Shoichi Yoshikawa

Electrostatic Drift Instability of Tokamak Plasmas

We present a comprehensive theory of the electrostatic drift instabilities of a collisionless plasma in a toroidal device. The effects of inhomogeneities (density, electron and ion temperature gradients), plasma current, radial electric field, magnetic shear and toroidal curvature drift are simultaneously examined; we derive the general but simple criteria for the drift stability. The instabilities are found to be excited owing to the plasma current, ion temperature gradient, curvature of ion cross-field flow and toroidal effects, although the magnetic shear has a prominent stabilizing power. Drift waves are expected to be almost always unstable in tokamak plasmas.

Critical Conditions for Drift, Drift-Alfven and Drift-Tearing Instabilities of Finite-β Plasma in Sheared Magnetic Field

Kinetic theory of low frequency instabilities of a current-carrying finite-β plasma in a sheared magnetic field is investigated. Drift mode, drift-Alfven mode and drift-tearing mode are identified both in collisionless and collisional regimes and each critical stability condition is obtained, We find a new electromagnetic localized mode driven by the plasma current in a finite-β plasma. Both the current and finite-β effects are required to excite this mode. It is also shown that, in the absence of the plasma current, any electromagnetic localized mode which is propagating in the direction of the electron diamagnetic drift is stable in the collisionless limit of a finite ion temperature plasma. For the collisional mode, stability holds if ω>ω * (electron diamagnetic frequency) or ω<0.

Nonlinear Magnetohydrodynamic Instability and Disruptive Instability

A new model of the disruptive instability is presented. Nonlinear MHD instability of m = n =0 mode is solved in a cylindrical tokamak configuration. The stability threshold of this mode is obtained in terms of the amplitude of the co-existing higher m mode instabilities. Below the threshold, this mode has finite amplitude, and above the threshold, it grows catastrophically. The experimental characteristics of the disruptive instability well conform to the properties of the m = n =0 nonlinear MHD instability.

Shear Stabilization of Collisional Drift Instability

Using the normal mode expansion method, the collisional drift waves of the slab plasma in a sheared magnetic field are investigated. In the strong shear parameter regime, \(1{\lesssim}\kappa L_{s}{\ll}m_{i}/m_{e}\) (κ: density gradient, L s : shear length and m i / m e : ion to electron mass ratio), the growth rate is found to be proportional to \(\sqrt{\nu/\omega_{*}}\). The diffusion coefficient is also estimated and a density limitation of high density tokamak is shown.

Helical Resonance in Tokamak Equilibrium

Helical equilibria of tokamak are investigated with the self-consistent equilibrium equation. These are divided into three cases; 1) The shell is circular without an error field, 2) circular shell with external helical field such as helical windings field, and 3) the shell is helically deformed. In the first case, helical equilibrium is found for a particular q value. In the second case, an equilibrium is found for any q value, and there appears the resonance of the plasma with the external field. The plasma deformation is found to be very large for the imposition of a slight helical field. And for the last case, the analysis gives the similar result as the second case. These resonant phenomena cannot be derived from the mere superposition of the fields.

Nonlinear Helical Equilibrium of a Current-Carrying Plasma

Finite amplitude solution of helical equlibria of current-carrying plasmas bounded by a perfectly conducting cylinder is obtained. The nonlinear saturation levels of the fixed boundary MHD modes are also obtained near the marginal stable points. It is shown that by shaping the current density profile the saturation levels can be suppressed.