100,641 research outputs found
Three-dimensional solutions of the magnetohydrostatic equations : rigidly rotating magnetized coronae in spherical geometry
No full textContext. Magnetohydrostatic (MHS) equilibria are often used to model astrophysical plasmas, for example, planetary magnetospheres or coronae of magnetized stars. However, finding realistic three-dimensional solutions to the MHS equations is difficult, with only a few known analytical solutions and even finding numerical solution is far from easy. Aims. We extend the results of a previous paper on three-dimensional solutions of the MHS equations around rigidly rotating massive cylinders to the much more realistic case of rigidly rotating massive spheres. An obvious application is to model the closed field line regions of the coronae of rapidly rotating stars. Methods. We used a number of simplifying assumptions to reduce the MHS equations to a single elliptic partial differential equation for a pseudo-potential U, from which all physical quantities, such as the magnetic field, the plasma pressure, and the density, can be derived by differentiation. The most important assumptions made are stationarity in the co-rotating frame of reference, a particular form for the current density, and neglect of outflows. Results. In this paper we demonstrate that standard methods can be used to find numerical solutions to the fundamental equation of the theory. We present three simple different cases of magnetic field boundary conditions on the surface of the central sphere, corresponding to an aligned dipole field, a non-aligned dipole field, and a displaced dipole field. Our results show that it should be possible in the future to use this method without dramatically increasing the demands on computational resources to improve upon potential field models of rotating magnetospheres and coronae.Peer reviewe
On the theory of translationally invariant magnetohydrodynamic equilibria with anisotropic pressure and magnetic shear
No full textFunding: STFC Doctoral Training Grant ST/K502327/1 (Jonathan Hodgson) and STFC Consolidated Grant ST/K000950/1 (Thomas Neukirch)We present an improved formalism for translationally invariant magnetohydrodynamic equilibria with anisotropic pressure and currents with a field aligned component. The derivation of a Grad-Shafranov type equation is given along with a constraint which links the shear field to the parallel pressure. The difficulties of the formalism are discussed and various methods of circumventing these difficulties are given. A simple example is then used to highlight the methods and difficulties involved.Peer reviewe
Aspects of three-dimensional MHD : magnetic reconnection and rotating coronae
No full textSolutions of the magnetohydrodynamic (MHD) equations are very important for modelling laboratory, space and astrophysical plasmas, for example the solar and stellar coronae, as well as for modelling many of the dynamic processes that occur in these different plasma environments such as the fundamental process of magnetic reconnection. Our previous understanding of the behavior of plasmas and their associated dynamic processes has been developed through two-dimensional (2D) models. However, a more realistic model should be three-dimensional (3D), but finding 3D solutions of the MHD equations is, in general, a formidable task. Only very few analytical solutions are known and even calculating solutions with numerical methods is usually far from easy.
In this thesis, 3D solutions which model magnetic reconnection and rigidly rotating magnetized coronae are presented. For magnetic reconnection, a 3D stationary MHD model is used. However, the complexity of the problem meant that so far no generic analytic solutions for reconnection in 3D exist and most work consists of numerical simulations. This has so far hampered progress in our understanding of magnetic reconnection. The model used here allows for analytic solutions at least up to a certain order of approximation and therefore gives some better insight in the significant differences between 2D and 3D reconnection. Three-dimensional numerical solutions are also obtained for this model.
Rigidly rotating magnetized coronae, on the other hand, are modeled using a set of magnetohydrostatic (MHS) equations. A general theoretical framework for calculating 3D MHS solutions outside massive rigidly rotating central bodies is presented. Under certain assumptions, the MHS equations are reduced to a single linear partial differential equation referred to as the fundamental equation of the theory. As a first step, an illustrative case of a massive rigidly rotating magnetized cylinder is considered, which somehow allows for analytic solutions in a certain domain of validity. In general, the fundamental equation of the theory can only be solved numerically and hence numerical example solutions are presented. The theory is then extended to include a more realistic case of massive rigidly rotating spherical bodies. The resulting fundamental equation of the theory in this case is too complicated to allow for analytic solutions and hence only numerical solutions are obtained using similar numerical methods to the ones used in the cylindrical case
Equilibrium and stability properties of collisionless current sheet models
No full textThe work in this thesis focuses primarily on equilibrium and stability properties of collisionless current sheet models, in particular of the force-free Harris sheet model.
