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

Global particle simulation of field reversed configuration with field aligned mesh in cylindrical coordinates
Jian Bao1, Calvin Lau1, Daniel Fulton2, Zhihong Lin1, Toshiki Tajima1,2 and TAE team
1University of California, Irvine, CA 92697, 2TAE Technologies, Inc., 19631 Pauling, Foothill Ranch, CA 92610
Parallel transport model
 Sheath region
 Theoretical basis:
 Different models for pre-sheath potential 𝜙𝑞𝑛 and sheath potential
drop 𝛥𝜙𝑠.
 Relax time and spatial resolution
without resolving plasma
frequency and Debye length!
 Still capture steady-state sheath
solution!
Electron and ion particle fluxes are equal at wall in steady state: 𝜞𝒊 = 𝜞𝒆.
 Numerical implementation [6]:
1. Calculate: 𝑁 ions and 𝑁 electrons across the wall at each time step. 𝑖𝑒
Typical 𝑁 < 𝑁 : 𝑖𝑒
2. Remove: 𝑁 ions and 𝑁 fastest electrons. 𝑖𝑖
Reflect: 𝑁 − 𝑁 slower electrons. 𝑒𝑖
3. Sheath potential drop is given by the slowest absorbed electron: 𝑒𝛥𝜙=0.5𝑚𝑣2 .
𝑠 𝑒 ||𝑐
 Pre-sheath region
 Only use particles to simulate the non-adiabatic (non-Boltzmann) electron response, and use the quasi-neutrality condition to solve the ambipolar potential.
en nhNAdv
T
e0 i e
References
[1] M. W. Binderbauer et al, Phys. Plasmas 22, 056110 (2015). [2] L. Schmitz et al, Nature Communications 7, 13860 (2016). [3] D. P. Fulton et al, Phys. Plasmas 23, 012509 (2016).
[4] D. P. Fulton et al, Phys. Plasmas 23, 056111 (2016).
[5] C. K. Lau et al, Phys. Plasmas 24, 082512 (2017). [6] S. Parker et al, J. Comput. Phys. 104, 657 (1993). [7] http://www.trialphaenergy.com/research-library/
 This work is supported by the TAE subcontract to UCI. See posters by C. Lau and D. Fulton!
 Contact info: jianb@uci.edu
Motivation
 A high performance FRC has been sustained for 5ms, which is beyond the turbulent transport time scale [1,2].
 Local simulation of FRC finds that the drift wave instability is stable in the core region while is unstable in the SOL region [3,4,5]. Global particle in cell simulation cross the separatrix is required to study the turbulent transport.
 Parallel transport in the SOL region determines the plasma profile, and thus determines the turbulent transport.
 C-2W (Norman) constitutes an FRC inside a mirror machine with expander divertors. Electron parallel heat loss, self-consistent potential, pre-sheath and sheath must be resolved.
Global particle simulation of drift wave instability in FRC  Comparison of drift wave instability between FRC and tokamak
 In FRC, the most unstable electrostatic drift mode is in the SOL region while the drift wave instability is stable in the core region.
 Tokamak core: radial streamers cause Bohm like and gyro-Bohm like anomalous turbulent transports.
 FRC core: drift wave instability is linearly stable!!!
(opposite direction between diamagnetic drift and grad-B drift, short
electron transit distance, large ion FLR effect et al. [5])
 Global effects
Fully Laplacian solver 𝛾 = 1.6 𝑅 𝐶 Only toroidal spectrum solver 𝛾 = 2.6 𝑅 𝐶
0𝑠 0𝑠
Kishimoto, Tajima and Horton et al, 96 POP
 Non-local effects form radially global eigenmode and decrease growth rate.
Gyrokinetic Toroidal Code (GTC) developments  Field aligned mesh
 Laplacian Poisson solver
 The simulation grids are aligned along the field line to suppress the high 𝑘|| noise.
 Core region and sol region share the grids on separatrix, which enables core and sol regions coupling.
 Greatly decrease computational costs by using much fewer grids along parallel direction since 𝑘|| ≪ 𝑘⊥ is generally true to drift-type instabilities.
 Particle trajectory
 Boris Push for 6D Vlasov particle, drift kinetic equation for guiding center particle.
Acknowledgements
Simulations were performed using resources at Oak Ridge Leadership Computing Facility, a DOE Office of Science User Facility supported under Contract No. DE-AC05-00OR22725, and the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported under Contract No. DEAC02-05CH11231.