Adaptive Mesh Refinement for Electromagnetic Simulation

We consider problems related to initial meshing and adaptive mesh refinement for the electromagnetic simulation of various structures. The quality of the initial mesh and the performance of the adaptive refinement are of great importance for the finite element solution of the Maxwell equations, since they directly affect the accuracy and the computational time. In this paper, we describe the complete meshing workflow, which allows the simulation of arbitrary structures. Test simulations confirm that the presented approach allows to reach the quality of the industrial simulation software

Wave-induced loss of ultra-relativistic electrons in the Van Allen radiation belts.

The dipole configuration of the Earth's magnetic field allows for the trapping of highly energetic particles, which form the radiation belts. Although significant advances have been made in understanding the acceleration mechanisms in the radiation belts, the loss processes remain poorly understood. Unique observations on 17 January 2013 provide detailed information throughout the belts on the energy spectrum and pitch angle (angle between the velocity of a particle and the magnetic field) distribution of electrons up to ultra-relativistic energies. Here we show that although relativistic electrons are enhanced, ultra-relativistic electrons become depleted and distributions of particles show very clear telltale signatures of electromagnetic ion cyclotron wave-induced loss. Comparisons between observations and modelling of the evolution of the electron flux and pitch angle show that electromagnetic ion cyclotron waves provide the dominant loss mechanism at ultra-relativistic energies and produce a profound dropout of the ultra-relativistic radiation belt fluxes

An Empirical Model of the Equatorial Electron Pitch Angle Distributions in Earth's Outer Radiation Belt

In this study, we present an empirical model of the equatorial electron pitch angle distributions (PADs) in the outer radiation belt based on the full data set collected by the Magnetic Electron Ion Spectrometer (MagEIS) instrument onboard the Van Allen Probes in 2012–2019. The PADs are fitted with a combination of the first, third and fifth sine harmonics. The resulting equation resolves all PAD types found in the outer radiation belt (pancake, flat‐top, butterfly and cap PADs) and can be analytically integrated to derive omnidirectional flux. We introduce a two‐step modeling procedure that for the first time ensures a continuous dependence on L, magnetic local time and activity, parametrized by the solar wind dynamic pressure. We propose two methods to reconstruct equatorial electron flux using the model. The first approach requires two uni‐directional flux observations and is applicable to low‐PA data. The second method can be used to reconstruct the full equatorial PADs from a single uni‐ or omnidirectional measurement at off‐equatorial latitudes. The model can be used for converting the long‐term data sets of electron fluxes to phase space density in terms of adiabatic invariants, for physics‐based modeling in the form of boundary conditions, and for data assimilation purposes.Plain Language Summary: Pitch angle distributions (PADs) are critically important for understanding the dynamics of trapped electrons in Earth's radiation belt region. Specific PAD types are linked to processes acting within the radiation belts which relate to the origins and loss mechanisms of the particle populations, as well as wave activity. In this study we present a polynomial model of the equatorial electron PADs at energies 30 keV–1.6 MeV with a continuous dependence on L‐shell, magnetic local time and activity driven by the solar wind dynamic pressure. The model can be used to reconstruct equatorial electron flux from observations at high latitudes and can be applied for converting the long‐term electron flux data sets to phase space density, driving the boundary conditions for the physics‐based simulations and for data assimilation.Key Points: A sum of the first, third, and fifth sine harmonics is used to approximate equatorial electron Pitch angle distributions (PADs) measured by the MagEIS detector onboard the Van Allen Probes. We present a PAD model with a continuous dependence on L, magnetic local time and activity, driven by the solar wind dynamic pressure. The model allows reconstructions of equatorial PADs from uni‐ and omni‐directional measurements at off‐equatorial latitudes.Deutsche Forschungsgemeinschaft http://dx.doi.org/10.13039/501100001659Alexander von Humboldt‐Stiftung http://dx.doi.org/10.13039/100005156https://doi.org/10.5880/GFZ.2.7.2022.00

The Effect of Plasma Boundaries on the Dynamic Evolution of Relativistic Radiation Belt Electrons

Understanding the dynamic evolution of relativistic electrons in the Earth's radiation belts during both storm and nonstorm times is a challenging task. The U.S. National Science Foundation's Geospace Environment Modeling (GEM) focus group “Quantitative Assessment of Radiation Belt Modeling” has selected two storm time and two nonstorm time events that occurred during the second year of the Van Allen Probes mission for in-depth study. Here, we perform simulations for these GEM challenge events using the 3D Versatile Electron Radiation Belt code. We set up the outer L* boundary using data from the Geostationary Operational Environmental Satellites and validate the simulation results against satellite observations from both the Geostationary Operational Environmental Satellites and Van Allen Probe missions for 0.9-MeV electrons. Our results show that the position of the plasmapause plays a significant role in the dynamic evolution of relativistic electrons. The magnetopause shadowing effect is included by using last closed drift shell, and it is shown to significantly contribute to the dropouts of relativistic electrons at high L*. We perform simulations using four different empirical radial diffusion coefficient models for the GEM challenge events, and the results show that these simulations reproduce the general dynamic evolution of relativistic radiation belt electrons. However, in the events shown here, simulations using the radial diffusion coefficients from Brautigam and Albert (2000) produce the best agreement with satellite observations

