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.

/pdf/on-the-stabilization-of-neoclassical-magnetohydrodynamic-56cyj2qivl.pdf

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

The nonlinear behaviour of tearing modes in a plasma with density and temperature gradients is reviewed. The effects of inhomogeneities can essentially modify the evolution of small scale islands from that predicted by Rutherford theory. Plasma gradient effects provide the mechanism for island excitation even in situations when the linear tearing mode stability parameter Delta is negative. The magnetic islands are sustained by the differential response of electron and ion components of a plasma in a fluctuating electric field. Such nonlinear magnetic islands are not related to the linear instability of drift-tearing modes. The nonlinear equations describing the evolution of the width and frequency of the rotating islands are derived. In the framework of one-fluid MHD, the general equation for a neighbouring equilibrium in a finite pressure plasma is considered. The dynamics of unstable m=2 and m=1 magnetic islands based on this equation is described. The quasilinear saturation of island growth in a finite pressure plasma leads to the bifurcation of the island type equilibrium into states without islands. A new evolution equation of m=1 islands is derived. For monotonic safety factor and temperature profiles this equation predicts saturation of the m=1 island growth.

https://iopscience.iop.org/article/10.1088/0741-3335/35/6/002/pdf

Nonlinear evolution of tearing modes in inhomogeneous plasmas

Magnetic islands are a ubiquitous feature of magnetically confined plasmas. They arise as the result of plasma instabilities as well as externally imposed symmetry-breaking perturbations. In the core, effective suppression techniques have been developed. Even thin islands, however, are observed to have nonlocal effects on the profiles of rotation and current. This has stimulated interest in using magnetic islands to control plasma transport, particularly in the edge. They are also of interest as a tool to improve our understanding of microscopic plasma dynamics.

/pdf/theory-and-observations-of-magnetic-islands-1y02kmcljo.pdf

Theory and observations of magnetic islands

. We present observations which provide strong support for a substorm expansion phase onset scenario in which a localized inner magnetospheric instability developed first and was later followed by the development of a Near Earth Neutral Line (NENL) farther down-tail. Specifically, we find that the onset began as a localized brightening of an intensified growth phase arc which developed as a periodic series of arc-aligned (i.e. azimuthally arrayed) bright spots. As the disturbance grew, it evolved into vortical structures that propagated poleward and eventually morphed into an east-west aligned arc system at the poleward edge of the auroral substorm bulge. The evolution of the auroral intensity is consistent with an exponential growth with an e-folding time of around 188 s (corresponding to a linear growth rate, γ of 5.33×10−3 s−1). During the initial breakup, no obvious distortions of auroral forms to the north were observed. However, during the expansion phase, intensifications of the poleward boundary of the expanding bulge were observed together with the equatorward ejection of auroral streamers into the bulge. A strong particle injection was observed at geosynchronous orbit, but was delayed by several minutes relative to onset. Ground magnetometer data also shows a two phase development of mid-latitude positive H-bays, with a quasi-linear increase in H between the onset and the injection. We conclude that this event provides strong evidence in favor of the so-called "inside-out" substorm onset scenario in which the near Earth region activates first followed at a later time by the formation of a near-to-mid tail substorm X-line. The ballooning instability is discussed as a likely mechanism for the initial onset.

/pdf/observational-evidence-for-an-inside-out-substorm-onset-287xy6fvog.pdf

Observational evidence for an inside-out substorm onset scenario

The formation of magnetic islands as a result of plasma pressure in three‐dimensional equilibria is investigated by a boundary‐layer analysis. Away from a rational surface (‘‘exterior region’’), the plasma current is calculated exactly from the equilibrium equations. The singularity in the current thus calculated is resolved by analysis of the equilibrium equations in the vicinity of the rational surface (‘‘inner region’’). The Δ’ parameter of tearing mode theory is used to match the inner and outer regions. The island width is found to depend on the resistive interchange criterion, as seen in the work of Glasser, Greene, and Johnson [Phys. Fluids 18, 875 (1975)]. Estimates of island sizes for different stellarator experiments are given.

Magnetic island formation in three-dimensional plasma equilibria

The effect of an energetic ion population on the nonlinear stability of a tearing mode of single helicity is determined using kinetic theory. A dynamical equation is derived for the magnetic-island width. It is shown that the island growth can be suppressed in a tokamak when the energetic ion-density profile peaks just outside the rational surface. Effects due to resistive interchanges and bootstrap currents are included in the model.

Suppression of the tearing mode by energetic ions.

Widths of magnetic islands induced by finite plasma pressure are computed for the Heliotron‐E configuration [Phys. Rev. Lett. 53, 2242 (1984); Nucl. Fusion 27, 895 (1987)]. Equilibrium beta limits are obtained from the criterion of island overlap. Earlier experimental observations on internal disruptions in Heliotron‐E are revisited.

Equilibrium beta limits in Heliotron‐E due to magnetic island overlap

Nonlinear Ballooning Instability in the Near-Earth Magnetotail: Growth, Structure, and Possible Role in Substorms

We consider the problem of steady Euler flows in a torus. We show that in the absence of a direction of symmetry the solution for the vorticity contains δ-function singularities at the rational surfaces of the torus. We study the effect of a small but finite viscosity on these singularities. The solutions near a rational surface contain cat's eyes or islands, well known in the classical theory of critical layers. When the islands are small, their widths can be computed by a boundary-layer analysis. We show that the islands at neighbouring rational surfaces generally overlap. Thus, steady toroidal flows exhibit a tendency towards Beltramization.

C. C. Hegna

Papers

Magnetic island formation in three-dimensional plasma equilibria

Suppression of the tearing mode by energetic ions.

Equilibrium beta limits in Heliotron‐E due to magnetic island overlap

Nonlinear Ballooning Instability in the Near-Earth Magnetotail: Growth, Structure, and Possible Role in Substorms

Islands in three-dimensional steady flows