Gyrokinetic particle simulation of a field reversed configuration

PHYSICS OF PLASMAS 23, 052307 (2016)
Transport studies in high-performance field reversed configuration plasmas
S. Gupta,a) D. C. Barnes, S. A. Dettrick, E. Trask, M. Tuszewski, B. H. Deng, H. Gota,
D. Gupta, K. Hubbard, S. Korepanov, M. C. Thompson, K. Zhai, T. Tajima, and TAE Team Tri Alpha Energy, Inc., P.O. Box 7010, Rancho Santa Margarita, California 92688, USA
(Received 9 March 2016; accepted 4 May 2016; published online 20 May 2016)
A significant improvement of field reversed configuration (FRC) lifetime and plasma confinement times in the C-2 plasma, called High Performance FRC regime, has been observed with neutral beam injection (NBI), improved edge stability, and better wall conditioning [Binderbauer et al., Phys. Plasmas 22, 056110 (2015)]. A Quasi-1D (Q1D) fluid transport code has been developed and employed to carry out transport analysis of such C-2 plasma conditions. The Q1D code is coupled to a Monte-Carlo code to incorporate the effect of fast ions, due to NBI, on the background FRC plasma. Numerically, the Q1D transport behavior with enhanced transport coefficients (but with otherwise classical parametric dependencies) such as 5 times classical resistive diffusion, classical thermal ion conductivity, 20 times classical electron thermal conductivity, and classical fast ion behavior fit with the experimentally measured time evolution of the excluded flux radius, line- integrated density, and electron/ion temperature. The numerical study shows near sustainment of
poloidal flux for nearly 1 ms in the presence of NBI. [http://dx.doi.org/10.1063/1.4950835]
I. INTRODUCTION
The field-reversed configuration (FRC) is a prolate, high beta compact toroid with nearly zero toroidal magnetic field.2 In the absence of any external sources of sustainment, these plasmas may be destroyed by stability issues or may decay in time due to transport losses. The C-2 experiment3,4 at Tri Alpha Energy (TAE) is the largest experiment where neutral beams are used for sustaining these plasmas.1,5–7 Transverse neutral beams are injected into the C-2 plasma in the ion diamagnetic direction. In the past few years, a signifi- cant improvement has been made in extending the plasma lifetime (measured by diamagnetism). It is denoted as high- performance FRC (HPF) regime. The improvement of C-2 normalized excluded flux radius2 under different experimen- tal conditions is shown in Fig. 1. The plasma lifetime has been extended from 1 ms to 5 ms with neutral beams, better wall conditioning, and edge stability. Similarly, multifold improvements have also been observed in the plasma con- finement times, e.g., particle, flux, and energy confinement times.5,7
In C-2 experiments, a vast number of diagnostics have been employed8 which has contributed to filling in the gap of knowledge of confinement related physical quantities such as the radial profiles of the plasma density,9 electron and ion temperatures,10–12 and magnetic field,13,14 though there still remain certain uncertainties. These newly inferred radial plasma profiles are also finely time-resolved. Moreover, we are capable of launching highly repetitive discharges (typi- cally every 10 min), which has allowed accumulation of tens of thousands of shot data for statistical analysis of transport.
Earlier, there was a significant amount of analytical and computational work done to understand the plasma transport
a)Author to whom correspondence should be addressed. Electronic mail: sgupta@trialphaenergy.com
Published by AIP Publishing.
in FRC. The particle, energy, and flux confinement times were calculated using zero-dimensional power balance anal- ysis.15 Particle transport was studied by solving the one- dimensional diffusion equation in the steady state, under the condition of axial compression maintaining the radial density profile.16 The long time evolution of plasma has been studied using a series of one-dimensional fluid equilibria with some features of the two-dimensional equilibrium.17,18 Recently, a two-dimensional kinetic equilibrium model has been devel- oped to interpret the evolving equilibrium properties.19 A one-and-a-quarter dimensional transport code called CFRX has been developed in the past to study FRC time evolu- tion.20,21 In this code, the FRC was assumed as a straight cyl- inder and two-dimensional effects such as axial contraction, averaging along field line, and axial parallel losses in the open field region are included. Effects of geometry on the evolution of FRC plasma have been studied using a one-and- a-half dimensional code, where the evolution of FRC plasma was simulated by alternating between the solution of two- dimensional equilibrium and one-dimensional transport equations.22 In all these calculations, the background plasma comprised ion and electron species, and no fast ion popula- tions due to neutral beam injection (NBI). The dynamics of fast ions due to neutral beams, e.g., their orbits, current pro- file, etc., have been studied in FRC equilibria using Monte- Carlo (MC) code.23,24 Hybrid simulations of neutral beam injection into an infinitely long FRC where both beam ions and background ions are treated as particles and electron as fluid, or neutral beam ions as particles with MHD plasma, have been carried out to study the effect of neutral beams such as flux supply, axial expansion, and beam heating.25–27
The rapid advances of C-2 HPF performance, coupled with reliable experimental plasma profiles, now allow sys- tematic comparison between experimental and simulated profiles. This is an opportunity to ask two questions
1070-664X/2016/23(5)/052307/9/$30.00 23, 052307-1 Published by AIP Publishing.