Applications of topology in magnetic fields

This thesis concerns applications of topology in magnetic fields. First, we examine the influence of writhe in the stretch-twist-fold dynamo. We consider a thin flux tube distorted by simple stretch, twist, and fold motions and calculate the helicity and energy spectra. The writhe number assists in the calculations, as it tells us how much the internal twist changes as the tube is distorted. In addition it provides a valuable diagnostic for the degree of distortion. Non mirror-symmetric dynamos typically generate magnetic helicity of one sign on large-scales and of the opposite sign on small-scales. The calculations presented here confirm the hypothesis that the large-scale helicity corresponds to writhe and the small-scale corresponds to twist. In addition, the writhe helicity spectrum exhibits an interesting oscillatory behaviour. Second, we examine the effect of reconnection on the structure of a braided magnetic field. A prominent model for both heating of the solar corona and the source of small flares involves reconnection of braided magnetic flux elements. Much of this braiding is thought to occur at as yet unresolved scales, for example braiding of threads within an EUV or X-ray loop. However, some braiding may be still visible at scales accessible to Trace or the EIS imager on Hinode. We suggest that attempts to estimate the amount of braiding at these scales must take into account the degree of coherence of the braid structure. We demonstrate that simple models of braided magnetic fields which balance input of topological structure with reconnection evolve to a self-organized critical state. An initially random braid can become highly ordered, with coherence lengths obeying power law distributions. The energy released during reconnection also obeys a power law

Learning by Arguing About Evidence and Explanations

Collaborative learning with cases characteristically involves discussing and developing shared explanations. We investigated the argumentation scheme which learners use in constructing shared explanations over evidence. We observed medical students attempting to explain how a judge had arrived at his verdict in a case of medical negligence. The students were learning within a virtual learning environment and their communication was computer mediated. We identify the dialogue type that these learners construct and show that their argumentation conforms with an abductive form of argumentation scheme ('inference to the best explanation'). We also assessed the students' learning and propose that it is related to particular features of this argumentation scheme

Effects of Density Fluctuations on Alfvén Wave Turbulence in a Coronal Hole

We present a study of density fluctuations in coronal holes. We used a reduced magnetohydrodynamic (RMHD) model that incorporated observationally constrained density fluctuations to determine whether density fluctuations in coronal holes can enhance Alfvén wave reflection and dissipation, thereby heating coronal holes and driving the fast solar wind. We show results for two models of the background atmosphere. Each model is a solution of the momentum equation and includes the effects of wave pressure on the solar wind outflow. In the first model, the plasma density and Alfvén speed vary smoothly with height. Wave reflection is relatively weak in the smooth model, resulting in a low energy dissipation rate. In the second model, we include additional density fluctuations along the flux tube based on the observations. We find that density ρ fluctuations on the order of δρ/ρ ∼ 0.24 increase the Alfvén wave turbulence to levels sufficient to heat the open field regions in coronal holes

Self-organized braiding in solar coronal loops

In this paper, we investigate the evolution of braided solar coronal loops. We assume that coronal loops consist of several internal strands which twist and braid about each other. Reconnection between the strands leads to small flares and heating of the loop to X-ray temperatures. Using a method of generating and releasing braid structure similar to a forest fire model, we show that the reconnected field lines evolve to a self-organised critical state. In this state, the frequency distributions of coherent braid sequences as well as flare energies follow power law distributions. We demonstrate how the presence of net helicity in the loop alters the distribution laws.Leverhulme TrustAI

On the Relationship Between Photospheric Footpoint Motions and Coronal Heating in Solar Active Regions

PublishedArticleCoronal heating theories can be classified as either direct current (DC) or alternating current (AC) mechanisms, depending on whether the coronal magnetic field responds quasi-statically or dynamically to the photospheric footpoint motions. In this paper we investigate whether photospheric footpoint motions with velocities of 1-2 km s–1 can heat the corona in active regions, and whether the corona responds quasi-statically or dynamically to such motions (DC versus AC heating). We construct three-dimensional magnetohydrodynamic models for the Alfvén waves and quasi-static perturbations generated within a coronal loop. We find that in models where the effects of the lower atmosphere are neglected, the corona responds quasi-statically to the footpoint motions (DC heating), but the energy flux into the corona is too low compared to observational requirements. In more realistic models that include the lower atmosphere, the corona responds more dynamically to the footpoint motions (AC heating) and the predicted heating rates due to Alfvén wave turbulence are sufficient to explain the observed hot loops. The higher heating rates are due to the amplification of Alfvén waves in the lower atmosphere. We conclude that magnetic braiding is a highly dynamic process

The heating of solar coronal loops by Alfvèn wave turbulence

This project was supported under contract NNM07AB07C from NASA to the Smithsonian Astrophysical Observatory (SAO) and contract SP02H1701R from Lockheed Martin Space and Astrophysics Laboratory (LMSAL) to SAO.In this paper we further develop a model for the heating of coronal loops by Alfvèn wave turbulence (AWT). The Alfvèn waves are assumed to be launched from a collection of kilogauss flux tubes in the photosphere at the two ends of the loop. Using a three-dimensional magneto-hydrodynamic (MHD) model for an active-region loop, we investigate how the waves from neighboring flux tubes interact in the chromosphere and corona. For a particular combination of model parameters we find that AWT can produce enough heat to maintain a peak temperature of about 2.5 MK, somewhat lower than the temperatures of 3 – 4 MK observed in the cores of active regions. The heating rates vary strongly in space and time, but the simulated heating events have durations less than 1 minute and are unlikely to reproduce the observed broad Differential Emission Measure distributions of active regions. The simulated spectral line non-thermal widths are predicted to be about 27 km s−1, which is high compared to the observed values. Therefore, the present AWT model does not satisfy the observational constraints. An alternative “magnetic braiding” model is considered in which the coronal field lines are subject to slow random footpoint motions, but we find that such long period motions produce much less heating than the shorter period waves launched within the flux tubes. We discuss several possibilities for resolving the problem of producing sufficiently hot loops in active regions.PostprintPeer reviewe

Argumentation scheme and shared online diagramming in case-based collaborative learning

Argumentation schemes describe patterns of reasoning in discourse. We report an investigation into whether the argumentation scheme known as 'inference to the best explanation' (IBE) captures the argumentation found in collaborative case-based learning. We examine the dialogue of three students working in an online learning environment as they attempt to explain the verdict in a legal case of medical negligence; the IDE scheme is clearly visible in the dialogue. We also report the exploratory development of shared argument diagramming tools that allow learners to draw their explanations while they discuss them. The tools passively reinforce the IBE argumentation scheme. Evaluation of the tools provided the clearest evidence to date that learners are able to integrate their shared online argument diagramming with their computer-mediated dialogue

Physical Characteristics of Unstructured Coronal Clouds

Active regions in the inner solar corona, when observed in X-ray emission, consist of bright, hot loops surrounded by unstructured clouds. The emission from the clouds extends to a height of ≈4–5 × 104 km at temperatures of ≈2–3 MK. These “hot clouds” are variable, but persist for many days and do not appear to connect directly to the active region streamers or other large-scale structures observed higher in the corona. We present an observational analysis of these diffuse structures to establish basic plasma parameters such as magnetic field strength, particle density, and temperature. The values of β, the ratio of the plasma pressure to the magnetic field pressure, were found to be generally less than unity, though often approaching unity in the upper portions of the active region, where the hot clouds are located. The magnetic field may therefore only partially confine these regions and inhibit flare-like instabilities that could otherwise be driven by gradients of plasma pressure and current density