Axisymmetric Solutions in the Geomagnetic Direction Problem

The magnetic field outside the earth is in good approximation a harmonic vector field determined by its values at the earth’s surface. The direction problem seeks to determine harmonic vector fields vanishing at infinity and with the prescribed direction of the field vector at the surface. In general this type of data neither guarantees the existence nor the uniqueness of solutions of the corresponding nonlinear boundary value problem. To determine conditions for existence, to specify the non-uniqueness and to identify cases of uniqueness is of particular interest when modeling the earth’s (or any other celestial body’s) magnetic field from these data. Here we consider the case of axisymmetric harmonic fields $$\mathbf{B}$$ B outside the sphere $$S^2 \subset {{\mathbb {R}}}^3$$ S 2 ⊂ R 3 . We introduce a rotation number $${r\!o}\in {{\mathbb {Z}}}$$ r o ∈ Z along a meridian of $$S^2$$ S 2 for any axisymmetric Hölder continuous direction field $$\mathbf{D}\ne 0$$ D ≠ 0 on $$S^2$$ S 2 and, moreover, the (exact) decay order $$3 \le \delta \in {{\mathbb {Z}}}$$ 3 ≤ δ ∈ Z of any axisymmetric harmonic field $$\mathbf{B}$$ B at infinity. Fixing a meridional plane and in this plane $${r\!o}- \delta +1 \geqq 0$$ r o - δ + 1 ≧ 0 points $$z_n$$ z n (symmetric with respect to the symmetry axis and with $$|z_n| > 1$$ | z n | > 1 , $$n = 1,\ldots ,{r\!o}-\delta +1$$ n = 1 , … , r o - δ + 1 ), we prove the existence of an (up to a positive constant factor) unique harmonic field $$\mathbf{B}$$ B vanishing at $$z_n$$ z n and nowhere else, with decay order $$\delta $$ δ at infinity, and with direction $$\mathbf{D}$$ D at $$S^2$$ S 2 . The proof is based on the global solution of a nonlinear elliptic boundary value problem, which arises from a complex analytic ansatz for the axisymmetric harmonic field in the meridional plane. The coefficients of the elliptic equation are discontinuous and singular at the symmetry axis, and this requires solution techniques that are adapted to this special situation.

Ion distribution functions in magnetotail reconnection: global hybrid-Vlasov simulation results

We present results of noon–midnight meridional plane global hybrid-Vlasov simulations of the magnetotail ion dynamics under a steady southward interplanetary magnetic field using the Vlasiator model. The simulation results show magnetotail reconnection and formation of earthward and tailward fast plasma outflows. The hybrid-Vlasov approach allows us to study ion velocity distribution functions (VDFs) that are self-consistently formed during the magnetotail evolution. We examine the VDFs collected by virtual detectors placed along the equatorial magnetotail within earthward and tailward outflows and around the quasi-steady X line formed in the magnetotail at X≈-14RE. This allows us to follow the evolution of VDFs during earthward and tailward motion of reconnected flux tubes as well as study signatures of unmagnetized ion motion in the weak magnetic field near the X line. The VDFs indicate actions of Fermi-type and betatron acceleration mechanisms, ion acceleration by the reconnection electric field, and Speiser-type motion of ions near the X line. The simulated VDFs are compared and show good agreement with VDFs observed in the magnetotail by the Time History of Events and Macroscale Interactions during Substorms (THEMIS) and Acceleration, Reconnection, Turbulence and Electrodynamics of Moon's Interaction with the Sun (ARTEMIS) spacecraft. We find that the VDFs become more gyrotropic but retain transverse anisotropy and counterstreaming ion beams when being convected earthward. The presented global hybrid-Vlasov simulation results are valuable for understanding physical processes of ion acceleration during magnetotail reconnection, interpretation of in situ observations, and for future mission development by setting requirements on pitch angle and energy resolution of upcoming instruments.

