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PHYSICS OF PLASMAS 25, 022503 (2018) Coupled transport in field-reversed configurations
L. C. Steinhauer,1,a) H. L. Berk,2 and TAE Team
1Tri Alpha Energy, Inc., P.O. Box 7010, Rancho Santa Margarita, California 92688, USA 2Institute for Fusion Studies, the University of Texas, Austin, Texas 78712, USA
(Received 1 November 2017; accepted 18 January 2018; published online 6 February 2018)
Coupled transport is the close interconnection between the cross-field and parallel fluxes in differ- ent regions due to topological changes in the magnetic field. This occurs because perpendicular transport is necessary for particles or energy to leave closed field-line regions, while parallel trans- port strongly affects evolution of open field-line regions. In most toroidal confinement systems, the periphery, namely, the portion with open magnetic surfaces, is small in thickness and volume com- pared to the core plasma, the portion with closed surfaces. In field-reversed configurations (FRCs), the periphery plays an outsized role in overall confinement. This effect is addressed by an FRC- relevant model of coupled particle transport that is well suited for immediate interpretation of experiments. The focus here is particle confinement rather than energy confinement since the two track together in FRCs. The interpretive tool yields both the particle transport rate vn and the end- loss time sjj. The results indicate that particle confinement depends on both vn across magnetic sur- faces throughout the plasma and sjj along open surfaces and that they provide roughly equal trans- port barriers, inhibiting particle loss. The interpretation of traditional FRCs shows Bohm-like vn and inertial (free-streaming) sjj. However, in recent advanced beam-driven FRC experiments, vn approaches the classical rate and sjj is comparable to classic empty-loss-cone mirrors. Published by AIP Publishing. https://doi.org/10.1063/1.5011679
I. INTRODUCTION
Field-reversed configurations (FRCs) are compact toroi- dal plasmas without a center column. The plasma is composed of a core and a periphery: the core of closed magnetic surfaces is surrounded by a periphery of open surfaces. The two regions border each other at an elongated, ellipsoidal separa- trix which closes at X-points located on the geometric axis. The periphery, or scrape-off layer (SOL), surrounds the core properly and also has long spindle-like sections extending beyond the X-points at each end of the core. FRCs have been investigated for several decades and reviewed elsewhere.1,2
In FRCs, the plasma and energy transport rates are closely tied, in contrast to other toroidal systems where they are somewhat independent.3 In traditional FRCs (formed in h- pinches), the overall energy confinement time sE is 1/2 to 1/3 of the plasma confinement time sN (see Sec. V D of Ref. 2).4 Comparable trends appeared in advanced beam-driven FRCs produced in the C-25 and C-2U6 facilities, with much longer confinement times, stretching to several milliseconds instead of the previous 20–200ls range. This paper focuses on plasma (particle) confinement to simplify the analysis and develop understanding of the relevant processes.
In the conventional view of toroidal confinement, the particle transport rate vn regulates cross-field diffusion in the core, while the periphery primarily serves as a buffer between the hot core and cold material walls. In FRCs, the periphery plays a more prominent role, in part because it is relatively hot and dense, with density and temperature com- parable to the core. Moreover, the gradients in the core con- nect smoothly to those in the periphery. These facts hint that
a)E-mail: lstein@uw.edu
the periphery may profoundly affect overall confinement. Here, we consider both the cross-field particle transport rate, vn, which acts in both the core and the periphery, and the end loss with timescale sjj, which acts in the periphery. “Coupled transport” is the self-consistent interlinking of ? (vn) and jj (1/sjj) particle transport rates; here, vn is the particle diffusiv- ity across magnetic surfaces, and sjj is the end-loss time along open magnetic surfaces.
Coupled transport works in the following way. Particle end loss (sjj) in the periphery pulls down the edge density and steepens the density gradient. This produces a relatively thin SOL, with thicknesses of 1/4–1/10 of the separatrix radius. The steepened SOL density gradient increases the dif- fusive flux out of the core. It may also trigger drift- turbulence in the SOL, elevating vn itself to an anomalously high value. In brief, both ? and jj processes contribute fun- damentally to particle confinement.
The importance of coupled particle transport in open systems, specifically in h-pinches with high-b (plasma pres- sure 􏰁 magnetic pressure), has been recognized. The ? and jj processes were predicted to be equal partners in confine- ment, i.e., a hybrid scaling sN 1⁄4 (sjjs?)1/2, where sN is the global plasma confinement time and s? and sjj are the stand- alone confinement times for perpendicular and parallel trans- port processes.7 This differed from the expectation that sjj should dominate in open systems. Similar coupling was later projected for linear plasmas enclosing field-reversed islands.8 In short order, the likelihood of ?-jj coupling was recognized in the context of FRCs properly (see citations in Ref. 9).
The first detailed treatment of coupled particle transport in FRCs was that of Tuszewski and Linford.10 Adopting an
1070-664X/2018/25(2)/022503/8/$30.00 25, 022503-1 Published by AIP Publishing.