Masayoshi Taguchi

Electrical Conductivity of a High-Temperature Plasma in a Uniform Magnetic Field

The Ohm and Hall conductivities of a plasma composed of electrons and singly charged positive ions, are evaluated by use of the Boltzmann equation. Since the electron-to-ion mass ratio is small, the distribution function for ions is assumed to be Maxwellian. The distribution function for electrons is expanded in terms of Sonines polynomials (the Chapman-Enskog method). Numbers of the expansion terms are changed from 6 to 50, and the convergence of this method is examined. Both the Ohm and Hall conductivities evaluated from the expansion with 50 terms have accuracy of at least six decimal places for various strength of magnetic field.

The Effect of Trapped Electrons on the Beam-Induced Current

A simple expression of the fast-ion-induced current in the toroidal magnetic field is obtained by use of the adjoint drift-kinetic equation for electrons. The inverse aspect ratio is assumed to be small. The lowest-order terms of this ratio are retained in the calculation. By this expression, the beam-induced current for any beam distribution is easily evaluated. When the fast ions are monoenergetic, the beam-induced current is practically computed.A simple expression of the fast-ion-induced current in the toroidal magnetic field is obtained by use of the adjoint drift-kinetic equation for electrons. The inverse aspect ratio is assumed to be small. The lowest-order terms of this ratio are retained in the calculation. By this expression, the beam-induced current for any beam distribution is easily evaluated. When the fast ions are monoenergetic, the beam-induced current is practically computed.

Bootstrap Current Generated by Alpha Particles

The expression for the bootstrap current density due to fusion-produced alpha particles is derived in an axisymmetric plasma by solving a drift kinetic equation in the presence of both drag and pitch-angle scattering. From this expression the alpha-particle induced bootstrap current for a D-T plasma is explicitly evaluated in a tokamak with circular cross-section. The evaluated results show that the ratio of this bootstrap current to that due to bulk particles does not become a large value for burning plasmas presently considered. However, the use of this bootstrap current for current profile control and a seed current for a steady-state tokamak may be possible.

Magnetohydrodynamic Stability of Spheromak Plasma in Toroidal Flux Conserver with Rectangular Cross Section. II. Application of Mercier Criterion

The magnetohydrodynamic equilibrium states by Hills vortex model and by the Coulomb-wave-function model are proved to be unstable. New MHD equilibrium configurations are determined by using another model for which d p /dψ=0 on the magnetic axis. Here p is the pressure and ψ is the flux function. The values of the safety factor on the magnetic axis, q axis , are evaluated for these configurations. The MHD stability of these equilibrium states is investigated by the Mercier criterion. The values of the maximum beta ratio β max are evaluated for this model. The optimized pressure distributions are determined by use of the Mercier criterion and the values of β max are also evaluated for these pressure distributions. The values of β max are shown to be at most 12%, if the condition q axis <1 is required.

Magnetohydrodynamic stability of spheromak plasma in toroidal flux conserver with rectangular cross section

The stability of axially symmetric force-free equilibrium plasma is investigated. As a model of the flux conserver, a toroidal vessel with a rectangular cross section is considered. The radii of the inner and the outer walls of the vessel are denoted by R i and R , and the height h . The plasma is shown to be stable for the ideal magnetohydrodynamic perturbations when h / R <( h / R ) * , and unstable when R i / R <0.11 and ( h / R ) * <( h / R )<( h / R ) + . The values of the critical ratios ( h / R ) * and ( h / R ) + are evaluated as a function of R i / R .

Magnetohydrodynamic Equilibrium and Stability of Spheromak Plasma in Flux Conserver

The Green-function method is applied to the Grad-Shafranov equation for the plasma in a flux conserver with a rectangular cross section. The linear and the nonlinear MHD equilibrium configurations for various strengths of the toroidal magnetic field B ϕ are determined by this method. The average beta value and the safety factor are also evaluated. When B ϕ is increased from zero, decreases and vanishes at a force-free configuration. The safety factor takes a maximum value on the magnetic axis. A sufficient condition for stability to axisymmetric perturbations is derived by use of Edenstrassers condition. This sufficient condition holds for the flux conserver of any shape. As an example, the region, in which this sufficient condition is fulfilled, is shown graphically for the flux conserver with rectangular cross section.

Bootstrap Current for Tokamak Plasma with Anisotropic Electron Temperature

The neoclassical bootstrap current for an anisotropic plasma has been studied in a large aspect-ratio tokamak. The enhancement factor due to the temperature anisotropy in the equilibrium electron distribution function is explicitly calculated, and is shown to reach to about 1.5 when the perpendicular temperature is twice as large as the parallel temperature. This bootstrap current is also predicted to have the component proportional to the radial electric field even in an axisymmetric magnetic field.

The Effect of Trapped Electrons on ECRH Current Drive in a Weakly Relativistic Plasma

The wave-induced current by electron cyclotron resonance heating (ECRH) is investigated in an axisymmetric toroidal plasma. The plasma is assumed to be so weakly relativistic that the only relativistic correction to the resonance condition is considered. The effect of trapped electrons are also calculated to the order of \(\sqrt{\varepsilon}\), where e is the inverse aspect ratio. The trapped electrons and the relativistic resonance condition are shown to have important effect on the efficiency of current drive by ECRH.

Neoclassical Transport Theory for Tokamak Plasma with Anisotropic Temperature in the Banana Regime.

The neoclassical transport theory in a presence of the temperature anisotropy in the equilibrium distribution function is developed in a large aspect-ratio tokamak. Using a model collision operator, the transport coefficients for the cross-field fluxes and the bootstrap current are explicitly calculated in the banana regime. The electron perpendicular (parallel) heating is found to increase (decrease) the cross-field particle and energy fluxes of electrons and the bootstrap current. The cross-field energy flux of ions are increased (decreased) by the perpendicular (parallel) ion heating. The cross-field fluxes and the bootstrap current are also shown to have the component proportional to the radial electric field.

Generation of Poloidal Electric Field by Anisotropic Heating

A poloidally varying electrostatic potential due to a plasma heating anisotropic in velocity space is investigated in the collisionless regime for an axisymmetric plasma. Based on a linearized drift kinetic equation in a presence of external energy-source term, an analytic expression for this electrostatic potential is derived by means of an eigenfunction technique and a variational method. By using this analytic expression, the enhancement of the neoclassical transport coefficients by the anisotropic heating is discussed.