Physics of Earth’s Radiation Belts

This open access book serves as textbook on the physics of the radiation belts surrounding the Earth. Discovered in 1958 the famous Van Allen Radiation belts were among the first scientific discoveries of the Space Age. Throughout the following decades the belts have been under intensive investigation motivated by the risks of radiation hazards they expose to electronics and humans on spacecraft in the Earth’s inner magnetosphere. This textbook teaches the field from basic theory of particles and plasmas to observations which culminated in the highly successful Van Allen Probes Mission of NASA in 2012-2019. Using numerous data examples the authors explain the relevant concepts and theoretical background of the extremely complex radiation belt region, with the emphasis on giving a comprehensive and coherent understanding of physical processes affecting the dynamics of the belts. The target audience are doctoral students and young researchers who wish to learn about the physical processes underlying the acceleration, transport and loss of the radiation belt particles in the perspective of the state-of-the-art observations

Magnetic cloud prediction model for forecasting space weather relevant properties of Earth-directed coronal mass ejections

Context. Coronal mass ejections (CMEs) are major eruptive events on the Sun that result in the ejection of large-scale magnetic clouds (MCs) in interplanetary space, consisting of plasma with enhanced magnetic fields whose direction changes coherently when measured in situ. The severity of CME-induced geomagnetic perturbations and space weather impacts depends on the direction and strength of the interplanetary magnetic field (IMF), as well as on the speed and duration of the passage of the magnetic cloud associated with the storm. The coupling between the heliospheric environment and Earth's magnetosphere is strongest when the IMF direction is persistently southward (i.e. negative B-z) for a prolonged period. Predicting the magnetic profile of such Earth-directed CMEs is therefore critical for estimating their space weather consequences; this remains an outstanding challenge, however. Aims. Our aim is to build upon and integrate diverse techniques towards the development of a comprehensive magnetic cloud prediction (MCP) model that can forecast the magnetic field vectors, Earth-impact time, speed, and duration of passage of solar storms. Methods. The configuration of a CME is approximated as a radially expanding force-free cylindrical structure. Combining near-Sun geometrical, magnetic, and kinematic properties of CMEs with the probabilistic drag-based model and cylindrical force-free model, we propose a method for predicting the Earth-arrival time, propagation speed, and magnetic vectors of MCs during their passage through 1 AU. Our model is able to predict the passage duration of the storm without recourse to computationally intensive time-dependent dynamical equations. Results. Our method is validated by comparing the MCP model output with observations of ten MCs at 1 AU. In our sample, we find that eight MCs show a root mean square (rms) deviation smaller than 0.1 between the predicted and observed magnetic profiles, and the passage durations of seven MCs fall within the predicted range. Conclusions. Based on the success of this approach, we conclude that predicting the near-Earth properties of MCs based on an analysis and modelling of near-Sun CME observations is a viable endeavour with potential applications for the development of early-warning systems for space weather and enabling mitigation strategies.Peer reviewe

On the Radial and Longitudinal Variation of a Magnetic Cloud : ACE, Wind, ARTEMIS and Juno Observations

We present observations of the same magnetic cloud made near Earth by the Advance Composition Explorer (ACE), Wind, and the Acceleration, Reconnection, Turbulence and Electrodynamics of the Moon's Interaction with the Sun (ARTEMIS) mission comprising the Time History of Events and Macroscale Interactions during Substorms (THEMIS) B and THEMIS C spacecraft, and later by Juno at a distance of 1.2 AU. The spacecraft were close to radial alignment throughout the event, with a longitudinal separation of 3.6 degrees between Juno and the spacecraft near Earth. The magnetic cloud likely originated from a filament eruption on 22 October 2011 at 00:05 UT, and caused a strong geomagnetic storm at Earth commencing on 24 October. Observations of the magnetic cloud at each spacecraft have been analysed using minimum variance analysis and two flux rope fitting models, Lundquist and Gold-Hoyle, to give the orientation of the flux rope axis. We explore the effect different trailing edge boundaries have on the results of each analysis method, and find a clear difference between the orientations of the flux rope axis at the near-Earth spacecraft and Juno, independent of the analysis method. The axial magnetic field strength and the radial width of the flux rope are calculated using both observations and fitting parameters and their relationship with heliocentric distance is investigated. Differences in results between the near-Earth spacecraft and Juno are attributed not only to the radial separation, but to the small longitudinal separation which resulted in a surprisingly large difference in the in situ observations between the spacecraft. This case study demonstrates the utility of Juno cruise data as a new opportunity to study magnetic clouds beyond 1 AU, and the need for caution in future radial alignment studies.Peer reviewe

