Relativistic Electron Flux Research Articles

Quantifying the non-linear dependence of energetic electron fluxes in the Earth's radiation belts with radial diffusion drivers

Abstract. In this study, we use mutual information to characterise statistical dependencies of seed and relativistic electron fluxes in the Earth's radiation belts on ultra-low-frequency (ULF) wave power measured on the ground and at geostationary orbit. The benefit of mutual information, in comparison to measures such as the Pearson correlation, lies in the capacity to distinguish non-linear dependencies from linear ones. After reviewing the property of mutual information and its relationship with the Pearson correlation for Gaussian bivariates, we present a methodology to quantify and distinguish linear and non-linear statistical dependencies that can be generalised to a wide range of solar wind drivers and magnetospheric responses. We present an application of the methodology by revisiting the case events studied by Rostoker et al. (1998). Our results corroborate the conclusions of Rostoker et al. (1998) that ULF wave power and relativistic electron fluxes are statistically dependent upon one another. We also estimate that the Pearson correlation is missing between 20 % and 30 % of the statistical dependency between ULF wave power and relativistic electron fluxes. Thus, the Pearson correlation underestimates the impact of ULF waves on energetic electron fluxes. However, we find that observed enhancements in relativistic electron fluxes correlate modestly, both linearly and non-linearly, with the ULF power spectrum when compared with values found in previous studies (Simms et al., 2014) and with correlational values found between seed electrons and ULF wave power for the same case events. Our results are indicative of the importance of incorporating data analysis tools that can quantify linear and non-linear interdependencies of various solar wind drivers.

Relativistic Electron Model in the Outer Radiation Belt Using a Neural Network Approach

AbstractWe present a machine‐learning‐based model of relativistic electron fluxes >1.8 MeV using a neural network approach in the Earth's outer radiation belt. The Outer RadIation belt Electron Neural net model for Relativistic electrons (ORIENT‐R) uses only solar wind conditions and geomagnetic indices as input. For the first time, we show that the state of the outer radiation belt can be determined using only solar wind conditions and geomagnetic indices, without any initial and boundary conditions. The most important features for determining outer radiation belt dynamics are found to be AL, solar wind flow speed and density, and SYM‐H indices. ORIENT‐R reproduces out‐of‐sample relativistic electron fluxes with a correlation coefficient of 0.95 and an uncertainty factor of ∼2. ORIENT‐R reproduces radiation belt dynamics during an out‐of‐sample geomagnetic storm with good agreement to the observations. In addition, ORIENT‐R was run for a completely out‐of‐sample period between March 2018 and October 2019 when the AL index ended and was replaced with the predicted AL index (lasp.colorado.edu/home/personnel/xinlin.li). It reproduces electron fluxes with a correlation coefficient of 0.92 and an out‐of‐sample uncertainty factor of ∼3. Furthermore, ORIENT‐R captured the trend in the electron fluxes from low‐earth‐orbit (LEO) SAMPEX, which is a completely out‐of‐sample data set both temporally and spatially. In sum, the ORIENT‐R model can reproduce transport, acceleration, decay, and dropouts of the outer radiation belt anywhere from short timescales (i.e., geomagnetic storms) and very long timescales (i.e., solar cycle) variations.

Relative Contribution of ULF Waves and Whistler‐Mode Chorus to the Radiation Belt Variation During the May 2017 Storm

AbstractWe investigate the time and location where ULF waves and whistler‐mode chorus contributed to the net flux enhancement of relativistic electrons during the magnetic storm of May 2017. During the early recovery phase, both ULF and chorus waves contribute to the enhancement of relativistic electron fluxes, but ULF waves play roles of the inward diffusion. During the late recovery phase, both Van Allen Probe‐B and Arase show that whistler‐mode chorus contributes to the flux enhancement confined in the L‐value. The CRCM coupled with BATS‐R‐US simulation qualitatively reproduces the global evolution of ULF waves. Although the electron flux is underestimated by the simulation, this study reveals a large anisotropy of hot electrons in the region where whistler‐mode chorus waves were actually observed by satellites. In addition, the estimated magnetic field curvature on the dayside is small during the recovery phase. Furthermore, we investigate the control of wave evolution. Both observations and the simulation suggest that the observed ULF waves in the frequency range of ∼2–5 mHz are excited by the enhancement of the solar wind dynamic pressure. Observations also indicate that whistler‐mode chorus on the nightside is predominantly excited by hot electrons with temperature anisotropy, whereas the dayside chorus is enhanced by the change of the magnetic field line configuration. The estimated spatial distributions of electron anisotropy and magnetic field curvature provide an explanation for the presence of enhanced whistler‐mode chorus in the dusk sector, which is far from the usual location of wave generation.

