Cross-separatrix simulations of turbulent transport in the field-reversed configuration
P. 1

          International Atomic Energy Agency Nuclear Fusion Nucl. Fusion 59 (2019) 066018 (7pp)
Cross-separatrix simulations of turbulent transport in the field-reversed configuration
C.K. Lau1 , D.P. Fulton1, J. Bao2, Z. Lin2, T. Tajima1,2, L. Schmitz1,3, S. Dettrick1 and the TAE Team1
1 TAE Technologies, Foothill Ranch, CA, United States of America
2 Department of Physics and Astronomy, University of California, Irvine, CA, United States of America
3 Department of Physics and Astronomy, University of California, Los Angeles, CA, United States of America
Received 3 January 2019, revised 28 February 2019 Accepted for publication 2 April 2019
Published 2 May 2019
Recent local simulations of the field-reversed configuration (FRC) have reported drift-wave stability in the core and instability in the scrape-off layer (SOL). However, experimental measurements indicate the existence of fluctuations in both FRC core and SOL, with much lower amplitude fluctuations measured in the core. With the updated cross-separatrix capabilities of the simulation code used in this paper, nonlinear turbulence simulations find that linear instabilities grow in the SOL, generating fluctuations which spread from SOL
to core. After saturation of the linear instabilities, a balance of the inward spread and local damping in the core is achieved. The steady state toroidal wavenumber spectrum shows lower amplitude core fluctuations and larger SOL fluctuations with amplitude decreasing towards shorter wavelengths, which are consistent with experimental measurements.
Keywords: field-reversed configuration, turbulence, particle-in-cell, cross-separatrix (Some figures may appear in colour only in the online journal)
                1. Introduction
An ideal field-reversed configuration (FRC) is an elongated prolate compact toroid (CT) with purely poloidal magnetic fields, consisting of two regions separated by a separatrix: an inner, closed field-line core region and an outer, open field- line scrape-off layer (SOL) region [1, 2]. Research interest in the FRC has persisted due to potential reactor benefits [1]: β (the ratio of plasma pressure to magnetic energy density) near unity suggests cheaper magnetic energy costs than low β approaches such as the tokamak [2]; compact shape simpli- fies construction of the device hull and external magnetic field coils [3]; on-axis SOL which may be connected to the divertor arbitrarily far from the FRC core; and [4] the lack of toroidal magnetic fields radically changes the magnetic topology and the consequential stability of the plasma [3, 4].
In recent years at the C-2/C-2U FRC experiment, exper- imental progress by TAE Technologies, Inc. (TAE) led to successful reduction of major macro-instabilities (rotational n = 2, wobble, and tilt n = 1 modes [1], where n is the toroidal mode number). By doing so, FRC plasma sustainment times
have been increased to the order of several milliseconds [5, 6, 7], and this confinement approach is now in transport-limited regimes [7, 8]. After the necessary stabilization of the macro- instabilities, the next essential step to a viable FRC fusion reactor is to understand the transport processes within FRC plasmas.
Experimental measurements of density fluctuations using Doppler Backscattering (DBS [9]) in the C-2/C-2U FRC device have shown that fluctuations of the core and SOL of FRC plasmas exhibit distinct qualities. In the SOL, the fluctu- ation spectrum is exponentially decreasing towards electron- scale wavelengths and highest in amplitude towards ion-scale wavelengths. In the core, the fluctuation spectrum is overall lower in amplitude with a dip in the ion-scale wavelengths and a slight peak in electron-scale lengths, which further decrease towards even shorter lengths [10].
Local linear simulations [11, 12, 13] using the gyrokinetic toroidal code (GTC) [14] have found qualitatively similar results. The SOL is linearly unstable for a wide range of length scales and varying pressure gradients. In addition, the critical instability thresholds found for the SOL in the local linear
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