Akio Ishida

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.

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.

Gyroviscous stability theory with application to the internal tilt mode of a field-reversed configuration

The variational formulation for a gyroviscous fluid plasma is constructed. This theory offers a fluid‐based description of perpendicular kinetic effects, generally called finite Larmor radius (FLR) effects. This approach avoids the complexity of a more complete kinetic treatment and avoids local singularities that can appear in the standard FLR expansion treatment. The method is applied to the internal tilt mode of a field‐reversed configuration (FRC), an instance where standard FLR theory clearly breaks down. The relative simplicity of the variational gyroviscous fluid theory allows easy computation of stability properties, including the scaling of marginal stability conditions.

Profile consistency in equilibria of field‐reversed configurations

Experimental evidence is presented for a regulatory principle governing field‐reversed configuration (FRC) equilibria. This leads to a form of ‘‘profile consistency’’ with which the current profile exhibits a remarkable correlation with xs (the ratio of the separatrix radius to the coil radius). The proposed explanation is that these equilibria are regulated by an instability which maintains the profile at a marginally stable condition.

Equilibrium analysis of a flowing two-fluid plasma

An improved formalism for a flowing two-fluid equilibrium with constant density is developed. This extends the usual single-fluid model. In this generalization, the magnetic field is replaced by two quantities, the generalized vorticities of each species. Criteria are found for when the single-fluid model is adequate and when the more general two-fluid model is necessary. The two-dimensional equilibria with purely azimuthal ion flow are studied analytically and numerically. Spherical torus and compact toroid equilibria are found that are relevant to the current experiment. The ion flow and plasma beta as well as the size parameter are found to play a major role in the question of whether two-fluid corrections are needed.

Two-fluid flowing equilibria of compact plasmas

The properties of two-fluid flowing equilibria are explored. This is facilitated by limiting attention to compact toroids in a “stationary-energy” state with uniform density. Flowing equilibria are found to fall into two classes, force-free and non-force-free, referring to the absence or presence of a j×B force. The force-free class may have significant flows. Spheromaks are in this class. The non-force-free class is diamagnetic and has Alfvenic poloidal flows. Field reversed configurations (FRCs) are in this class. Both classes admit arbitrarily large equilibria. Both classes occupy certain “allowed” regions in “helicity space,” a two-dimensional parameter map with the electron and ion helicities as coordinates. Allowed regions for the two classes overlap; in the overlap region the non-force-free class is energetically favorable. This sheds light on the FRC-spheromak bifurcation observed in experiments. Two-dimensional analytic equilibria are also found that span both classes. These may play a role simil...

Tilt mode stability scaling in field-reversed configurations with finite Larmor radius effect

The marginal stability of a static plasma with finite-Larmor-radius (FLR) effects depends on a combination of the FLR effect and the ideal magnetohydrodynamic (MHD) potential energy. For the tilt mode in a field-reversed configuration (FRC) previous computations of these two factors led to a prediction of stability for S*⩽(3−5)E where S* is the macroscale parameter (separatrix radius/ion skin depth) and E is the elongation (separatrix half length/separatrix radius). This prediction explained the observed stability of most experiments. However, recent computations of actual MHD eigenfunctions indicate that the MHD growth rate has a much weaker scaling with elongation than previously believed. As a consequence, most of the long-lived, stable FRC experiments lie in the region predicted to be unstable. It appears then that the stability of FRC experiments is not explained by FLR effects in a static equilibrium.The marginal stability of a static plasma with finite-Larmor-radius (FLR) effects depends on a combination of the FLR effect and the ideal magnetohydrodynamic (MHD) potential energy. For the tilt mode in a field-reversed configuration (FRC) previous computations of these two factors led to a prediction of stability for S*⩽(3−5)E where S* is the macroscale parameter (separatrix radius/ion skin depth) and E is the elongation (separatrix half length/separatrix radius). This prediction explained the observed stability of most experiments. However, recent computations of actual MHD eigenfunctions indicate that the MHD growth rate has a much weaker scaling with elongation than previously believed. As a consequence, most of the long-lived, stable FRC experiments lie in the region predicted to be unstable. It appears then that the stability of FRC experiments is not explained by FLR effects in a static equilibrium.

Tilt stability of a gyroviscous field‐reversed configuration with realistic equilibria

The gyroviscous fluid theory [L. C. Steinhauer and A. Ishida, Phys. Fluids B 2, 2422 (1990)] is applied to the tilting instability of field‐reversed configurations (FRC) using realistic equilibria and a more complete basis set than in the previous treatment. This leads to two important new results. (1) Quantitative agreement is found for the first time between experiment and the theory of FRC tilting stability, i.e., the stability of nearly all FRCs can be explained by the gyroviscous theory. (2) Quantitative agreement (within 30%) is also found between the gyroviscous theory (with modifications to account approximately for parallel kinetics and the Hall effect) and the more complete—but harder to apply—Vlasov‐fluid model.

Ideal stability of a toroidal confinement system without a toroidal magnetic field

New results show that a toroidal plasma can be ideally stable to gross modes without a toroidal magnetic field. Previous ideal‐magnetohydrodynamic (MHD) studies for such systems [commonly called field‐reversed configurations (FRC)] have consistently predicted instability to the tilting mode (lowest‐order kink mode). However, a new range of equilibria not previously considered are found, which are stable to tilting in ideal‐MHD theory. The equilibrium properties that promote stability are hollow current profile, and racetrack separatrix shape. Stable equilibria may not be possible in a θ‐pinch system, but could be achieved with a properly designed vertical field coil set. The stability of FRC’s in past θ‐pinch experiments arises partly from nonideal effects, but benefits considerably from hollow current profile and racetrack separatrix shape.