A detailed investigation is carried out into the properties of the distribution function found by Harrison and Neukirch (Physical Review Letters 102, 135003, 2009) for the force-free Harris sheet, which is so far the only known nonlinear force-free Vlasov-Maxwell equilibrium. Exact conditions on the parameters of the distribution function are found, which show when it can be single or multi-peaked in two of the velocity space directions. This is important because it may have implications for the stability of the equilibrium.
One major aim of this thesis is to find new force-free equilibrium distribution functions. By using a new method which is different from that of Harrison and Neukirch, it is possible to find a complete family of distribution functions for the force-free Harris sheet, which includes the Harrison and Neukirch distribution function (Physical Review Letters 102, 135003, 2009). Each member of this family has a different dependence on the particle energy, although the dependence on the canonical momenta remains the same. Three detailed analytical examples are presented. Other possibilities for finding further collisionless force-free equilibrium distribution functions have been explored, but were unsuccessful.
The first linear stability analysis of the Harrison and Neukirch equilibrium distribution function is then carried out, concentrating on macroscopic instabilities, and considering two-dimensional perturbations only. The analysis is based on the technique of integration over unperturbed orbits. Similarly to the Harris sheet case (Nuovo Cimento, 23:115, 1962), this is only possible by using approximations to the exact orbits, which are unknown. Furthermore, the approximations for the Harris sheet case cannot be used for the force-free Harris sheet, and so new techniques have to be developed in order to make analytical progress. Full analytical expressions for the perturbed current density are derived but, for the sake of simplicity, only the long wavelength limit is investigated. The dependence of the stability on various equilibrium parameters is investigated
Progettazione e sintesi di una libreria di architetture supramolecolari basata sul legame ad alogeno
No full textSintesi e proprietà di riconoscimento di recettori eteroditopici basati sul legame ad alogeno
No full textParticle energisation in a collapsing magnetic trap model : the relativistic regime
No full textThe authors acknowledge financial support by the UK’s Science and Technology Facilities Council through a Doctoral Training Grant (SEO) and Consolidated Grant ST/K000950/1 (SEO and TN).Context. In solar flares, a large number of charged particles is accelerated to high energies. By which physical processes this is achieved is one of the main open problems in solar physics. It has been suggested that during a flare, regions of the rapidly relaxing magnetic field can form a collapsing magnetic trap (CMT) and that this trap may contribute to particle energisation. Aims. In this Research Note we focus on a particular analytical CMT model based on kinematic magnetohydrodynamics. Previous investigations of particle acceleration for this CMT model focused on the non-relativistic energy regime. It is the specific aim of this Research Note to extend the previous work to relativistic particle energies. Methods. Particle orbits were calculated numerically using the relativistic guiding centre equations. We also calculated particle orbits using the non-relativistic guiding centre equations for comparison. Results. For mildly relativistic energies the relativistic and non-relativistic particle orbits mainly agree well, but clear deviations are seen for higher energies. In particular, the final particle energies obtained from the relativistic calculations are systematically lower than the energies reached from the corresponding non-relativistic calculations, and the mirror points of the relativistic orbits are systematically higher than for the corresponding non-relativistic orbits. Conclusions. While the overall behaviour of particle orbits in CMTs does not differ qualitatively when using the relativistic guiding centre equations, there are a few systematic quantitative differences between relativistic and non-relativistic particle dynamics.Peer reviewe
A halogen-bonding-based heteroditopic receptor for alkali metal halides
No full textA new heteroditopic receptor for alkali metal halides has been designed and synthesized. It is comprised of a well-established motif for cation binding and a motif for halogen-bonding-based anion recognition processes. The single-crystal X-ray structure of the complex between the heteroditopic receptor and sodium iodide is reported. Thanks to the cooperativity of metal coordination and the strong I-···I halogen bonding, the ion pair is fully separated. The boosting effect of the binding of the anion through halogen bonding on the coordination of the cation by the receptor has been proved also in solution by NMR experiments. The selectivity of the new heterotopic receptor toward different alkali metal halides has been tested by ESI mass experiments
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