On the Radial and Longitudinal Variation of a Magnetic Cloud: ACE, Wind, ARTEMIS and Juno Observations, Solar Physics

We present observations of the same magnetic cloud made near Earth by the Advance Composition Explorer (ACE), Wind, and the Acceleration, Reconnection, Turbulence and Electrodynamics of the Moon’s Interaction with the Sun (ARTEMIS) mission comprising the Time History of Events and Macroscale Interactions during Substorms (THEMIS) B and THEMIS C spacecraft, and later by Juno at a distance of 1.2 AU. The spacecraft were close to radial alignment throughout the event, with a longitudinal separation of 3.6∘ between Juno and the spacecraft near Earth. The magnetic cloud likely originated from a filament eruption on 22 October 2011 at 00:05 UT, and caused a strong geomagnetic storm at Earth commencing on 24 October. Observations of the magnetic cloud at each spacecraft have been analysed using minimum variance analysis and two flux rope fitting models, Lundquist and Gold–Hoyle, to give the orientation of the flux rope axis. We explore the effect different trailing edge boundaries have on the results of each analysis method, and find a clear difference between the orientations of the flux rope axis at the near-Earth spacecraft and Juno, independent of the analysis method. The axial magnetic field strength and the radial width of the flux rope are calculated using both observations and fitting parameters and their relationship with heliocentric distance is investigated. Differences in results between the near-Earth spacecraft and Juno are attributed not only to the radial separation, but to the small longitudinal separation which resulted in a surprisingly large difference in the in situ observations between the spacecraft. This case study demonstrates the utility of Juno cruise data as a new opportunity to study magnetic clouds beyond 1 AU, and the need for caution in future radial alignment studies

Estimating the Magnetic Structure of an Erupting CME Flux Rope From AR12158 Using Data-Driven Modeling

We investigate here the magnetic properties of a large-scale magnetic flux rope related to a coronal mass ejection (CME) that erupted from the Sun on September 12, 2014 and produced a well-defined flux rope in interplanetary space on September 14-15, 2014. We apply a fully data-driven and time-dependent magnetofrictional method (TMFM) using Solar Dynamics Observatory (SDO) magnetograms as the lower boundary condition. The simulation self-consistently produces a coherent flux rope and its ejection from the simulation domain. This paper describes the identification of the flux rope from the simulation data and defining its key parameters (e.g., twist and magnetic flux). We define the axial magnetic flux of the flux rope and the magnetic field time series from at the apex and at different distances from the apex of the flux rope. Our analysis shows that TMFM yields axial magnetic flux values that are in agreement with several observational proxies. The extracted magnetic field time series do not match well with in-situ components in direct comparison presumably due to interplanetary evolution and northward propagation of the CME. The study emphasizes also that magnetic field time-series are strongly dependent on how the flux rope is intercepted which presents a challenge for space weather forecasting.Peer reviewe

Spatial coherence of interplanetary coronal mass ejection sheaths at 1 AU

The longitudinal spatial coherence near 1 AU of the magnetic field in sheath regions driven by interplanetary coronal mass ejection (ICME) is studied by investigating ACE and Wind spacecraft measurements of 29 sheaths. During 2000-2002 Wind performed prograde orbits, and the non-radial spacecraft separation varied from 0.001 to 0.012 AU between the studied events. We compare the measurements by computing the Pearson correlation coefficients for the magnetic field magnitude and components and estimate the magnetic field coherence by evaluating the scale lengths that give the extrapolated distance of zero correlation between the measurements. The correlation is also separately examined for low- and high-pass filtered data. We discover magnetic fields in ICME sheaths have scale lengths that are larger than those reported in the solar wind but that, in general, are smaller than the ones of the ICME ejecta. Our results imply that magnetic fields in the sheath are more coherently structured and well correlated compared to the solar wind. The largest sheath coherence is reported in the GSE y-direction that has the scale length of 0.149 AU while the lengths for B-x, B-z, and vertical bar B vertical bar vary between 0.024 and 0.035 AU. The same sheath magnitude ordering of scale lengths also apply for the low-pass filtered magnetic field data. We discuss field line draping and the alignment of preexisting discontinuities by the shock passage giving reasoning for the observed results.Peer reviewe