Hybrid-Vlasov modelling of three-dimensional dayside magnetopause reconnection

<p>Dayside magnetic reconnection at the magnetopause, which is a major driver of space weather, is studied for the first time in a three-dimensional (3D) realistic setup using the Vlasiator hybrid-Vlasov kinetic model. A noon–midnight meridional plane simulation is extended in the dawn–dusk direction to cover 7 Earth radii. The southward interplanetary magnetic field causes magnetic reconnection to occur at the subsolar magnetopause. Perturbations arising from kinetic instabilities in the magnetosheath appear to modulate the reconnection. Its characteristics are consistent with multiple, bursty, and patchy magnetopause reconnection. It is shown that the kinetic behavior of the plasma, as simulated by the model, has consequences on the applicability of methods such as the four-field junction to identify and analyse magnetic reconnection in 3D kinetic simulations.</p>

Influence of the CME orientation on the ICME propagation

<p>Beyond certain distance the ICME propagation becomes mostly governed by the interaction of the ICME and the ambient solar wind. Configuration of the interplanetary magnetic field and features of the related ambient solar wind in the ecliptic and meridional plane are different. Therefore, one can expect that the inclination of the CME flux rope axis i.e. tilt, influences the propagation of the ICME itself. In order to study the relation between the tilt parameter and the ICME propagation we investigated isolated Earth-impacting CME-ICME evets in the time period from 2006. to 2014. We determined the CME tilt in the “near-Sun” environment from the 3D reconstruction of the CME, obtained by the Graduated Cylindrical Shell model using coronagraphic images provided by the STEREO and SOHO missions. We determined the tilt of the ICME in the “near-Earth” environment using in-situ data. We constrained our study to CME-ICME events that show no evidence of rotation while propagating, i.e. have a similar tilt in the “near-Sun” and “near-Earth” environment. We present preliminary results of our study and discuss their implications for space-weather forecasting using the drag-based(ensemble) [DB(E)M] model of heliospheric propagation.</p>

Ion distribution functions in magnetotail reconnection: Global hybrid-Vlasov simulation results

We present results of noon–midnight meridional plane global hybrid-Vlasov simulations of the magnetotail ion dynamics under steady southward interplanetary magnetic field using the Vlasiator model. The simulation results show magnetotail reconnection and formation of earthward and tailward fast plasma outflows. The hybrid-Vlasov approach allows us to study ion velocity distribution functions (VDFs) that are self-consistently formed during the magnetotail evolution. We examine the VDFs collected by virtual detectors placed along the equatorial magnetotail within earthward and tailward outflows and around the quasi-steady X-line formed in the magnetotail at X ≈ −14 RE. This allows us to follow the evolution of VDFs during earthward and tailward motion of reconnected flux tubes as well as study signatures of unmagnetized ion motion in the weak magnetic field near the X-line. The VDFs indicate actions of Fermi-type and betatron acceleration mechanisms, ion acceleration by the reconnection electric field, and Speiser-type motion of ions near the X-line. The simulated VDFs are compared and show good agreement with VDFs observed in the magnetotail by the Time History of Events and Macroscale Interactions during Substorms (THEMIS) and Acceleration, Reconnection, Turbulence and Electrodynamics of Moon's Interaction with the Sun (ARTEMIS) spacecraft. We find that the VDFs become more gyrotropic but retain transverse anisotropy and counter-streaming ion beams when being convected earthward. The presented global hybrid-Vlasov simulation results are valuable for understanding physical processes of ion acceleration during magnetotail reconnection, interpretation of in-situ observations, and for future mission development by setting requirements on pitch-angle and energy resolution of upcoming instruments.

Design simulations of a horizontally deflecting high-heat-load monochromator

The performance of a liquid-nitrogen-cooled high-heat-load monochromator with a horizontal scattering plane has been analysed, aiming to preserve the high quality of the X-ray beam in the vertical plane for downstream optics. Using finite-element analysis, height profiles of the crystal surface for various heat loads and the corresponding slope errors in the meridional and sagittal planes were calculated. Then the angular distortions of the reflected beam in both meridional and sagittal planes were calculated analytically and also modelled by ray tracing, revealing a good agreement of the two approaches. The results show that with increasing heat load in the crystal the slope errors of the crystal surface reach their smallest values first in the sagittal and then in the meridional plane. For the considered case of interest at a photon energy of 14.412 keV and the Si(111) reflection with a Bragg angle of 7.88°, the angular distortions of the reflected beam in the sagittal plane are an order of magnitude smaller than in the meridional one. Furthermore, they are smaller than the typical angular size of the beam source at the monochromator position. For a high-heat-load monochromator operating in the horizontal scattering plane, the sagittal angular distortions of the reflected beam appear in the vertical plane. Thus, such an instrument perfectly preserves the high quality of the X-ray beam in the vertical plane for downstream optics. Compared with vertical scattering, the throughput of the monochromatic beam with the horizontal scattering plane is reduced by only 3.3% for the new EBS source, instead of 34.3% for the old ESRF-1 machine. This identifies the horizontal-scattering high-heat-load monochromator as a device essentially free of the heat-load effects in the vertical plane and without significant loss in terms of throughput.