Green function for the Grad-Shafranov operator

The Grad-Shafranov equation, often written in cylindrical coordinates, is an elliptic partial differential equation in two dimensions. It describes magnetohydrodynamic equilibria in axisymmetric toroidal plasmas, such as tokamaks, and yields the poloidal magnetic flux function, which is related to the azimuthal component of the vector potential for the magnetic field produced by a circular (toroidal) current density. The Green function for the differential operator can be obtained from the vector potential for the magnetic field of a circular current loop, which is a typical problem in magnetostatics. The purpose of the paper is to collect results scattered in electrodynamics and plasma physics textbooks for the benefit of students in the field, as well as attracting the attention of a wider audience, in the context of electrodynamics and partial differential equations.

A New Thermal-Solar Field Configuration: The Rotatory Fresnel Collector or Sundial

A new type of Fresnel array has been devised and constructed as an answer to the need to reduce the investment costs of solar thermal collectors, without jeopardizing their efficiency in capturing solar radiation at high temperatures. The array of mirror bands is fixed onto a horizontal platform, which rotates around a virtual vertical axis, so that the sun is in the extrapolated vertical plane of symmetry of the array. The receptor central line is also placed in said plane, and it is physically made of at least one tube at each side of the plane. The geometrical relation between the mirrors and the receptor is therefore fixed. The platform rotates with the same speed as that of the sunlight’s azimuthal component. On the contrary, the angle of incidence of the sunlight on the mirrors changes as the sun rises and declines in its daily apparent motion, but this effect does not disturb the radiation concentration kinematics, although it induces a shift along the receptor. This is a new configuration based on the use of simple and cheap flat mirrors to obtain circular cylindrical mirrors. These mirrors are made of originally flat mirrors that are bent by applying an inexpensive and simple bending technique patented by our research group. The radius of curvature of each mirror is tuned to the distance from the mirror to the receiver central line. The integration of different scientific domains (such as structural analysis) and elementary technologies (such as 3D printing) in this innovative solar radiation concentrator and receiver can lead to a large reduction in costs. Nevertheless, the first experimental campaign has shown additional problems in the receiver configuration, which should be addressed in a next stage of research. This paper explains the methodology used and procedures in the development of the first prototype of the Sundial.

Dynamics of the field-aligned currents distribution asymmetry during substorms in the equinox season

We continue to study the physical processes occurring during the August 17, 2001 magnetospheric storm by analyzing the dynamics of the intensity of field-aligned currents (FACs) in Iijima—Potemra Region 1 in the polar ionospheres of two hemispheres, using the modernized magnetogram inversion technique. The results obtained on the dynamics of the FAC asymmetry of two types (dawn–dusk and interhemispheric), as well as the previously obtained regularities in the behavior of Hall currents and polar cap boundaries depending on the large azimuthal component of the interplanetary magnetic field (IMF), observed during the storm, and the seasonal behavior of the conductivity are consistent with the open magnetosphere model and with satellite observations of auroras in two hemispheres. We have shown that the weakening of the asymmetry of two types in the FAC distribution during substorms in the storm under study occurs almost completely in the winter hemisphere and is much weaker in the summer one. We associate this phenomenon with the predominance of the effect of long-term exposure to the azimuthal IMF component in the sunlit polar ionosphere of the summer hemisphere over the substorm symmetrization effect of the night magnetosphere. A symmetrization effect of the polar cap and FACs, created by the solar wind pressure pulse at the end of the storm, is observed. We propose a qualitative explanation of this effect.

Dynamics of field-aligned currents in two hemispheres during a magnetospheric storm from magnetogram inversion technique data

We continue to study the physical processes occurring during the August 17, 2001 magnetospheric storm by analyzing the dynamics of the intensity of field-aligned currents (FACs) in Iijima—Potemra Region 1 in the polar ionospheres of the two hemispheres, using the modernized magnetogram inversion technique. The results obtained on the dynamics of two types of FAC asymmetry (dawn-dusk and interhemispheric), as well as the previously obtained regularities in the behavior of Hall currents and the polar cap boundaries depending on the large azimuthal component of the interplanetary magnetic field (IMF), observed during the storm, and the seasonal behavior of the conductivity are consistent with the open magnetosphere model and with satellite observations of auroras in two hemispheres. We have shown that the weakening of the asymmetry of two types in the FAC distribution during substorms in the storm under study occurs almost completely in the winter hemisphere and is much weaker in the summer one. We associate this phenomenon with the predominance of the effect of long-term exposure to the azimuthal IMF component in the sunlit polar ionosphere of the summer hemisphere over the substorm symmetrization effect of the night magnetosphere. A symmetrization effect of the polar cap and FACs, created by the solar wind pressure pulse at the end of the storm, is observed. We propose a qualitative explanation of this effect.

Dynamics of field-aligned currents in two hemispheres during a magnetospheric storm from magnetogram inversion technique data

We continue to study the physical processes occurring during the August 17, 2001 magnetospheric storm by analyzing the dynamics of the intensity of field-aligned currents (FACs) in Iijima—Potemra Region 1 in the polar ionospheres of the two hemispheres, using the modernized magnetogram inversion technique. The results obtained on the dynamics of two types of FAC asymmetry (dawn-dusk and interhemispheric), as well as the previously obtained regularities in the behavior of Hall currents and the polar cap boundaries depending on the large azimuthal component of the interplanetary magnetic field (IMF), observed during the storm, and the seasonal behavior of the conductivity are consistent with the open magnetosphere model and with satellite observations of auroras in two hemispheres. We have shown that the weakening of the asymmetry of two types in the FAC distribution during substorms in the storm under study occurs almost completely in the winter hemisphere and is much weaker in the summer one. We associate this phenomenon with the predominance of the effect of long-term exposure to the azimuthal IMF component in the sunlit polar ionosphere of the summer hemisphere over the substorm symmetrization effect of the night magnetosphere. A symmetrization effect of the polar cap and FACs, created by the solar wind pressure pulse at the end of the storm, is observed. We propose a qualitative explanation of this effect.