Planar magnetic structures in coronal mass ejection-driven sheath regions

Planar magnetic structures (PMSs) are periods in the solar wind during which interplanetary magnetic field vectors are nearly parallel to a single plane. One of the specific regions where PMSs have been reported are coronal mass ejection (CME)-driven sheaths. We use here an automated method to identify PMSs in 95 CME sheath regions observed in situ by the Wind and ACE spacecraft between 1997 and 2015. The occurrence and location of the PMSs are related to various shock, sheath, and CME properties. We find that PMSs are ubiquitous in CME sheaths; 85% of the studied sheath regions had PMSs with the mean duration of 6 h. In about one-third of the cases the magnetic field vectors followed a single PMS plane that covered a significant part (at least 67%) of the sheath region. Our analysis gives strong support for two suggested PMS formation mechanisms: the amplification and alignment of solar wind discontinuities near the CME-driven shock and the draping of the magnetic field lines around the CME ejecta. For example, we found that the shock and PMS plane normals generally coincided for the events where the PMSs occurred near the shock (68% of the PMS plane normals near the shock were separated by less than 20 degrees from the shock normal), while deviations were clearly larger when PMSs occurred close to the ejecta leading edge. In addition, PMSs near the shock were generally associated with lower upstream plasma beta than the cases where PMSs occurred near the leading edge of the CME. We also demonstrate that the planar parts of the sheath contain a higher amount of strong southward magnetic field than the non-planar parts, suggesting that planar sheaths are more likely to drive magnetospheric activity.Peer reviewe

Using mutual information to investigate non-linear correlation between AE index, ULF Pc5 wave activity and electron precipitation

In this study, we use mutual information from information theory to investigate non-linear correlation between geomagnetic activity indicated by auroral electrojet (AE) index with both the global ultra low frequency (ULF) Pc5 wave power and medium energy (>= 30 keV) electron precipitation at the central outer radiation belt. To investigate the energy and magnetic local time (MLT) dependence of the non-linearity, we calculate the mutual information and Pearson correlation coefficient separately for three different energy ranges (30-100 keV, 100-300 keV and >= 300 keV) and four different MLT sectors (0-6, 6-12, 12-18, 18-24). We compare results from 2 years 2004 and 2007 representing geomagnetically more active and less active years, respectively. The correlation analysis between the AE index and electron precipitation shows a clear MLT and energy dependence in both active and quiet conditions. In the two lowest energy ranges of the medium energy electrons (30-100 keV and 100-300 keV) both non-linear correlation and Pearson correlation indicate strong dependence with the AE index in the dawn sector. The linear dependence indicated by the Pearson correlation coefficient decreases from dawn to dusk while the change in the non-linear correlation is smaller indicating an increase in the non-linearity from dawn to dusk. The non-linearity between the AE index and electron precipitation is larger at all MLT sectors except MLTs 6-12 during geomagnetically more active year when larger amount of the activity is driven by interplanetary coronal mass ejections (ICMEs) compared to lower activity year with high speed stream (HSS) and stream interaction region (SIR) driven activity. These results indicate that the processes leading to electron precipitation become more non-linear in the dusk and during geomagnetically more active times when the activity is driven by ICMEs. The non-linearity between the AE index and global ULF Pc5 activity is relatively low and seems not to be affected by the difference in the geomagnetic activity during the 2 years studied.Peer reviewe

The Automatic Identification and Tracking of Coronal Flux Ropes -- Part I: Footpoints and Fluxes

Investigating the early-stage evolution of an erupting flux rope from the Sun is important to understand the mechanisms of how it looses its stability and its space weather impacts. Our aim is to develop an efficient scheme for tracking the early dynamics of erupting solar flux ropes and use the algorithm to analyse its early-stage properties. The algorithm is tested on a data-driven simulation of an eruption that took place in active region AR12473. We investigate the modelled flux rope's footpoint movement and magnetic flux evolution and compare with observational data from the Solar Dynamics Observatory's Atmospheric Imaging Assembly in the 211 \unicode{x212B} and 1600 \unicode{x212B} channels. To carry out our analysis, we use the time-dependent data-driven magnetofrictional model (TMFM). We also perform another modelling run, where we stop the driving of the TMFM midway through the flux rope's rise through the simulation domain and evolve it instead with a zero-beta magnetohydrodynamic (MHD) approach. The developed algorithm successfully extracts a flux rope and its ascend through the simulation domain. We find that the movement of the modelled flux rope footpoints showcases similar trends in both TMFM and relaxation MHD run: they recede from their respective central location as the eruption progresses and the positive polarity footpoint region exhibits a more dynamic behaviour. The ultraviolet brightenings and extreme ultraviolet dimmings agree well with the models in terms of their dynamics. According to our modelling results, the toroidal magnetic flux in the flux rope first rises and then decreases. In our observational analysis, we capture the descending phase of toroidal flux. In conclusion, the extraction algorithm enables us to effectively study the flux rope's early dynamics and derive some of its key properties such as footpoint movement and toroidal magnetic flux.Comment: Accepted for publication in Astronomy & Astrophysic