Feasibility study of microwave electron heating on the C-2 field-reversed configuration device

PHYSICS OF PLASMAS 23, 012509 (2016)
Gyrokinetic particle simulation of a field reversed configuration
D. P. Fulton,1,a) C. K. Lau,1 I. Holod,1 Z. Lin,1,b) and S. Dettrick2
1Department of Physics and Astronomy, University of California, Irvine, California 92697, USA 2Tri Alpha Energy, Inc., Rancho Santa Margarita, California 92688, USA
(Received 23 June 2015; accepted 26 August 2015; published online 19 January 2016)
Gyrokinetic particle simulation of the field-reversed configuration (FRC) has been developed using the gyrokinetic toroidal code (GTC). The magnetohydrodynamic equilibrium is mapped from cylindrical coordinates to Boozer coordinates for the FRC core and scrape-off layer (SOL), respec- tively. A field-aligned mesh is constructed for solving self-consistent electric fields using a semi-spectral solver in a partial torus FRC geometry. This new simulation capability has been suc- cessfully verified and driftwave instability in the FRC has been studied using the gyrokinetic simu- lation for the first time. Initial GTC simulations find that in the FRC core, the ion-scale driftwave is stabilized by the large ion gyroradius. In the SOL, the driftwave is unstable on both ion and elec- tron scales. VC 2016 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4930289]
I. INTRODUCTION
A field-reversed configuration (FRC) is an elongated prolate compact toroid formed without toroidal magnetic field.1 FRCs were accidentally discovered in the late 1950s upon the application of a reversed-direction bias magnetic fields to theta pinches.2,3 They were not studied intensively until two decades later, when they were recog- nized to have several properties favorable for fusion reac- tors. The FRC represents a high b plasma with surprisingly good macroscopic stability. The compact na- ture of the plasma and lack of toroidal magnetic field simplify many engineering requirements of a fusion reac- tor. Engineering is also aided by the scrape-off-layer (SOL), which encloses the plasma core and extends to the device ends, acting as a natural divertor. The high b, high temperature, low collisionality plasma of laboratory FRCs is also characteristic of a number of space and astrophysical plasmas, including those in the outer solar corona, solar superflares,4 and in accretion discs.5 A resurgence of interest in FRCs since the late 1980s has contributed to both theoretical and experimental advances in FRC physics in the last 25 years.6
It was suggested by Rostoker et al., in 1993, that adding a significant energetic ion population via neutral beam injec- tion (NBI) would improve FRC macro-stability but, due to the large ratio of the fast ion Larmor radius to the plasma size, would not significantly contribute to the destabilization of micro-turbulence, thus preserving the FRCs favorable transport properties.7–12 In 2008, Tri Alpha Energy, Inc. (TAE) launched a campaign on the FRC experiment, C-2, a facility designed to demonstrate the viability of the NBI con- jecture as a step towards an aneutronic fusion reactor con- cept.13 Goals of this campaign included understanding fast particle effects on stability and transport in an FRC, develop- ing tightly coupled simulation and theory capabilities, and
a)Author to whom correspondence should be addressed. Electronic mail: dfulton@uci.edu
b)Electronic mail: zhihongl@uci.edu
building global collaborations to achieve these ends. To date, the C-2 campaign has succeeded in demonstrating sig- nificantly longer and reproducible confinement using NBI.14–16 Analysis of data from over 40 000 C-2 discharges is ongoing with great need for simulation and theoretical analysis to rigorously understand transport scaling.
Historically, short confinement times in FRCs have lim-
ited thorough studies of transport, however, much work has
been done to identify contributing physics. Particle,17,18
flux,19 and energy confinement are well identified as anoma-
lous. Possible electrostatic micro-instabilities have been
investigated,20 with the lower hybrid drift instability (LHDI)
identified as the most linearly unstable. Numerical simula-
tions of the linear LHDI have been carried out,21–23 however
nonlinear transport and saturation mechanisms have not been
investigated. Electron-temperature-gradient-driven electro-
magnetic modes may also be present in FRCs (Refs. 24
and 25) but have not been studied in detail. The per-
turbed magnetic field associated with these electromag-
netic instabilities can disrupt flux tubes thus contributing
to anomalous resistivity.26 In general, electromagnetic
effects may be important to drift instabilities due to the
high-b characteristic of FRC plasmas.27 The plasma edge,
near the separatrix, is of particular interest in understand-
ing confinement properties. Confinement is significantly
affected by radial diffusion through the edge,28,29 where
particles may move from the closed field lines of the core
to the open field lines of the SOL. A number of analyti-
cal studies have been made of classical transport in sim-
ple equilibria30–33 and using quasi-steady 1-D plasma
profiles.34–36 Numerical models of transport have included
more details using both simple 1-D and 2-D equilibria.17,19,37–40
A thorough, theoretical understanding of FRC transport scaling is critical to predict confinement properties as experi- ments move towards fusion relevant densities and tempera- tures. To our knowledge, first-principles simulation of turbulent transport in a realistic FRC geometry has not been previously carried out. To investigate the FRC transport, we
1070-664X/2016/23(1)/012509/12/$30.00 23,012509-1 VC 2016AIPPublishingLLC