Loren C. Steinhauer

Review of field-reversed configurations

This review addresses field-reversed configurations (FRCs), which are compact-toroidal magnetic systems with little or no toroidal field and very high β (ratio of plasma pressure to magnetic pressure). Although enthusiasm for the FRC has primarily been driven by its potential for an attractive fusion reactor, this review focuses on the physics rather than on technological or engineering aspects. Major advances in both theory and experiment have taken place since the previous comprehensive FRC review in 1988. Even so many questions remain. In particular, even though FRC experiments have exhibited remarkable stability, how well this extrapolates to larger systems remains unresolved. The review considers FRCs under familiar topical categories: equilibrium, global stability, self-organization, transport, formation, and sustainment.

Conceptual design of the D-3He reactor artemis

AbstractA comprehensive design study of the D-3He-fueled field-reversed configuration (FRC) reactor Artemis is carried out for the purpose of proving its attractive characteristics and clarifying the critical issues for a commercial fusion reactor. The FRC burning plasma is stabilized and sustained in a steady equilibrium by means of preferential trapping of D-3He fusion-produced energetic protons. A novel direct energy converter for 15-MeV protons is also presented. On the bases of consistent fusion plasma production and simple engineering, a compact and simple reactor concept is presented. The D-3He FRC power plant offers a most attractive prospect for energy development. It is environmentally acceptable in terms of radioactivity and fuel resources, and the estimated cost of electricity is low compared with a light water reactor. Critical physics and engineering issues in the development of the D-3He FRC reactor are clarified.

A high performance field-reversed configurationa)

Conventional field-reversed configurations (FRCs), high-beta, prolate compact toroids embedded in poloidal magnetic fields, face notable stability and confinement concerns. These can be ameliorated by various control techniques, such as introducing a significant fast ion population. Indeed, adding neutral beam injection into the FRC over the past half-decade has contributed to striking improvements in confinement and stability. Further, the addition of electrically biased plasma guns at the ends, magnetic end plugs, and advanced surface conditioning led to dramatic reductions in turbulence-driven losses and greatly improved stability. Together, these enabled the build-up of a well-confined and dominant fast-ion population. Under such conditions, highly reproducible, macroscopically stable hot FRCs (with total plasma temperature of ∼1 keV) with record lifetimes were achieved. These accomplishments point to the prospect of advanced, beam-driven FRCs as an intriguing path toward fusion reactors. This paper reviews key results and presents context for further interpretation.

Relaxation of a two-species magnetofluid and application to finite-β flowing plasmas

The relaxation theory of a two-species magnetofluid is presented. This generalizes the familiar magnetohydrodynamic (single-fluid) theory. The two-fluid invariants are the self-helicities, one for each species. Their “local” invariance follows from the helicity transport equations, which are derived. The global forms of the self-helicities are examined in a weakly dissipative system. They are shown to pass three tests of ruggedness (“relative” invariance compared with the magnetofluid energy): the cascade test; the selective decay test; and the stability to resistive modes test. Once ruggedness is established, relaxed states can be found by minimizing the magnetofluid energy subject to constrained self-helicities. The Euler equations are found by a variational procedure. Example equilibria are presented that resemble field-reversed configurations (FRCs) and tokamaks. These states are characterized by finite pressure and significant sheared flows. Throughout the analysis it is shown how this more general t...

Variational formulation for a multifluid flowing plasma with application to the internal tilt mode of a field-reversed configuration

Standard magnetohydrodynamic (MHD) equations are extended to include arbitrary equilibrium flows and multiple fluids and an equivalent variational form is developed. This system is appropriate for the study of stability in any multifluid flowing plasma, e.g., allowing for arbitrary poloidal and toroidal equilibrium flows and accounting for the Hall terms. The variational formalism is applied to the particular case of the internal tilting instability in a field‐reversed configuration (FRC). A solution by means of the Rayleigh–Ritz technique leads to the dispersion relation, from which the growth rate and marginal stability conditions are determined. A new stability regime is found for sufficiently elongated FRC’s, arising as a consequence of the Hall effect. These results are compared with experiment and related theory.

Formalism for multi-fluid equilibria with flow

A formalism is developed for flowing multifluid equilibria. In the standard reduced case (massless electrons, quasineutrality) this system simplifies to a pair of second-order partial differential equations for the magnetic and ion flow stream functions plus a Bernoulli equation giving the density. Each species has its own characteristic surfaces, which are the drift surfaces, and three arbitrary surface functions associated with each species. In the case of minimum energy equilibria, the surface functions are no longer arbitrary. The flowing equilibrium system is a generalization of the familiar Grad–Shafranov system for magnetostatic equilibria.

Propagation of coherent radiation in a cylindrical plasma column

Refraction plays a very significant role in the absorption of laser energy in high temperature plasmas. The geometry considered here is a long cylindrical magnetically confined plasma. The laser pulse is assumed to enter the plasma from the ends. It is then necessary that the radiation propagate the full length of the plasma so that it will be absorbed. The refraction of the laser radiation in the plasma column depends on the radial distribution of the density. Several representative density profiles are considered and solutions for the propagation are presented. It is shown that a profile with the maximum density on the axis is very difficult to heat over long distances; but, if the density has a minimum on the axis, then the plasma column acts like a “light pipe” and traps the laser beam. In this case the effective absorption length of the laser beam is also reduced.

Formation of a long-lived hot field reversed configuration by dynamically merging two colliding high-β compact toroidsa)

A high temperature field reversed configuration (FRC) has been produced in the newly built, world’s largest compact toroid (CT) facility, C-2, by colliding and merging two high-β CTs produced using the advanced field-reversed θ-pinch technology. This long-lived, stable merged state exhibits the following key properties: (1) apparent increase in the poloidal flux from the first pass to the final merged state, (2) significantly improved confinement compared to conventional θ-pinch FRCs with flux decay rates approaching classical values in some cases, (3) strong conversion from kinetic energy into thermal energy with total temperature (Te + Ti) exceeding 0.5 keV, predominantly into the ion channel. Detailed modeling using a new 2-D resistive magnetohydrodynamic (MHD) code, LamyRidge, has demonstrated, for the first time, the formation, translation, and merging/reconnection dynamics of such extremely high-β plasmas.

Electrostatic confinement in the edge layer of field-reversed configurations

Although a field‐reversed configuration (FRC) has closed magnetic field lines, its particle confinement time is strongly influenced by the flow in the edge layer located outside the separatrix. Previous simple analyses of the edge layer have used fluid models with freely streaming end loss. However, a review of experimental results uncovers major inconsistencies between the fluid picture and actual measurements. In particular, the edge layer is unusually broad; the global particle confinement does not show the expected scaling with FRC length; the magnetic flux imbedded in the edge layer is inconsistent with that in the jet region; and the outflow speed in the jet is anomalously high. The most promising explanation for these anomalies is electrostatic confinement, which is well known in mirror and magnetic cusp plasmas. A tentative description of the electrostatic structure and plasma flow in the edge layer is presented.

Poloidal flux loss in a field‐reversed theta pinch

Poloidal flux loss has been measured in field‐reversed configurations and related to anomalous resistivity near the magnetic field null. The results indicate that mechanisms in addition to the lower hybrid drift instability are affecting transport.