Dynamics of the field-aligned currents distribution asymmetry during substorms in the equinox season

We continue to study the physical processes occurring during the August 17, 2001 magnetospheric storm by analyzing the dynamics of the intensity of field-aligned currents (FACs) in Iijima—Potemra Region 1 in the polar ionospheres of two hemispheres, using the modernized magnetogram inversion technique. The results obtained on the dynamics of the FAC asymmetry of two types (dawn–dusk and interhemispheric), as well as the previously obtained regularities in the behavior of Hall currents and polar cap boundaries depending on the large azimuthal component of the interplanetary magnetic field (IMF), observed during the storm, and the seasonal behavior of the conductivity are consistent with the open magnetosphere model and with satellite observations of auroras in two hemispheres. We have shown that the weakening of the asymmetry of two types in the FAC distribution during substorms in the storm under study occurs almost completely in the winter hemisphere and is much weaker in the summer one. We associate this phenomenon with the predominance of the effect of long-term exposure to the azimuthal IMF component in the sunlit polar ionosphere of the summer hemisphere over the substorm symmetrization effect of the night magnetosphere. A symmetrization effect of the polar cap and FACs, created by the solar wind pressure pulse at the end of the storm, is observed. We propose a qualitative explanation of this effect.

Parameters controlling the substorm onset location

<p>Substorm onset location varies over a range of magnetic local time (MLT) and magnetic latitudes (MLat). It is well known that about 5% of the variation in onset MLT can be explained by variations in interplanetary magnetic field orientation and dipole tilt angle. Both parameters introduce an azimuthal component in the magnetic field in the magnetosphere such that the projection of the onset MLT in the ionosphere is shifted. The MLT of the onset near the magnetopsheric equatorial plane is even less predictable. Recent studies have suggested that gradients in the ionospheric Hall conductance lead to a duskward shift of tail dynamics, which could also influence the location of substorm onset. Our goal is to test these ideas by quantifying the dependence of the spatial variation of the onset location on external and internal conditions. We focus on the correlation between the substorm onset location with conditions prior to the onset, such as the interplanetary magnetic field By component, dipole tilt angle, and estimates of the Hall conductance. Linear regression analysis is used to determine the substorm onset location dependence on the proposed variables.</p>

Axisymmetric dynamo action produced by differential rotation, with anisotropic electrical conductivity and anisotropic magnetic permeability

The effect on dynamo action of an anisotropic electrical conductivity conjugated to an anisotropic magnetic permeability is considered. Not only is the dynamo fully axisymmetric, but it requires only a simple differential rotation, which twice challenges the well-established dynamo theory. Stability analysis is conducted entirely analytically, leading to an explicit expression of the dynamo threshold. The results show a competition between the anisotropy of electrical conductivity and that of magnetic permeability, the dynamo effect becoming impossible if the two anisotropies are identical. For isotropic electrical conductivity, Cowling's neutral point argument does imply the absence of an azimuthal component of current density, but does not prevent the dynamo effect as long as the magnetic permeability is anisotropic.

Transient magnetic field formulation for solid source conductors

The formulation for the azimuthal component of the magnetic vector potential for axisymmetric magnetostatic applications is well known. However for transient magnetic fields with solid source conductors and eddy currents the formulation has to be revised. A variable transformation is introduced to remove the singularity from the numerical scheme. The numerical error cannot accumulate and is put instead to the postprocessing at every time step.

Numerical and Experimental Flame Stabilization Analysis in the New Spinning Combustion Technology Framework

Global warming, climate change and pollution are burning environmental issues. To reduce the carbon footprint of the aviation sector, aeronautical companies have been striving to lower engine emissions via the development of reliable lean combustors. In this context, effort has been devoted to the better understanding of various flame dynamics with emphasis on thermoacoustic instabilities, lean blow-off and extinctions. In line with this effort, Safran Helicopter Engines has recently developed and patented the revolutionary spinning combustion technology (SCT) for its next generation of combustors. This technology has indeed great flexibility when it comes to ignition and blow-off capabilities. To better understand the various physical mechanisms occurring in a SCT combustor, a joint numerical and experimental analysis of the flame stabilization in this spinning combustion technology framework has been devised. On the experimental side, the NTNU atmospheric annular combustor has been modified to introduce a relevant azimuthal component of velocity while operating under premixed fuel conditions, following the SCT concept. Note that to reduce temperature at the backplane of the chamber, film cooling is incorporated to avoid fuel injector damage. On the numerical side, high fidelity Large Eddy Simulations of the test bench have been carried out with the AVBP code developed at CERFACS, providing insights on the flame stabilization in this unique SCT geometry. In particular, it is noted that there is a strong interaction between the cooling film and the highly swirled flames exiting from the fuel injector bend. In that respect, changing the injector or global equivalence ratios while operating the SCT is shown to affect the combustion of this design.