J. F. Luciani

A Twisted Flux Rope Model for Coronal Mass Ejections and Two-Ribbon Flares

We present a new approach to the theory of large-scale solar eruptive phenomena such as coronal mass ejections and two-ribbon flares, in which twisted flux tubes play a crucial role. We show that it is possible to create a highly nonlinear three-dimensional force-free configuration consisting of a twisted magnetic flux rope representing the magnetic structure of a prominence (surrounded by an overlaying, almost potential, arcade) and exhibiting an S-shaped structure, as observed in soft X-ray sigmoid structures. We also show that this magnetic configuration cannot stay in equilibrium and that a considerable amount of magnetic energy is released during its disruption. Unlike most previous models, the amount of magnetic energy stored in the configuration prior to its disruption is so large that it may become comparable to the energy of the open field.

Coronal Mass Ejection: Initiation, Magnetic Helicity, and Flux Ropes. II. Turbulent Diffusion-driven Evolution

We consider a three-dimensional bipolar magnetic field B, occupying a half-space, which is driven into evolution by the slow turbulent diffusion of its normal component on the boundary. The latter is imposed by fixing the tangential component of the electric field and leads to flux cancellation. We first present general analytical considerations on this problem and then construct a class of explicit solutions in which B keeps evolving quasi-statically through a sequence of force-free configurations without exhibiting any catastrophic behavior. Thus, we report the results of a series of numerical simulations in which B evolves from different force-free states, the electric field on the boundary being imposed to have a vanishing electrostatic part (the latter condition is not enforced in the analytical model, and thus it is possible a priori for the results of the two types of calculations to be different). In all the cases, we find that the evolution conserves the magnetic helicity and exhibits two qualitatively different phases. The first one, during which a twisted flux rope is created, is slow and almost quasi-static, while the second one is associated with a disruption, which is confined for a small initial helicity and global for a large initial helicity. Our calculations may be relevant for modeling the coronal mass ejections that have been observed to occur in the late dispersion phase of an active region. In particular, they may allow us to understand the role played by a twisted flux rope in these events.

CORONAL MASS EJECTION INITIATION BY CONVERGING PHOTOSPHERIC FLOWS: TOWARD A REALISTIC MODEL

In the context of coronal mass ejections triggering, we reconsider the class of models in which the evolution of an active region (AR) is driven by imposed boundary motions converging toward the polarity inversion line (PIL). We introduce a new model problem in which there is a large-scale flow with a diverging structure on the photosphere. This flow is reminiscent of that of the well-known moat flow around each of the two spots of a bipolar AR and transports only part of the magnetic flux toward the PIL. It is thus more compatible with observations than the one used in our previous study, which forced the whole positive and negative polarity parts of the AR approaching each other. We also include a diffusion term associated with small-scale turbulent photospheric motions, but keep the associated diffusivity at a low value in the particular study described here. We show that the evolution of an initial sheared force-free field first leads to the formation of a twisted flux rope which stays in equilibrium for some time. Eventually, however, the configuration suffers a global disruption whose underlying mechanism is found by energetic considerations to be nonequilibrium. It begins indeed when the magnetic energy becomes of the order of the energy of an accessible partially open field. For triggering an eruption by converging flows, it is thus not necessary to advect the whole AR toward the PIL, but only its central part.

Non-current-free coronal closure of subphotospheric MHD models

We propose a method that allows the matching of two classes of models that have been well developed so far, but largely independently from each other: (1) convection zone (CZ) models, which generally either end up below the photosphere or are matched with an external potential field, and (2) coronal models of eruptive processes and heating, which usually consider the evolution of current-carrying magnetic fields driven by given photospheric changes. In our approach, the thin turbulent photospheric layer between the two large regions is modeled as a resistive layer across which the physical quantities suffer stiff variations. We show that this layer enables the transport of an electric current into the corona through the tangential component of the electric field (continuous across the various interfaces), as well as good conservation of the global magnetic helicity. To illustrate our general approach, we present in detail a model problem in which the rising of an initially twisted flux rope through the CZ is described kinematically while the physics inside the corona is described by a full magnetohydrodynamic model. We show that the evolution leads to the emergence of magnetic flux and electric current into the corona, with the creation of a flux rope that eventually suffers a dynamical transition toward fast expansion.

Oscillation regimes of the internal kink mode in tokamak plasmas

The long-term dynamics of the internal kink mode are studied using the non-linear, two-fluid magnetohydrodynamics (MHD) code XTOR-2F (Lutjens et al 2010 J. Comput. Phys. 229 8130). The dynamics of the internal kink are studied in resistive MHD plus transport, and, in addition, also including some two-fluid effects. The simulation results yield a pattern of kink cycles or stationary states with m/n = 1/1 helicity. The threshold for sustained (non-decaying) kink cycles, which characterize sawtooth oscillations, is shown to depend on the plasma pressure, the current and energy diffusion times, and the ion and electron diamagnetic drifts. In particular, the diamagnetic flow stabilization extends the cyclic kink regime into a parameter space that is adequate to carry out studies of sawtooth oscillations in ohmic tokamak discharges.

