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Title: The deceiving Δ′: On the equilibrium dependent dynamics of nonlinear magnetic islands

Abstract

The linear stability parameter Δ′ is commonly used as a figure of merit for the nonlinear dynamics of the tearing mode. It is shown, through numerical simulations, that factors other than Δ′ can play a very important role in determining the evolution of nonlinear magnetic islands, even relatively close to marginal stability. In particular, two different equilibria are analysed and it is shown that, once perturbed, they have a qualitatively and quantitatively different response despite the fact that they are characterised by the same Δ′. However, the different behaviour can still be associated with linear properties of the equilibrium. It is also studied how the nonlinear and saturation phase are affected by an increasing Δ′ in the two equilibria. As the instability drive is increased, the systems move from a dynamics characterised by a “universal” generalised Rutherford equation to a Y-point configuration and then to a plasmoid unstable Y-point. Remarkably, in certain configurations the Rutherford phase is absent and the system forms a current ribbon without an X-point collapse.

Authors:
 [1];  [2];  [3]
  1. CCFE, Culham Science Centre, Abingdon, Oxon OX14 3DB (United Kingdom)
  2. Istituto Sistemi Complessi-CNR, Torino, Italy and Politecnico di Torino, Dipartimento Energia, Torino (Italy)
  3. Physics Department, University of Pisa, Pisa (Italy)
Publication Date:
OSTI Identifier:
22299685
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 21; Journal Issue: 10; Other Information: (c) 2014 EURATOM; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; COMPUTERIZED SIMULATION; CONFIGURATION; EQUILIBRIUM; MAGNETIC ISLANDS; NONLINEAR PROBLEMS; STABILITY; TEARING INSTABILITY

Citation Formats

Militello, F., Grasso, D., and Borgogno, D. The deceiving Δ′: On the equilibrium dependent dynamics of nonlinear magnetic islands. United States: N. p., 2014. Web. doi:10.1063/1.4900643.
Militello, F., Grasso, D., & Borgogno, D. The deceiving Δ′: On the equilibrium dependent dynamics of nonlinear magnetic islands. United States. doi:10.1063/1.4900643.
Militello, F., Grasso, D., and Borgogno, D. Wed . "The deceiving Δ′: On the equilibrium dependent dynamics of nonlinear magnetic islands". United States. doi:10.1063/1.4900643.
@article{osti_22299685,
title = {The deceiving Δ′: On the equilibrium dependent dynamics of nonlinear magnetic islands},
author = {Militello, F. and Grasso, D. and Borgogno, D.},
abstractNote = {The linear stability parameter Δ′ is commonly used as a figure of merit for the nonlinear dynamics of the tearing mode. It is shown, through numerical simulations, that factors other than Δ′ can play a very important role in determining the evolution of nonlinear magnetic islands, even relatively close to marginal stability. In particular, two different equilibria are analysed and it is shown that, once perturbed, they have a qualitatively and quantitatively different response despite the fact that they are characterised by the same Δ′. However, the different behaviour can still be associated with linear properties of the equilibrium. It is also studied how the nonlinear and saturation phase are affected by an increasing Δ′ in the two equilibria. As the instability drive is increased, the systems move from a dynamics characterised by a “universal” generalised Rutherford equation to a Y-point configuration and then to a plasmoid unstable Y-point. Remarkably, in certain configurations the Rutherford phase is absent and the system forms a current ribbon without an X-point collapse.},
doi = {10.1063/1.4900643},
journal = {Physics of Plasmas},
number = 10,
volume = 21,
place = {United States},
year = {Wed Oct 15 00:00:00 EDT 2014},
month = {Wed Oct 15 00:00:00 EDT 2014}
}
  • Saturation of magnetic islands at large values of the tearing mode stability parameter Δ{sup ′} is investigated numerically. In such regimes, the island dynamics exhibit a number of transient features such as coalescence instability, X-point collapse, and plasmoid generation. It is shown that while conditions for these transient instabilities to appear depend on the viscosity and resistivity, the final width of the saturated island is independent of such phenomena, as well as viscosity and resistivity values. It is found that the saturated island width is strongly influenced by global properties of the current profile and related to the equilibrium reconnectedmore » flux across the magnetic island.« less
  • Resonant magnetic perturbations (RMPs) produce magnetic islands in toroidal plasmas. Self-healing (annihilation) of RMP-induced magnetic islands has been observed in helical systems, where a possible mechanism of the self-healing is shielding of RMP penetration by plasma flows, which is well known in tokamaks. Thus, fundamental physics of RMP shielding is commonly investigated in both tokamaks and helical systems. In order to check this mechanism, detailed informations of magnetic island phases are necessary. In experiments, measurement of radial magnetic responses is relatively easy. In this study, based on a theoretical model of rotating magnetic islands, behavior of radial magnetic fields duringmore » the self-healing is investigated. It is confirmed that flips of radial magnetic fields are typically observed during the self-healing. Such behavior of radial magnetic responses is also observed in LHD experiments.« less
  • An analytic theory of nonlinear pressure driven magnetic island evolution is presented which includes both neoclassical and curvature effects. This work differs from prior analytic treatments where large aspect ratio, small beta expansions were employed that are not appropriate for tight aspect ratio applications. In this work, this calculation is revisited by deriving and analyzing an island Grad{endash}Shafarnov equation using an asymptotic expansion based solely on a small island width expansion. In conventional high-temperature tokamaks, the stabilizing curvature effects are weaker than the destabilizing neoclassical tearing mode instability drive in regions of monotonically increasing {ital q}-profile. At low aspect ratio,more » these two effects become comparable which suggests that tight aspect ratio configurations are less susceptible to the neoclassical tearing mode than are conventional tokamaks. {copyright} {ital 1999 American Institute of Physics.}« less
  • Curvature and finite pressure are known to have a dramatic influence on linear magnetic tearing stability. An analytic theory of the nonlinear resistive growth of magnetic islands in tokamaks that includes the interchange driving term in presented here. A Grad-Shafranov equation to describe the magnetohydrodynamic (MHD) equilibrium of thin islands is derived. The resistive evolution of these islands is then obtained. Interchange effects are found to become progressively less important with increasing island width.
  • The nonlinear dynamics of magnetic tearing islands imbedded in a pressure gradient driven turbulence is investigated numerically in a reduced magnetohydrodynamic model. The study reveals regimes where the linear and nonlinear phases of the tearing instability are controlled by the properties of the pressure gradient. In these regimes, the interplay between the pressure and the magnetic flux determines the dynamics of the saturated state. A secondary instability can occur and strongly modify the magnetic island dynamics by triggering a poloidal rotation. It is shown that the complex nonlinear interaction between the islands and turbulence is nonlocal and involves small scales.