameter
Modified velocity update
Modified position update
𝛼6 ≡
1 +
Fully kinetic : 𝛼6 Ω76Δ𝑡 → 0 Drift-kinetic : 𝛼6 Ω76Δ𝑡 → ∞
→ 1 → 0
1
Ω76Δ𝑡 3 2
𝑣!,#$% = 𝑣!,&'( + [Δ𝑣!&)$#*+ + 1 − 𝛼 Δ𝑣,∇.]
𝑥#/0 = 𝑥# + 𝑣#/0/3Δ𝑡 $11
𝑣$11 ≡ 𝑣∥,! + 𝛼𝑣5,! + 1 − 𝛼 𝑣(
frequency turbulence of interest, cut-off parallel velocity
set for electrons:
n faster than cut-off velocity: assumed adiabatic response LHS n slower than cut-off velocity: modeled with simulation markers,
perturbed electron density RHS
ion polarization density
non-adiabatic electron perturbed density
electron polarization density
electron adiabatic response
n Equilibrium generated by LREq_MI[6] based on shot 119739
n Fast ions from neutral beam injection à important component of TAE FRC
n previous ANC simulations only included thermal ions and electrons
n beam ions à large pressure contribution in C-2W, now included (initialized
based on distribution function) n Electron density profile differences
n Inclusion of fast ion à density variation along field-line
n Density peaks outside separatrix; temperatures peak inside n Preliminary simulations show unstable modes form in SOL
n Fluctuations in core remain lower in amplitude vs SOL
n Mode location corresponds to region where density peaksàlarge ratio of temperature gradients to density gradients
Fig (ABOVE): Fast ions in velocity space. Injected beam has preferential direction in distribution function. Fig (BELOW): Electrostatic potential near saturation of mode. Instability arises in the SOL while fluctuations barely spread into core (colorbar is symmetric-log to allow for weaker core fluctuations to be visible).
𝑒𝜙/𝑇!
References
[1] L Schmitz et al, Nature Comm. (2016) [2] CK Lau et al, Nucl. Fusion (2019)
[3] CK Lau et al, Phys. Plasma (2020)
[4] RH Cohen et al, NIM Phys. Res. (2007) [5] M Onofri et al, Phys. Plasma (2017)
[6] L Galeotti et al, Phys. Plasma (2011)
Other TAE publications/presentations
https://tae.com/research-library
Acknowledgements
Simulations used the resources of DOE Office of Science User Facilities: National Energy Research Scientific Computing Center (DOE Contract No. DE-AC02- 05CH11231) and Innovative and Novel Computational Impact on Theory and Experiment (INCITE) program at Argonne Leadership Computing Facility at Argonne National Laboratory (DOE Contract No. DE-AC02-06CH11357).
Non-adiabatic electron response