Zensho Yoshida

Eigenfunction expansions associated with the curl derivatives in cylindrical geometries: Completeness of Chandrasekhar–Kendall eigenfunctions

Eigenfunctions of the curl derivatives are used in many different fields of theoretical physics. For example, in plasma physics, an eigenfunction of curl represents a certain eigenstate of a plasma that has the force‐free property. The present theory proves that the spectral resolution of the curl operator gives a complete eigenfunction expansion of a solenoidal vector field with homogeneous boundary and flux conditions. Useful decomposition theories and a previous abstract result [Math. Z. 204, 235 (1990)] are concisely summarized. Explicit eigenfunctions have been studied in cylindrical geometries. Chandrasekhar–Kendall functions [Astrophys. J. 126, 457 (1957)], which are eigenfunctions of the curl derivatives in a cylindrical domain, give an orthogonal complete basis of the Hilbert space that is the orthogonal complement of the space of irrotational vector fields.

On the Ohm-Navier-Stokes system in magnetohydrodynamics

We study a mathematical structure of the Ohm–Navier–Stokes system that describes the incompressible dissipative evolution of a plasma. We apply the nonlinear semigroup theory and construct a unique regular solution which satisfies the system at least locally‐in‐time. We show that, for small initial data, this solution solves the system globally‐in‐time. We also introduce another scheme to construct solutions for less regular initial data.

Self‐organization of the reversed‐field‐pinch quiescence

The self‐organization of the reversed‐field‐pinch quiescence is studied by introducing a deterministic approach to the incompressible dissipative magnetohydrodynamics. The reversed‐field configuration is shown to be a quasisteady state that is stable as an attractor. The tokamak‐type branch of the attractor and the turbulence in the usual Navier–Stokes system are also discussed.

Ultra low-q discharge and high temperature experiments in REPUTE-1.

The outline and necessity of research in the ultra low-q regime are discussed from the view point of the total understanding of the current carrying systems. The ultra low-q state lies between tokamak and reversed field pinch and has a safety factor profile of 1/ (n+1) <q (r) <1/n, n=1, 2, 3, 4…. In REPUTE-1, the radiation barrier has been overcome and achieved plasma temperatures, Ti and Te, exceed 0.5 keV with electron density of 0.7×1020m-3. Resistivity anomaly due to m=1 kink activity is observed and considered to be related to a peaked temperature profile with a rather broad current density profile. The plasma resistivity in the ultra low-q regime is proved to be much lower than predicted values and decreases with increasing plasma current.

Application of multivariate data analysis method to plasma experiment.

Multivariate-analysis methods have been applied to plasma-data analyses. Many parameters obtained in plasma experiments are strongly coupled with each other, and are generally difficult to be resolved into simple physics laws. Multivariate-analysis methods are to find simple relations lying in data and to create scaling laws, which we may use, for example, to optimize operation parameters of devices. This paper introduces the factor-analysis method and describes an example of its applications to the REPUTE-1 RFP experiments.

Ignition Conditions of Ohmically Heated DT TOKAMAK Reactors Operated in the Ultra-Low-q, Regime

This paper studies the energy-balance characteristics of an ultra low-q (ULQ) confinement concept, and shows the possibility of the Ohmic-Heating ignition. The ULQ equilibrium considered here has the safety factor q in the intermediate range 0< q< 1 lying between tokamaks (1<q) and reversed-field pinches (q< 0 in a peripheral region). Our calculation of the energy balance is based on the experimental observation in the REPUTE-1 experiments, however, assumes a lot to consider the reactor-parameter regime. The aim of this paper is to provide a reasonable direction of researches on engineering bases. Our basic findings are as follows. There is a possibility of the Ohmic-Heating ignition for a compact and high-power density ULQ system with minor radius s 1 m, major radius ≤s 4 m, toroidal field= 8-10 T, and the total wall loading 12.5 MW/m2. To ignite ULQ plasma, temporal control of the plasma density in the start-up phase is important, and Zeff should be greater than 2 to increase the net input power.

On the Quasi-Static Evolution of Two-Dimensional Plasmas

Structure mathematique de la quasi-statique de plasmas bi-dimensionnels porteurs de courant

A mathematical aspect of magnetohydrodynamics. On the convective nonlinearity in a dissipative dynamical system.

Recent theoretical contributions to magnetohydrodynamics (MHD) have been reviewed from a view-point of mathematical sciences. Analytical structures of the convective nonlinearity in the incompressible dissipative MHD have been discussed stressing on their relevance to the fundamental theory of dynamical systems.