0D Power Flow Analysis on the C-2W Device

Simulation of Fast Ion Effects on Global Stability of C-2W Equilibria: Early Results
Abstract
n In TAE Technologies’ current experimental device, C-2W, record breaking, advanced beam-driven FRC plasmas are produced and sustained in steady state utilizing variable NBI, advanced divertors, end bias electrodes, and active plasma control systems.
n In order to investigate the fast ion effects on FRCs, both TAE’s equilibrium code1 and hybrid code (FPIC2,3), have been modified to include fast ion components.
n We present FPIC simulations of the evolution of this new kind of equilibria and address the stabilizing and destabilizing effects of the fast ions.
FPIC Code
n FPIC is an hybrid 3D code which uses a combination of Ohm’s law, Faraday’s law, and Ampere’s law to advance the fields.
n A Cartesian staggered Yee mesh is used and shaped boundaries can be straightforwardly included.
n The Dey-Mittra method for cut-cell boundaries on a Yee mesh is used to model any kind of boundary4
n Finite resistivity is implemented for both the FRC inner “high density” and outer “low density” regions.
n Periodic boundary conditions can be selected.
n An arbitrary number of different ion species can be treated.
n The full Lorentz equation for ions is used in the particle advance. n Esirkepov’s current deposition scheme is used to obtain Ji 5
n The code has multi-level parallelism including load balanced 3D domain decomposition, MPI data parallelism in subdomains, and OpenMP threading
n Diagnostic tools to “measure” the FRC geometric evolution are available.
n Other codes with similar physics models exist6,7,8 Recent upgrades
n Through the help of “virtual mirror” particles the deposition of density and current near the wall has been significantly improved.
n As initial state FPIC can now accept equilibria obtained from the combination of TAE’s multifluid equilibrium and fast ion transport “MC” codes.
n Hence, a kinetic population representing fast ions can be directly treated and included in the Ohm’s law equations.
n n
n
Equilibrium Code + MC
Neutral beams with arbitrary parameters can be represented and selected to generate a fast ion population.
An equilibrium which combines both fluid and kinetic populations is obtained through an iterative process which goes through TAE’s equilibrium code and MC.
Example: Neutral beams with given parameters and orientation.
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Case A – Thermal Plasma n FPIC reconstruction of Case A at t=0
Thermal plasma density (D)
Case B – Thermal Plasma with Fast Ions FPIC reconstruction of Case B at t=0
Later Phase: n=1 m=1 Modes
n n=1 m=1 modes become significant in the FRC dynamics at later times with respect to rotational modes.
Francesco Ceccherini, Laura Galeotti, Sean Dettrick, Dan Barnes, Kevin Hubbard and the TAE team TAE Technologies, Inc., 19631 Pauling, Foothill Ranch, CA 92610
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Two Cases Under Study
plasma density (D)
Case A - Thermal plasma only generated through TAE’s equilibrium code
Case B: Thermal plasma and fast ions (generated through TAE’s equilibrium code +MC.
ttt tt2 t312 3
Neutral beams seem to drive higher order rotational modes (n=2,3,4,8) in an early phase and stabilize them later on (no plasma disruption).
n n
n
3 4
Case A – Thermal Plasma
1
Case B
Case A
Z
Rotational and Toroidal n=1 Axial m=1 Modes
C2-W provided experimental evidences that the presence of neutral
beams are required for good plasma performance
Previous numerical investigations (R. Milroy, A. Necas, D. Barnes) have shown that the presence of fast ions can alternatively:
Case B
Electron density at z=0
Case A
Case B
Case A
t3
n n
suppress the tilt mode and drive higher order rotational modes stabilize higher order rotational modes
t1
t2
Fast Ion density (H)
8
9 INCITE 2018 - Kinetic Simulation of FRC Stability and Transport (P.I. Sean Dettrick, co-P.I. Toshi Tajima)
FPIC has been deployed to study the time evolution of equilibria with and without fast ions. This preliminary study was conducted for a modest fast ion population, ~10% of fast ion current with respect to total thermal plasma current.
Case B – Thermal Plasma with Fast Ions
n
n
Rotational modes strength vs time
Case A
Case B
n Thermal
Fast Ion density (H)
Early Phase: Rotational Modes
n
The fast ions component is not refueled
D. W. Swift, J. Comp. Phys. 12, 109 (1996)
t t2 t3 1
§ Ballooning mode n=1 m=1 gives rise to v +, v -
n Case A at 90 μs and later appear to be dominated by the ballooning mode.
n Atsuchalatertimeunrefueledfastionshavelosttheinitialdensityandcurrent
distribution reducing significantly their role in the FRC dynamics.
n On the basis of the effect played by fast ions in the evolution of rotational modes we can expect that toroidal modes can be as well affected if the fast ion component can be properly maintained through refueling.
Conclusions
n A significant upgrade of FPIC has been carried out. Combined equilibria with thermal and fast ion populations can be utilized for FPIC initialization.
n Preliminary results from first FPIC simulations show that fast ions may have a very significant role in the dynamics of rotational modes which are generated in the early phase of the FRC evolution.
n n=1 m=1 modes become significant at later times with respect to rotational. Therefore, a thorough investigation and analysis of the interaction between n=1 m=1 modes and fast ions require a “numerical refueling” of the latter ones.
n Taking advantage of the INCITE9 award a large campaign at ALCF is planned for the upcoming months and significant fast ion parameter spaces will be explored.
n Relevance to the experiment will be demonstrated in dedicated runs with higher fast ion contribution.
References
1 L.Galeotti et al. Phys. Plasmas, 18, 082509 (2011)
2 F. Ceccherini et al. CP10.00087, APS-DPP 2016
S. Dettrick et al. PP11.00097, APS-DPP 2018
S.Dey et al., IEEE Microw. and Guided Wave Lett. 7, 273 (1997)
5 T. Z. Esirkepov, Comput. Phys. Commun. 135, 144 (2001)
6 E. Belova, APS-DPP Meeting, New Orleans, LA (2014)
7 Y. Omelchenko, J. Comp. Phys. 231, 1766 (2012)
Acknowledgement
An award of computer time was provided by the Innovative and Novel Computational Impact on Theory and Experiment (INCITE) program. This research used resources of the Argonne Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract DE-AC02-06CH11357.
Case A
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