Takashi Tuda

Kinetic Theory of Nonlocal High-n Ballooning Mode

Kinetic theory of high- n ( n : toroidal mode number) electromagnetic ballooning mode is presented with consistent inclusion of plasma β-value, ion gyroradius, kinetic parallel conductivity, ∇ B drift and magnetic shear effects. A new unstable branch of nonlocal eixenmodes in a collisionless toroidal plasma is found. The growth rate of kinetic high- n ballooning mode is of order of drift frequency.

Critical β analyses with ferromagnetic and plasma rotation effects and wall geometry for a high steady state tokamak

The critical beta, which is limited by an external kink mode with Alfven wave time scale, is shown to be decreased by ferromagnetic effect by about 8% for μ/μ0 ~ 2 where μ and μ0 denote the permeability of a ferromagnetic wall and vacuum, respectively, for a tokamak of aspect ratio 3. The existence of the stability window in the wall distance for resistive wall mode opened by the effects of both the toroidal plasma rotation and the plasma dissipation, which was not observed for the high aspect ratio tokamak, is found for the tokamak of aspect ratio 3. The effect of ferromagnetism on them is also investigated. The critical beta analyses of the National Centralized Tokamak (NCT) plasma using the VALEN code are started by stabilizing plate and vacuum vessel geometry with finite resistivity, and the results of the passive effect of the stabilizing plate are obtained. The calculations including the stabilizing effect of the vacuum vessel and also active feedback control are performed for a design of the NCT plasma.

Electrostatic Ballooning Mode in Toroidal Plasma

The electrostatic high-n ballooning mode equation is solved, preserving the radial structures of the electron and ion Z-functions. Two branches of ballooning instability are found. The Pearlstein-Berk mode remains stable in a torus with magnetic shear, while the ballooning mode is always unstable and is especially important for Te/Ti?O(1). The instabilities are characterized by large growth rates and small real frequencies ?*??>|?|?0.

Toroidal Effects on Nonlocal Collisionless Drift Instability

Toroidal curvature effects on the electrostatic collisionless drift instability in a sheared magnetic field is investigated. The magnetic curvature drift of ions reduces or even annihilates the shear convective damping and causes the mode ballooning. It is found that the universal mode is stable (or marginally stable at most) so long as the convective damping remains finite, and the critical current density for the current-driven drift instability becomes lower.

Effect of electron and ion viscosity on sawtooth crash in a tokamak

The effect of anomalous electron and ion viscosity induced by the stochastization of magnetic field line on sawtooth crash in a tokamak is investigated by using the reduced set of resistive MHD equations. As the perturbation grows beyond some amplitude, the most unstable mode is turned from the pure resistive mode into the one induced by the anomalous electron viscosity, and the growth rate suddenly increases, as observed in some experiments. After that, the growth of perturbation is decreased due to the anomalous ion viscosity. The sawtooth crash time is prolonged in spite of the explosive growth due to the electron viscosity. However, it is not completely suppressed by the effect of anomalous ion viscosity.

Numerical Study on Drift and Alfven Waves in a Current-Carrying Plasma

A set of coupled eigenmode equations for drift and Alfven modes in a current-carrying stab plasma with magnetic shear is studied numerically. The modes with odd-φ and even- A // parity are investigated where φ and A // are the electrostatic potential and the parallel component of the vector potential of the perturbations, respectively. The shear Alfven mode of this parity is marginally stable for the high β value, and the drift mode of this parity is more stable than that with even-φ and odd- A // parity. Electron-ion collisions are found to stabilize both the modes. The current can not make both the shear Alfven mode and the drift mode unstable. The former remains marginally stable and may contribute to the anomalous transport.

Roles of the double tearing mode on the formation of a current hole

Tokamak plasma with negative central current density is known to be unstable for m = 1/n = O resistive kink magnetohydrodynamic instability and the explanation for the absence of negative neutral current, the so-called current hole Phenomena, is made by the destabilization of the mode, However, a strong reversed magnetic shear configuration has two resonant surfaces for low mode numbers and should be unstable for the double tearing mode (DTM). Here, we examine the effects of DTM on the formation of current hole and show that the occurrence of DTM does not change the situation completely. Tlie growth of DTM flattens the current profile near the minimum-q region: here q is the safety factor, and the current gradient to drive n = 0 mode usually remains after a reconnection event due to DTM and the stability of m = 1/n = O mode is not affected much by the DTM activity.

Kinetic Theory of Global n=1 Instabilities in Toroidal Plasmas

The kinetic theory of the global n =1 instabilities of finite-pressure tokamak plasmas with circular cross-section is investigated in collisionless limit ( m , n : poloidal and toroidal mode numbers). Wave-particle interactions and finite gyroradius effect are included. The radial-poloidal eigenmode equations are directly solved numerically. The m =1 internal/tearing mode, n =1 ballooning mode and m =2 tearing mode are identified with a fixed boundary condition. The m =1 internal mode turns out to be the collisionless tearing mode in low pressure regimes. The pressure driven ballooning mode is connected with the electrostatic-like ballooning mode. The toroidal coupling further stabilizes the m =2 tearing mode, which is destabilized by the parallel current and can be stabilized by coupling with drift branch. Analytical studies are made by using the energy integral.

On the Anomalous Diffusion Due to Electrostatic Ballooning Modes

Radial diffusion flux due to electrostatic ballooning modes is estimated by taking into account the lowest order toroidal effects and by assuming the saturation of the instabilities by a random frequency modulation due to E ×B fluid motion. The result gives a quantitative agreement with the experimentally observed diffusion flux.

“Universal” Ballooning Instability

High- n kinetic ballooning instability is obtained where the toroidal coupling, coupling of Alfven and drift modes, and the correct forms of plasma dispersion functions are retained. This mode is identified as a kinetic description of MHD ballooning mode, and is unstable both in the zero-pressure limit and in the second stability region of MHD analysis. Ballooning mode is universally unstable in toroidal plasmas.