First principles fluid modelling of magnetic island stabilization by electron cyclotron current drive (ECCD)

Tearing modes are MagnetoHydroDynamics (MHD) instabilities that reduce the performance of fusion devices. They can however be controlled and suppressed using electron cyclotron current drive (ECCD) as demonstrated in various tokamaks. In this work, simulations of island stabilization by ECCD-driven current have been carried out using the toroidal nonlinear 3D full MHD code XTOR-2F, in which a current source term modeling the ECCD has been implemented. The efficiency parameter, eta(RF), has been computed and its variations with respect to source width and location were also computed. The influence of parameters such as current intensity, source width and position with respect to the island was evaluated and compared to the modified Rutherford equation. We retrieved a good agreement between the simulations and the analytical predictions concerning the variations of control efficiency with source width and position. We also show that the 3D nature of the current source term can lead to the onset of an island if the source term is precisely applied on a rational surface. We report the observation of a flip phenomenon in which the O- and X-points of the island rapidly switch their position in order for the island to take advantage of the current drive to grow.

Nonlinear three-dimensional MHD simulations of tearing modes in tokamak plasmas

The comprehension of the dynamics of classical and neoclassical tearing modes is a key issue in high-performance tokamak plasmas. Avoiding these instabilities requires a good knowledge of all the physical mechanisms involved in their linear and/or nonlinear onset. Our tridimensional time evolution code XTOR, which solves the full magnetohydrodynamic (MHD) equations including thermal transport, is used to tackle this difficult problem. In this paper, to show the state of art in full-scale nonlinear MHD simulations of tokamak plasmas, we investigate the effect of plasma curvature on the tearing mode dynamics. For a realistic picture of this dynamics, heat diffusion is required in the linear regimes as well, as in the nonlinear regimes. We present a new dispersion relation including perpendicular and parallel transport, and show that it matches the linear and nonlinear regimes. This leads to a new tearing mode island evolution equation including curvature effects, valid for every island size in tokamak plasmas. This equation predicts a nonlinearly unstable regime for tearing instabilities, i.e. a regime which is linearly stable, but where the tearing mode can be destabilized nonlinearly by a finite-size seed island. These theoretical predictions are in good agreement with XTOR simulations. In particular, the nonlinear instability due to curvature effects is reproduced. Our results have an important impact on the onset mechanism of neoclassical tearing modes. They indeed predict that curvature effects lead to a resistive MHD threshold.

Non-linear modeling of core MHD in tokamaks

The fully implicit 3D two-fluid MHD code XTOR-2F has been developed to allow an easy implementation of physical models beyond MHD. The numerical method of solution used in XTOR-2F is presented briefly. The code is then applied to the investigation of the long time dynamics of internal kinks, first within the framework of resistive MHD including thermal transport and next adding more refined effects such as ion and electron diamagnetic rotations and separate density and pressure evolutions.

Extended MHD simulations of infernal mode dynamics and coupling to tearing modes

A numerical study of pressure driven magnetohydrodynamic (MHD) instabilities in a low-shear tight aspect ratio configuration is presented. When the magnetic shear is sufficiently small over an extended region in the core, enhanced instability occurs due to the coupling to poloidal sidebands, which itself occurs due to toroidicity. Numerical simulations have been performed with the initial value code XTOR-2F both in the ideal and resistive MHD frame. Two-fluid effects (plasma diamagnetic flows) have been retained as well. The predictions of the XTOR-2F code on the amplitude of the growth rate, and on the rotation frequency of the modes, have been compared with analytic linear theory of infernal modes. Qualitative agreement has been found between numerical and analytical results, in spite of the tight aspect ratio configuration. The intermediate scaling gamma similar to S-3/8, predicted by the linear theory (Brunetti et al 2014 Plasma Phys. Control. Fusion 56 075025), is recovered by the numerical results. A study of the nonlinear evolution of the magnetic island of the tearing sideband has been performed and the results from the simulations are compared with Rutherfords theory.

CORONAL CLOSURE OF SUBPHOTOSPHERIC MHD CONVECTION FOR THE QUIET SUN

We use our resistive layer model (RLM), which stresses the importance of the resistivity at the photospheric interface, to study the evolution of a solar coronal quiet region driven by subphotospheric convection. The initial version of the RLM is improved by introducing a new Boussinesq MHD model for the upper part of the convection zone (CZ), while the low-beta corona is still described by a MHD model. We compute the evolution of a weak magnetic field introduced initially in the CZ. We observe its amplification by the turbulence, the concentration of the photospheric flux at the boundaries of the convection cells, the coalescence and the cancellation of flux elements, and the transfer of about 10% of the magnetic energy into the corona. The currents associated with the nonpotential coronal field are found to be organized in filament-like localized structures due to the photospheric vortices and the complexity of the magnetic topology. Their resistive dissipation contributes to the heating of the quiet corona.