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.

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

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.

Electrostatic Drift Instability of Tokamak Plasmas

The kinetic theory of the drift-tearing mode in a finite-β, collisionless inhomogeneous cylindrical tokamak is investigated. It is found that 1) when the density is low, the kinetic drift-tearing modes are unstable whereas they become stabilized as the density increases, 2) the medium-m (poloidal mode number) modes have a smaller growth rate, and 3) the electron temperature gradient further stabilizes these modes. Because of the magnetic shear and the finite β value, the outgoing drift wave is associated with the tearing mode, and hence the ion Landau damping stabilizes the mode when β increases. The local current density is found to be crucial for the instability. It is noted that the stability criterion for the MHD tearing mode, Δ' < 0 (Δ' is the jump of the logarithmic derivative of r across the mode rational surface), is lo longer valid for kinetic tearing mode. – For future tokamak parameters, low- and medium-m (2 ≤ m 50) kinetic drift-tearing modes are found to be stable in cylindrical geometry.

http://iopscience.iop.org/article/10.1088/0029-5515/21/1/001/pdf

Kinetic theory of helical instabilities in a cylindrical tokamak

Stability properties of current‐driven drift waves are examined in the parametric environment typical of the toroidal reversed field pinch. In particular, the effects of field‐aligned current, plasma beta, collisionality, and magnetic shear are examined. Under conditions leading to instability, transport effects are calculated, and found to be dominated by the electromagnetic nature of this instability.

Current‐driven drift waves in reversed field pinches

Electrostatic drift ion cyclotron waves in the presence as well as in the absence of an ambipolar field in a sheet plasma of thickness of the order of the ion Larmor radius have been studied numerically. The frequency range considered is of the order of ion cyclotron frequency ω c i . The method is based on an integral equation in the wavenumber space derived from the Vlasov-Poisson system of equations. Eigenfrequencies and eigenfunctions of the waves with and without ambipolar field are studied by varying the plasma thickness, the perpendicular wavenumber and the parallel wavenumber. A strong ambipolar field seems to be effective for the suppression of the drift ion cyclotron instability in sheet plasmas. The validity of local dispersion relation is checked.

Electrostatic Drift Ion Cyclotron Waves in Sheet Plasmas with and without Ambipolar Field

Stability of the collisionless drift wave localized to the rational surface is studied numerically. Both the current and the finite- β effects are taken into account. The results confirm the previous analytical and/or numerical results concerning the stableness in the currentless case, instability driven by the current and its finite- β stabilitzation in the short wavelength region. In addition, a strong resonant coupling of the drift wave to the Alfven wave is found to occur due to the combined effect of the current and the finite- β value, resulting a destabilizing effect in the long wavelength region. The critical electron drift velocity for the onset of the instability is calculated. The result shows a substantial reduction of the critical velocity by the finite- β effect.

Numerical Analysis of Current-Driven Drift-Wave Instability in a Finite- β Plasma

A systematic iteration scheme is presented to numerically solve the eigenvalue problem described by a coupled set of second-order differential equations under the boundary conditions that the solution is localized near the origin. The method consists of the application of Newton's iteration scheme to the shooting method. A useful analytical expression for the correction to the trial eigenvalue is obtained. Application is made for two examples, simple harmonic oscillator and electro-magnetic drift-wave in a finite-β plasma in a sheared magnetic field, to demonstrate a remarkable stability, efficiency and accuracy of the method. In the latter example, reduction of the CPU time by factor 20–30 is obtained as compared with the standard simplex method.

Chikara Ueno

Papers

Numerical Analysis of Current-Driven Drift-Wave Instability in a Finite- β Plasma

New Numerical Method for Solving Eigenvalue Problems Described by Coupled Second-Order Differential Equations