The review is devoted to field reversed configurations and to the related field reversed mirrors; both are compact toroids with little or no toroidal magnetic field. Experimental and theoretical results on the formation, equilibrium, stability and confinement properties of these plasmas are presented. Although they have been known for about three decades, field reversed configurations have been studied intensively only in recent years. This renewed interest is due to the unusual fusion reactor potential of these high beta plasmas and also to their surprising macroscopic stability. At the present time, field reversed configurations appear to be completely free of gross instabilities and show relatively good confinement. The primary research goal for the near future is to retain these favourable properties in a less kinetic regime. Other important issues include the development of techniques for slow formation and stability, and a clearer assessment of the confinement scaling laws.

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Field reversed configurations

Der speziellen Relativitatstheorie liegt folgendes Postulat zugrunde, welchem auch durch die Galilei-Newtonsche Mechanik Genuge geleistet wird: Wird ein Koordinatensystem K so gewahlt, das in bezug auf dasselbe die physikalischen Gesetze in ihrer einfachsten Form gelten, so gelten dieselben Gesetze auch in Bezug auf jedes andere Koordinatensystem K′, das relativ zu K in gleichformiger Translationsbewegung begriffen ist. Dieses Postulat nennen wir „spezielles Relativitatsprinzip“. Durch das Wort „speziell“ soll angedeutet werden, das das Prinzip auf den Fall beschrankt ist, das K′ eine gleichformige Translationsbewegung gegen K ausfuhrt, das sich aber die Gleichwertigkeit von K′ und K nicht auf den Fall ungleichformiger Bewegung von K′ gegen K erstreckt.

Die Grundlage der allgemeinen Relativitätstheorie

The paper summarizes the theoretical basis for the RFP and reviews the status of research in this field. The RFP is a relaxed state system well described by Taylor's theory which explains many observations. The RFP is of interest because its study will increase the understanding of toroidal confinement in general, which might lead to better reactor designs, and the RFP itself has potential as a reactor, for example the improved, high energy density, compact RFP reactor. In the last five or ten years, RFP research has expanded, with some 15-20 machines operating or under construction, and the plasma parameters have improved substantially, with a confinement time of 0.5-1 ms and temperatures approaching 1 keV; values of βθ ~ 5-15% are reached routinely. Following an overview of recent results, three key problems are discussed in more detail: (1) resistivity, edge physics and ion heating (the ions are heated by fluctuations which drive the RFP dynamo); (2) operation of the RFP with an (electrically) thin shell which permits the growth of new unstable modes which degrade the confinement; and (3) scaling. Over the current range of 0.5 MA, favourable scaling trends of temperature and confinement with current are identified, but experiments at much higher currents on the two mega-ampere machines – RFX at Padua and CPRF at Los Alamos – due to operate in the early 1990s, are needed. A brief account of the compact RFP reactor is given, followed by a summary with an indication of future trends.

The reversed field pinch

Since the initial demonstration of negative refraction and cloaking using metamaterials, there has been enormous interest and progress in making practical devices based on metamaterials such as electrically small antennas, absorbers, modulators, detectors etc that span over a wide range of electromagnetic spectrum covering microwave, terahertz, infrared (IR) and optical wavelengths. We present metamaterial as an active substrate where each unit cell serves as an element for generation of plasma, the fourth state of matter. Sub-wavelength localization of incident electromagnetic wave energy, one of the most interesting properties of metamaterials is employed here for generating high electric field to ignite and sustain microscale plasmas. Frequency selective nature of the metamaterial unit cells make it possible to generate spatially localized microplasma in a large array using multiple resonators. A dual resonator topology is shown for the demonstration. Since microwave energy couples to the metamaterial through free space, the proposed approach is naturally wireless. Such spatially controllable microplasma arrays provide a fundamentally new material system for future investigations in novel applications, e.g. nonlinear metamaterials.

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Metamaterials for Remote Generation of Spatially Controllable Two Dimensional Array of Microplasma

The heat capacities of Fe 2+ and Ni 2+ formate dihydrates were measured. Fe 2+ salt showed a sharp peak at T N =3.75±0.05 K with total magnetic entropy N k /2(ln 5+ln 2). Ni 2+ salt exhibited a distinct peak at T N =15.5±0.2 K and a Schottky type maximum around 3.1 K. It was discussed that M 2+ ions in (200) layer in this series of compounds were magnetically free and that M 2+ ions in (100) layer behaved as magnetically two-dimensional spin system which ordered at T N . It was concluded theoretically, using R. P. A. method, that the broad shoulder generally found in the specific heat curve just above T N was characteristic to the low dimensional spin system. This tendency was remarkable in the system with isotropic coupling such as Mn 2+ ions and not so distinct in the case of anisotropic Co 2+ ions. The present cases of Fe 2+ and Ni 2+ ions gave the examples of those with intermediate anisotropy.

Magnetism and Phase Transition in Two-Dimensional Lattices; M(HCOO)2·2H2O (M; Mn, Fe, Ni, Co)

Theory of Harmonic Generation in a Gaseous Plasma

The Grad-Shafranov equation for a prolate spheroidal plasma is solved by using the prolate spheroidal coordinates. The magnetic field in the vacuum region surrounding the plasma is determined by use of the Maxwell equation and the pressure-balance condition on the plasma-vacuum interface. The result obtained in this letter is an exact solution to the magnetohydrodynamic equilibrium equation. The magnetic-field configuration of the spheroidal plasma is found to be considerably different from that of the spherical plasnla.

Magnetohydrodynamic Equilibrium with Prolate Spheroidal Plasma-Vacuum Interface

Vector laplacian in general curvilinear coordinates

The Grad-Shafranov equations for an oblate and a prolate spheroidal plasmas are solved analytically under the assumptions, B ϕ =0 and d p /dψ=constant. Here B ϕ is the toroidal magnetic field, p is the kinetic pressure, and ψ is the magnetic flux function. The plasmas in magnetohydrodynamic equilibrium are shown to be toroidal . The equilibrium magnetic-field configurations outside the spheroidal plasmas are considerably different from that of a spherical plasma. A line cusp or two point cusps appear outside the oblate or the prolate spheroidal plasma, respectively.

Magnetohydrodynamic Equilibrium with Spheroidal Plasma-Vacuum Interface : Compact Toroid without Toroidal Magnetic Field

Theoretical studies are made of the harmonic generation in a high frequency gaseous plasma under an external magnetic field on the basis of the Boltzmann equation. Expressions for the intensity of the higher harmonic radiations, especially of the second and the third, are derived and the results of their numerical calculation are graphically presented. These show that the higher harmonic radiations have sharp resonance peaks. The theory is compared with the experiment by Hill and Tetenbaum.

Katsuji Chiyoda

Papers

Theory of Harmonic Generation in a Gaseous Plasma

Magnetohydrodynamic Equilibrium with Prolate Spheroidal Plasma-Vacuum Interface

Vector laplacian in general curvilinear coordinates

Magnetohydrodynamic Equilibrium with Spheroidal Plasma-Vacuum Interface : Compact Toroid without Toroidal Magnetic Field

Theory of Harmonic Generation in a Microwave Gaseous Plasma under an External Magnetic Field