The stability of a test equilibrium relevant to the International Thermonuclear Experimental Reactor [Fusion Eng. Des. 36, 9 (1997)] has been studied within the framework of the neoclassical island theory. The most unstable modes, with the most positive matching index Δ′, have been found by solving the toroidal stability equation to have 3/2, 2/1, and 4/3 helicities. Quasilinear effects resulting from the flattening of the current profile as the island develops are important and stabilizing. Large saturated islands are predicted to arise from a combination of strong bootstrap current drive and weakly negative Δ′. The island size can be significantly reduced by applying a continuous current drive at the unstable rational surfaces. The so-obtained reduction of island width is approximately proportional to the current drive and inversely proportional to the square of the current channel. This stabilization relies on the removal of the free energy in the outer region and can thus be regarded as a Δ′ effect.

/pdf/stabilization-of-neoclassical-tearing-modes-using-a-1zwfk6r78o.pdf

Stabilization of neoclassical tearing modes using a continuous localized current drive

The influence of driven current on the m/n=2/1 resistive tearing mode is studied systematically using a three-dimensional toroidal magnetohydrodynamic code. A uniform driven current with Gaussian distribution in the radial direction is imposed around the unperturbed rational surface. It is found that the driven current can locally modify the profiles of the current and safety factor, such that the tearing mode becomes linearly stable. The stabilizing effect increases with the increase of the driven current Icd or the decrease of its width δcd, unless an excessively large driven current reverses the magnetic shear near the rational surface and drives other instabilities such as double or triple tearing modes. The stabilizing effect can be negligible or becomes reversed if the maximum driven current density is not at the unperturbed rational surface.

Influence of driven current on resistive tearing mode in Tokamaks

/pdf/influence-of-driven-current-on-resistive-tearing-mode-in-ukdbzqlqbj.pdf

Nonlinear resistive-magnetohydrodynamics (MHD) computation with heating and anisotropic transport is applied to examine the interaction between thermal energy and magnetic fluctuations in inductively driven reversed-field pinches (RFPs). The magnetic fluctuations underlie magnetic field reversal through dynamo-like correlations, and they enhance thermal energy transport through fluctuations of parallel heat flux density. With the unfavorable magnetic curvature that exists across the RFP profile, thermal energy also affects the magnetic fluctuations. Computations with the NIMROD code [Sovinec et al., J. Comput. Phys. 195, 355–386 (2004)] integrate nonlinear MHD dynamics with energy transport and reproduce an RFP state with experimentally relevant values of plasma- β. Equilibria constructed from results of the 3D computations are analyzed to assess the sources of free energy in the saturated nonlinear state. Linear computations for these profiles show unstable modes of tearing parity. Their eigenfunctions are used to evaluate and compare stabilizing and destabilizing contributions to the kinetic energy integral. An assessment of the drives in the integral reveals that the pressure gradient drive is of comparable magnitude to the parallel current drive, and only the sum of the two surpasses the stabilizing contributions. Correlation of magnetic and parallel heat flux density fluctuations in the nonlinear computations shows that fluctuation-induced thermal conduction is the dominant mode of energy loss, as expected from experimental evidence. Decomposition of the fluctuating heat flux density shows that second-order correlations, alone, do not explain the total energy transport. Higher-order correlations are also important.

Pressure-driven tearing and thermal transport in finite-beta reversed field pinch computations

A formalism for the construction of energy principles for dissipative systems is presented. It is shown that dissipative systems satisfy a conservation law for the bilinear Hamiltonian provided the Lagrangian is time invariant. The energy on the other hand, differs from the Hamiltonian by being quadratic and by having a negative definite time derivative (positive power dissipation). The energy is a Lyapunov functional whose definiteness yields necessary and sufficient stability criteria. The stability problem of resistive magnetohydrodynamic (MHD) is addressed: the energy principle for ideal MHD is generalized and the stability criterion by Tasso [Phys. Lett. 147, 28 (1990)] is shown to be necessary in addition to sufficient for real growth rates. An energy principle is found for the inner layer equations that yields the resistive stability criterion D-R<0 in the incompressible limit, whereas the tearing mode criterion Delta'<0 is shown to result from the conservation law of the bilinear concomitant in the resistive layer. (C) 1997 American Institute of Physics.

/pdf/energy-principles-for-linear-dissipative-systems-with-1dz7c3qs5o.pdf

A. Pletzer

Papers

Energy principles for linear dissipative systems with application to resistive MHD stability