Variational Integrators for Reduced Magnetohydrodynamics

Reduced magnetohydrodynamics is a simplified set of magnetohydrodynamics equations with applications to both fusion and astrophysical plasmas, possessing a noncanonical Hamiltonian structure and consequently a number of conserved functionals. We propose a new discretisation strategy for these equations based on a discrete variational principle applied to a formal Lagrangian. The resulting integrator preserves important quantities like the total energy, magnetic helicity and cross helicity exactly (up to machine precision). As the integrator is free of numerical resistivity, spurious reconnection along current sheets is absent in the ideal case. If effects of electron inertia are added, reconnection of magnetic field lines is allowed, although the resulting model still possesses a noncanonical Hamiltonian structure. After reviewing the conservation laws of the model equations, the adopted variational principle with the related conservation laws are described both at the continuous and discrete level. We verify the favourable properties of the variational integrator in particular with respect to the preservation of the invariants of the models under consideration and compare with results from the literature and those of a pseudo-spectral code.Comment: 35 page

Formation of Plasmoid Chains in Fusion Relevant Plasmas

The formation of plasmoid chains is explored for the first time within the context of the Taylor problem, in which magnetic reconnection is driven by a small amplitude boundary perturbation in a tearing-stable slab plasma equilibrium. Numerical simulations of a magnetohydrodynamical model of the plasma show that for very small plasma resistivity and viscosity, the linear inertial phase is followed by a nonlinear Sweet-Parker evolution, which gives way to a faster reconnection regime characterized by a chain of plasmoids instead of a slower Rutherford phase

Extended theory of the Taylor problem in the plasmoid-unstable regime

A fundamental problem of forced magnetic reconnection has been solved taking into account the plasmoid instability of thin reconnecting current sheets. In this problem, the reconnection is driven by a small amplitude boundary perturbation in a tearing-stable slab plasma equilibrium. It is shown that the evolution of the magnetic reconnection process depends on the external source perturbation and the microscopic plasma parameters. Small perturbations lead to a slow nonlinear Rutherford evolution, whereas larger perturbations can lead to either a stable Sweet-Parker-like phase or a plasmoid phase. An expression for the threshold perturbation amplitude required to trigger the plasmoid phase is derived, as well as an analytical expression for the reconnection rate in the plasmoid-dominated regime. Visco-resistive magnetohydrodynamic simulations complement the analytical calculations. The plasmoid formation plays a crucial role in allowing fast reconnection in a magnetohydrodynamical plasma, and the presented results suggest that it may occur and have profound consequences even if the plasma is tearing-stable.Comment: Accepted for publication in Physics of Plasma

Gyro-induced acceleration of magnetic reconnection

The linear and nonlinear evolution of magnetic reconnection in collisionless high-temperature plasmas with a strong guide field is analyzed on the basis of a two-dimensional gyrofluid model. The linear growth rate of the reconnecting instability is compared to analytical calculations over the whole spectrum of linearly unstable wave numbers. In the strongly unstable regime (large \Delta '), the nonlinear evolution of the reconnecting instability is found to undergo two distinctive acceleration phases separated by a stall phase in which the instantaneous growth rate decreases. The first acceleration phase is caused by the formation of strong electric fields close to the X-point due to ion gyration, while the second acceleration phase is driven by the development of an open Petschek-like configuration due to both ion and electron temperature effects. Furthermore, the maximum instantaneous growth rate is found to increase dramatically over its linear value for decreasing diffusion layers. This is a consequence of the fact that the peak instantaneous growth rate becomes weakly dependent on the microscopic plasma parameters if the diffusion region thickness is sufficiently smaller than the equilibrium magnetic field scale length. When this condition is satisfied, the peak reconnection rate asymptotes to a constant value.Comment: Accepted for publication on Physics of Plasma

World Englishes and the Challenge of Teaching Phonetics and Phonology at Higher Education Levels

El crecimiento del uso del inglés en todo el mundo y su reconocimiento como lengua franca ha cuestionado la idoneidad de ciertos modelos de pronunciación instruccional. Como consecuencia, también se han discutido los objetivos de la enseñanza de la pronunciación. La creciente aceptación de muchas variedades de inglés y la diversidad de contextos en los que se utilizan como una herramienta de comunicación exitosa parece haber cambiado el enfoque de lograr una pronunciación similar a la nativa a dar prioridad a la inteligibilidad. La enseñanza de la fonética y la fonología en entornos de educación superior como parte de los programas de formación de profesores y traductores amplía las posibilidades de desarrollar la capacidad de los estudiantes para adaptarse a la realidad cambiante del uso global del inglés. Después de considerar los contenidos y objetivos actuales y buscados en la enseñanza de la fonética del inglés a futuros especialistas, este artículo tiene como objetivo compartir posibles actividades en un intento de concientizar a los estudiantes sobre la existencia de diversas pronunciaciones escuchadas en diferentes partes del mundo, erradicar la noción de la supremacía de un acento sobre otros, analizar las diferencias entre los tipos de inglés hablados por personas en los círculos externos, internos y en expansión, y ayudar a los estudiantes a desarrollar las habilidades de percibir peculiaridades y comprender el idioma a pesar de estas diferencias

Magnetic island evolution under the action of electron cyclotron current drive

The magnetic island evolution under the action of an externally current generated by electron cyclotron (ECCD) wave beams is studied using a reduced resistive magnetohydrodynamics (RRMHD) plasma model. We found interesting and somewhat unexpected features of the actual nonlinear 2-D evolution of the magnetic perturbation depending on the injection time of the radio frequency control. In particular in the linear phase of the magnetic island growth we observe that the complete annihilation of the island width is followed by a spatial phase shift of the island, referred as «flip»instability. On the other hand, a current drive deposition in the Rutherford regime can be accompained by the occurrence of a Kelvin-Helmholtz type shear flow instability, responsible for the onset of a plasma turbulent behavio

Coupling between reconnection and Kelvin-Helmholtz instabilities in collisionless plasmas

Abstract. In a collisionless plasma, when reconnection instability takes place, strong shear flows may develop. Under appropriate conditions these shear flows become unstable to the Kelvin-Helmholtz instability. Here, we investigate the coupling between these instabilities in the framework of a four-field model. Firstly, we recover the known results in the low β limit, β being the ratio between the plasma and the magnetic pressure. We concentrate our attention on the dynamical evolution of the current density and vorticity sheets which evolve coupled together according to a laminar or a turbulent regime. A three-dimensional extension in this limit is also discussed. Secondly, we consider finite values of the β parameter, allowing for compression of the magnetic and velocity fields along the ignorable direction. We find that the current density and vorticity sheets now evolve separately. The Kelvin-Helmholtz instability involves only the vorticity field, which ends up in a turbulent regime, while the current density maintains a laminar structure