Magnetohydrodynamic Tearing Modes Research Articles

A new stabilizing regime of tearing mode entrainment in the presence of a static error field

Uncorrected static error fields (EFs) in axisymmetric fusion devices are one of the few remaining serious obstacles for advancing the present tokamak-based approach to a practical reactor. Magnetohydrodynamic tearing modes (TMs) lock to them, causing sudden losses of confinement known as disruptions. Recently, a hypothesis has been proposed that there may exist a self-healing stable regime in which a static resonant EF is effectively shielded by forcing these TMs to slowly rotate inductively by the applied non-axisymmetric field (Inoue et al 2017 Nucl. Fusion 57 116020; Inoue et al 2018 Plasma. Phys. Control. Fusion 60 025003; Inoue et al 2018 Preprint: 2018 IAEA Fusion Energy Conf. TH/P4-24). This is based on non-linear, resistive, reduced magnetohydrodynamic simulations using a cylindrical single helicity model. Proof-of-principle experiments in the DIII-D device showed that the magnetic mode structure on the plasma surface is qualitatively consistent with the simulation prediction. However, radial mode profiles revealed qualitatively different behavior. This led to a revised hypothesis that in actual non-circular toroidal devices, a tearing layer in forced rotation induces a shielding process at other rational surfaces when we take into account multiple resonant Fourier components. The time evolution experiment of the radial penetration is supportive of this hypothesis.

Reduced intermittency in the magnetic turbulence of reversed field pinch plasmas

The statistical temporal properties of broadband magnetic turbulence in the edge of reversed field pinch (RFP) plasmas are significantly altered when global magnetohydrodynamic tearing modes and magnetic relaxation are reduced. Standard RFP plasmas, having relatively large tearing fluctuations, exhibit broadband intermittent bursts of magnetic fluctuations in the bandwidth f<1.5MHz. When the global tearing is reduced via parallel current drive in the edge region, the magnetic turbulence is much less intermittent and has statistical behavior typical of self-similar turbulence (like that expected in self-organized criticality systems). A connection between intermittency and long wavelength plasma instabilities is therefore implied.

The physics of neoclassical magnetohydrodynamic tearing modes

Neoclassical effects alter the nonlinear evolution properties of magnetic islands in toroidal plasmas. While the perturbed bootstrap current effects tend to dominate the nonlinear evolution and mode saturation properties in tokamak plasmas, a number of additional effects complicate the picture. A novel aspect of the mode evolution properties is the appearance of a nonlinear threshold width, below which island formation is suppressed. The structure and strength of various closure relations for the ion viscosity and heat fluxes impact the size and scaling of the threshold width. The potential impact of this physics on low aspect ratio tokamaks and stellarator configurations is also discussed.

Geometrical influences on neoclassical magnetohydrodynamic tearing modes

The influence of geometry on the pressure drives of nonideal magnetohydrodynamic tearing modes is presented. In order to study the effects of elongation, triangularity, and aspect ratio, three different machines are considered to provide a range of tokamak configurations: Tokamak Fusion Test Reactor (circular) [Fusion Technol. 21, 1324 (1992)], DIII-D (D-shaped) [Plasma Physics and Controlled Nuclear Fusion Research 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. 1, p. 159], and Pegasus (extremely low aspect ratio) [Fonck et al., Bull. Am. Phys. Soc. 41, 1400 (1996)]. For large aspect ratio tokamaks, shaping does very little to influence the pressure gradient drives, while at low aspect ratios, a very strong sensitivity to the profiles is found. In particular, this sensitivity is connected to the strong dependence on the magnetic shear. This suggests that at low aspect ratio it may be possible to stabilize neoclassical tearing modes by a flattening the q profile near low order rational surfaces (e.g., q=2/1) using a combination of shaping and localized current drive, whereas at large aspect ratio it is more difficult.

On the stabilization of neoclassical magnetohydrodynamic tearing modes using localized current drive or heating

The effectiveness of using localized current drive or heating to suppress the formation and growth of neoclassical magnetohydrodynamic (MHD) tearing modes is addressed. The most efficient way to use an auxiliary current source is to cause current to flow in the same direction as the equilibrium bootstrap current and phase the current relative to the magnetic island such that the current is deposited on the O-point of the island. Theoretical estimates for the amount of required current to suppress the formation of a large magnetic island is of order a few percent of the equilibrium current. If the suppression is successful, the magnetic island will saturate at a width of order the radial localization width of the current source. Localized heating at the O-point of the magnetic island can also produce stabilizing effects relative to magnetic island growth. The effects of the driven current or heating can be illustrated by using a phase diagram of the island growth.

Computational modeling of neoclassical and resistive magnetohydrodynamic tearing modes in tokamaks

Numerical studies of the nonlinear evolution of magnetohydrodynamic-type tearing modes in three-dimensional toroidal geometry with neoclassical effects are presented. The inclusion of neoclassical physics introduces an additional free-energy source for the nonlinear formation of magnetic islands through the effects of a bootstrap current in Ohm’s law. The neoclassical tearing mode is demonstrated to be destabilized in plasmas which are otherwise Δ′ stable, albeit once an island width threshold is exceeded. The plasma pressure dynamics and neoclassical tearing growth is shown to be sensitive to the choice of the ratio of the parallel to perpendicular diffusivity (χ∥/χ⊥). The study is completed with a demonstration and theoretical comparison of the threshold for single helicity neoclassical magnetohydrodynamic tearing modes, which is described based on parameter scans of the local pressure gradient, the ratio of perpendicular to parallel pressure diffusivities χ⊥/χ∥, and the magnitude of an initial seed magnetic perturbation.

Long-wavelength limit of the EMHD tearing mode

The frequency spectrum of the modes that lead to fast reconnection of magnetic-field lines in a plasma configuration with sharp current density gradients is obtained and compared to that of the more familiar magnetohydrodynamic tearing modes.

Tearing modes in a general cross-section force-free cylindrical tokamak

The stability of magnetohydrodynamic tearing modes for a large aspect ratio force-free tokamak with general cross section is studied in terms of an energy principle. Determinations of the marginal stability boundary Δ′ and island size using this general two-dimensional method give good agreement with those of known methods for circular equilibria. Results for noncircular equilibria are also presented.

Density Threshold for Magnetohydrodynamic Activity in AlcatorC

Experimental measurements of magnetic fluctuations arising from resistive magnetohydrodynamic tearing modes reveal unexpected behavior in Alcator $C$. After the plasma current has risen to its steady-state level, no significant magnetohydrodynamic activity is observed unless the electron density is above a threshold value, ${\overline{n}}_{c}$. For a given toroidal field, ${\overline{n}}_{c}$ is remarkably repeatable. We find ${\overline{n}}_{c}$ to be proportional to ${B}^{2}$ and independent of ${I}_{p}$.