Drift-wave stability in the field-reversed configuration
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 PHYSICS OF PLASMAS 24, 092518 (2017) Magnetohydrodynamic transport characterization of a field reversed
M. Onofri, P. Yushmanov, S. Dettrick, D. Barnes, K. Hubbard, and T. Tajima Tri Alpha Energy, Inc., P.O. Box 7010, Rancho Santa Margarita, California 92688, USA
(Received 6 July 2017; accepted 6 September 2017; published online 28 September 2017)
The transport phenomenon of a Field Reversed Configuration (FRC) is studied using the newly developed two-dimensional code Q2D, which couples a magnetohydrodynamic code with a Monte Carlo code for the beam component. The simulation by Q2D of the transport parallel to the simple open h-pinch fields and its associated outflow phenomenon shows an excellent agreement with one of the leading theories, elevating the Q2D validity and simultaneously deepening the theoretical understanding of this fundamental process. We find a sharp distinction between the evolved radial density profiles of the FRC and mirror plasmas as a result of the transport processes, underpinning the crucial role of the closed flux surfaces of the FRC to enhance the confinement over that of the mirror. We characterize the scrap-off layer (SOL) transport by including the mirror trapping effects, and we find a relationship between the confinement time in the SOL and the ion collisional time. The Q2D code further illuminates the basic transport properties of the divertor region and the formation of an electrostatic potential in the divertor. Published by AIP Publishing. [http://dx.doi.org/10.1063/1.4994681]
The field reversed configuration (FRC) is an elongated compact toroid with little or no toroidal field.1,2 The interest for the FRC as a potential fusion reactor is due to its high beta, simple geometry, and a natural divertor. In the C-2 experiment, high performance FRCs (HPF) are formed and sustained for more than 4ms in the HPF14 regime3–7 and more than 5 ms in a steady state in the C-2U experiment.6 In these experiments, the plasma lifetime is not limited by instabilities, and the plasma is sustained by a fast ion popula- tion produced by neutral beam injection. The C-2U plasma is strongly driven by fast ions, and the fast ion pressure is com- parable to the thermal plasma pressure. Understanding trans- port in C-2 and C-2U is useful to predict the confinement properties of future machines that will operate at a higher temperature.37–39 The FRC evolution was studied in the past with several numerical codes.8–10 Different transport models have been tested with the Q1D code (a quasi 1D MHD code that includes neutral beams), such as the Bohm model, the classical transport model (with enhancement fudge factors for each transport coefficient), and others. In these Q1D stud- ies, the adoption of the Bohm coefficients leads to too abrupt plasma losses. On the other hand, the classical transport enhanced with fudge factors can reproduce various transport phenomena.11
C-2 experiments have shown a coupling between the transport in the scrape-off layer (SOL) and the FRC core.5 C-2 has mirror plugs between the formation section and the divertor, which reduce the particle loss in the SOL, and the magnetic field strength in the mirror plugs affects the trans- port in the FRC. In the present paper, we use the Q2D code, a 2D MHD code coupled to a Monte Carlo code, to study the transport properties of C-2, including 2D effects and the interaction of parallel and perpendicular transport, which
were missing in previous 1D studies. The code gives a self- consistent evolution of the FRC length and beam shine- through, which in 1D simulations were given as input param- eters. A realistic 2D geometry allows us to study the coupled transport between the SOL and the FRC. This kind of study was not possible in earlier numerical works that were done with a 1D code.
The properties of parallel transport in plasmas were studied in the past for linear systems, such as h-pinches and magnetic mirrors.12–14 Different theories have been proposed to explain the observed end loss process.18–23 Usually, these theories predict a confinement time that is different from the experimental observation, especially at high b.24,25 On the contrary, the theory proposed in Refs. 22 and 23 is in agree- ment with simulations and experiments. In Sec. III, we com- pare the Q2D results on parallel transport in h-pinches with the predictions of these theories.
Parallel transport has been studied experimentally and the- oretically in mirror confined plasmas for the collisional and collisionless regimes.26–29 The particle confinement time has a different dependence on the mirror ratio in the collisional and collisionless cases. Using large magnetic field expansion, good particle and energy confinement has been obtained in the Gas- Dynamic Trap (GDT), where electron temperatures up to 800eV have been measured.29–34 The confinement properties are different in FRCs, in which the parallel transport in the SOL is coupled to the perpendicular transport in the core, where closed magnetic field lines exist. The presence of closed field lines in the FRC produces a different density profile, with the formation of steep density gradients, which are not present in mirror machines. In Sec. IV, we use Q2D simulations to investigate the parallel particle transport in FRCs and mirror traps and the different density evolution in the two cases.
The plasma parallel outflow also has an effect on paral- lel electron heat transport due to the formation of an
1070-664X/2017/24(9)/092518/14/$30.00 24, 092518-1 Published by AIP Publishing.

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