Spectra of Saturn's proton belts revealed

International audienceSaturn is permanently surrounded by 6 discrete proton radiation belts that are rigidly separated by the orbits of its inner moons and dense rings. These radiation belts are ideal environments to study the details of radial diffusion and the CRAND source process, yet progress has been hindered by the fact that the energy spectra are not known with certainty: Reanalysis of the response functions of the LEMMS instrument on-board the Cassini orbiter has shown that measurements of ≲ 10 MeV protons may be easily contaminated by ≳ 10 MeV protons and that many available measurements characterize a very broad energy range, so that the calculation of an energy-resolved spectrum is not as straightforward as previously assumed. Here we use forward modeling of the measurements based on the instrument response and combine this technique where useful with numerical modeling of the proton belt physics in order to determine Saturn's spectra with higher certainty. We find significant proton intensities up to ≈ 1 GeV. While earlier studies reported on proton spectra roughly following a power law with exponent ≈ - 2 , our more advanced analysis shows harder spectra with exponent ≈ - 1 . The observed spectra provide independent confirmation that Saturn's proton belts are sourced by CRAND and are consistent with the provided protons being subsequently cooled in the tenuous gas originating from Saturn or Enceladus. The intensities at Saturn are found to be lower than at Jupiter and Earth, which is also consistent with the source of Saturn being exclusively CRAND, while the other planets can draw from additional processes. Our new spectra can be used in the future to further our understanding of Saturn's proton belts and the respective physical processes that occur at other magnetized planets in general. Also, the spectra have applications for several topics of planetary science, such as space weathering of Saturn's moons and rings, and can be useful to constrain properties of the main rings through their production of secondary particles

Wave-induced loss of ultra-relativistic electrons in the Van Allen radiation belts.

The dipole configuration of the Earth's magnetic field allows for the trapping of highly energetic particles, which form the radiation belts. Although significant advances have been made in understanding the acceleration mechanisms in the radiation belts, the loss processes remain poorly understood. Unique observations on 17 January 2013 provide detailed information throughout the belts on the energy spectrum and pitch angle (angle between the velocity of a particle and the magnetic field) distribution of electrons up to ultra-relativistic energies. Here we show that although relativistic electrons are enhanced, ultra-relativistic electrons become depleted and distributions of particles show very clear telltale signatures of electromagnetic ion cyclotron wave-induced loss. Comparisons between observations and modelling of the evolution of the electron flux and pitch angle show that electromagnetic ion cyclotron waves provide the dominant loss mechanism at ultra-relativistic energies and produce a profound dropout of the ultra-relativistic radiation belt fluxes

Preliminary Statistical Comparisons of Spin‐Averaged Electron Data From Arase and Van Allen Probes Instruments

Following the end of the Van Allen Probes mission, the Arase satellite offers a unique opportunity to continue in‐situ radiation belt and ring current particle measurements into the next solar cycle. In this study we compare spin‐averaged flux measurements from the MEPe, HEP‐L, HEP‐H, and XEP‐SSD instruments on Arase with those from the MagEIS and REPT instruments on the Van Allen Probes, calculating Pearson correlation coefficient and the mean ratio of fluxes at L* conjunctions between the spacecraft. Arase and Van Allen Probes measurements show a close agreement over a wide range of energies, observing a similar general evolution of electron flux, as well as average, peak, and minimum values. Measurements from the two missions agree especially well in the 3.6 = L* ≤ 4.4 range where Arase samples similar magnetic latitudes to Van Allen Probes. Arase tends to record higher flux for energies 1.4 MeV, Arase flux measurements are generally lower than those of Van Allen Probes, especially for L* > 4.4. The correlation coefficient values show that the >1.4 MeV flux from both missions are well correlated, indicating a similar general evolution, although flux magnitudes differ. We perform a preliminary intercalibration between the two missions using the mean ratio of the fluxes as an energy‐ and L*‐ dependent intercalibration factor. The intercalibration factor improves agreement between the fluxes in the 0.58–1 MeV range.Key Points: MEPe, HEPH, HEPL, XEPSSD, and MAGEIS/REPT show a good correlation at energies above 300 keV and 3 < L* < 4.6. Flux measurements at the same energy from the two missions are highly comparable in magnitude. Intercalibration via energy‐ and L*‐dependent factors improves the agreement between Arase and RBSP.Camargo Foundation http://dx.doi.org/10.13039/501100001666EC, Horizon 2020 Framework Programme (H2020) http://dx.doi.org/10.13039/100010661Deutsche Forschungsgemeinschaft (DFG) http://dx.doi.org/10.13039/50110000165