Optimal unstirred state of a passive scalar

Given a passive tracer distribution, what is the simplest unstirred pattern that may be reached under incompressible advection? This question is partially motivated by recent studies of three-dimensional (3-D) magnetic reconnection, in which the patterns of a topological invariant called the field line helicity greatly simplify until reaching a relaxed state. We test two approaches: a variational method with minimal constraints, and a magnetic relaxation scheme where the velocity is determined explicitly by the pattern of. Both methods achieve similar convergence for simple test cases. However, the magnetic relaxation method guarantees a monotonic decrease in the Dirichlet seminorm of, and is numerically more robust. We therefore apply the latter method to two complex mixed patterns modelled on the field line helicity of 3-D magnetic braids. The unstirring separates into a small number of large-scale regions determined by the initial topology, which is well preserved during the computation. Interestingly, the velocity field is found to have the same large-scale topology as. Similarity to the simplification found empirically in 3-D magnetic reconnection simulations supports the idea that advection is an important principle for field line helicity evolution.</p

Electric current circuits in astrophysics

Cosmic magnetic structures have in common that they are anchored in a dynamo, that an external driver converts kinetic energy into internal magnetic energy, that this magnetic energy is transported as Poynting fl ux across the magnetically dominated structure, and that the magnetic energy is released in the form of particle acceleration, heating, bulk motion, MHD waves, and radiation. The investigation of the electric current system is particularly illuminating as to the course of events and the physics involved. We demonstrate this for the radio pulsar wind, the solar flare, and terrestrial magnetic storms

75th Anniversary of ‘Existence of Electromagnetic-Hydrodynamic Waves’

We have recently passed the 75th anniversary of one of the most important results in solar and space physics: Hannes Alfv\'en's discovery of Alfv\'en waves and the Alfv\'en speed. To celebrate the anniversary, this article recounts some major episodes in the history of MHD waves. Following an initially cool reception, Alfv\'en's ideas were propelled into the spotlight by Fermi's work on cosmic rays, the new mystery of coronal heating and, as scientific perception of interplanetary space shifted dramatically and the space race started, detection of Alfv\'en waves in the solar wind. From then on, interest in MHD waves boomed, laying the foundations for modern remote observations of MHD waves in the Sun, coronal seismology and some of today's leading theories of coronal heating and solar wind acceleration. In 1970, Alfv\'en received the Nobel Prize for his work in MHD, including these discoveries. The article concludes with some reflection about what the history implies about the way we do science, especially the advantages and pitfalls of idealised mathematical models.Comment: 10 pages, accepted by Solar Physic

Extreme Ultra-Violet Spectroscopy of the Lower Solar Atmosphere During Solar Flares

The extreme ultraviolet portion of the solar spectrum contains a wealth of diagnostic tools for probing the lower solar atmosphere in response to an injection of energy, particularly during the impulsive phase of solar flares. These include temperature and density sensitive line ratios, Doppler shifted emission lines and nonthermal broadening, abundance measurements, differential emission measure profiles, and continuum temperatures and energetics, among others. In this paper I shall review some of the advances made in recent years using these techniques, focusing primarily on studies that have utilized data from Hinode/EIS and SDO/EVE, while also providing some historical background and a summary of future spectroscopic instrumentation.Comment: 34 pages, 8 figures. Submitted to Solar Physics as part of the Topical Issue on Solar and Stellar Flare

Evolution of Field Line Helicity in Magnetic Relaxation

Plasma relaxation in the presence of an initially braided magnetic field can lead to self-organization into relaxed states that retain non-trivial magnetic structure. These relaxed states may be in conflict with the linear force-free fields predicted by the classical Taylor theory, and remain to be fully understood. Here, we study how the individual field line helicities evolve during such a relaxation, and show that they provide new insights into the relaxation process. The line helicities are computed for numerical resistive-magnetohydrodynamic simulations of a relaxing braided magnetic field with line-tied boundary conditions, where the relaxed state is known to be non-Taylor. Firstly, our computations confirm recent analytical predictions that line helicity will be predominantly redistributed within the domain, rather than annihilated. Secondly, we show that self-organization into a relaxed state with two discrete flux tubes may be predicted from the initial line helicity distribution. Thirdly, for this set of line-tied simulations we observe that the sub-structure within each of the final tubes is a state of uniform line helicity. This uniformization of line helicity is consistent with Taylor theory applied to each tube individually. However, it is striking that the line helicity becomes significantly more uniform than the force-free parameter

Physical role of topological constraints in localized magnetic relaxation

Predicting the final state of turbulent plasma relaxation is an important challenge, both in astro-physical plasmas such as the Sun's corona and in controlled thermonuclear fusion. Recent numerical simulations of plasma relaxation with braided magnetic fields identified the possibility of a novel constraint, arising from the topological degree of the magnetic field-line mapping. This constraint implies that the final relaxed state is drastically different for an initial configuration with topological degree 1 (which allows a Taylor relaxation) and one with degree 2 (which does not reach a Taylor state). Here, we test this transition in numerical resistive-magnetohydrodynamic simulations, by embedding a braided magnetic field in a linear force-free background. Varying the background force-free field parameter generates a sequence of initial conditions with a transition between topological degree 1 and 2. For degree 1, the relaxation produces a single twisted flux tube, whereas for degree 2 we obtain two flux tubes. For predicting the exact point of transition, it is not the topological degree of the whole domain that is relevant, but only that of the turbulent region

Quasi-periodic Pulsations in Solar and Stellar Flares: An Overview of Recent Results (Invited Review)

Quasi-periodic pulsations (or QPPs) are periodic intensity variations in the flare emission that occur across all wavelength bands. In this article, we review the observational and modelling achievements since the previous review on this topic by Nakariakov and Melnikov (Space Sci. Rev.149, 119, 2009). In recent years, it has become clear that QPPs are an inherent feature of solar flares because almost all flares exhibit QPPs. Moreover, it is now firmly established that QPPs often show multiple periods. We also review possible mechanisms for generating QPPs. Up to now, it has not been possible to conclusively identify the triggering mechanism or cause of QPPs. The lack of this identification currently hampers possible seismological inferences of flare plasma parameters. QPPs in stellar flares have been detected for a long time, and the high-quality data of the Kepler mission allows studying the QPP more systematically. However, it has not been conclusively shown whether the timescales of stellar QPPs are different or the same as those in solar flares