Formation of Optical Images with Synchrotron Radiation Flux of Relativistic Electrons in the X-Ray Generator "Nestor"

When setting up physical experiments involving the use of the polarization properties of synchrotron radiation (SR) or a monoenergetic photon beam, detailed calculation of the spectral angular distribution of SR and its polarization components is of interest. Consideration of the electron beam size shows that in real conditions the radiation propagating in the plane of the equilibrium orbit will not be completely polarized, and the shape and dimensions of the angular distribution of radiation will be distorted. The motion of electrons in the uniform magnetic field and SR of the beam of relativistic particles in the storage ring of "NESTOR" are considered. The effect of the size of the electron beam with the energy of E=225 MeV in the 6-dimensional space on the formation of images of the flux of quanta of SR is analyzed. It is shown that the main contribution to the formation of images is made by the two-dimensional distribution of particles along the vertical direction axis and vertical oscillations. A software simulation code has been developed, the use of which made it possible to simulate the process of optical image formations by the flux of SR quanta (Этого предложения нет в русской аннотации). The formation of images of the radiation of electrons with an energy of E=225 MeV with change in the longitudinal distance L to the registration plane is considered. It is determined that at small longitudinal distances the main contribution to the image is made by the vertical distribution of particles in the beam. With an increase in the basic distance L, the contribution of the distribution of particles over vertical oscillations increases, which becomes decisive for large L value. Numerical simulation of image formation has been carried out. For the base distance of 300 cm and beam parameters with the vertical root mean square size of 0.2 mm and a vertical root mean square size of 0.15 mrad, the family of angular distributions is presented in the form of two-dimensional histograms for wavelengths , , , where , is the critical wavelength of SR. The dimensions of the optical window are obtained, the size of which makes it possible to reliably register the entire flux of SR quanta for the indicated registration characteristics.

Geomagnetically Quiet Period Analysis of Relativistic Electrons, Auroral Precipitation, Joule Heating, and Ring Current During the Years of 1999, 2000 and 2004

This work presents the study of the quietest time variation in relativistic electrons, auroral precipitation, ring current, and joule heating during 1999, 2000, and 2004. Geostationary Operational Environmental Satellite (GOES) data on relativistic electrons with energies above 0.6 MeV, 2 MeV, and 4 MeV were analyzed. The time-series analysis of the relativistic electrons over a 24-hour averaged interval reveals a precise 24-hour modulation of the relativistic electron population during all seasons for energies above 0.6 MeV and 2 MeV, and during the winter season for higher energies above 4 MeV. In addition, relativistic electron fluxes at energies above 0.6 MeV and above 2 MeV were higher during the descending phase of the solar cycle compared to the ascending and solar-maximum phases. The cross-correlation analysis presented a strong correlation of Joule heating, ring current, and auroral precipitation with the relativistic electron population in three energy bands considered, as indicated by the zero-time lag. Studying the quiet time variation of relativistic electrons will lead to more complete ionospheric models, which were previously limited to the geomagnetically disturbed period.

On the semi-annual variation of relativistic electrons in the outer radiation belt

Abstract. The nature of the semi-annual variation in the relativistic electron fluxes in the Earth's outer radiation belt is investigated using Van Allen Probes (MagEIS and REPT) and Geostationary Operational Environmental Satellite Energetic Particle Sensor (GOES/EPS) data during solar cycle 24. We perform wavelet and cross-wavelet analysis in a broad energy and spatial range of electron fluxes and examine their phase relationship with the axial, equinoctial and Russell–McPherron mechanisms. It is found that the semi-annual variation in the relativistic electron fluxes exhibits pronounced power in the 0.3–4.2 MeV energy range at L shells higher than 3.5, and, moreover, it exhibits an in-phase relationship with the Russell–McPherron effect, indicating the former is primarily driven by the latter. Furthermore, the analysis of the past three solar cycles with GOES/EPS indicates that the semi-annual variation at geosynchronous orbit is evident during the descending phases and coincides with periods of a higher (lower) high-speed stream (HSS) (interplanetary coronal mass ejection, ICME) occurrence.

Dynamics of Relativistic Electron Fluxes of the Outer Radiation Belt during Geomagnetic Disturbances of Different Intensity

Dynamics of Relativistic Electron Fluxes of the Outer Radiation Belt during Geomagnetic Disturbances of Different Intensity

Semiannual variation in relativistic electron fluxes of the outer radiation belt: Phases comparison with classical hypotheses predictions

Abstract Relativistic electron fluxes of the outer Van Allen belt present a clear semiannual signature, with maxima fluxes near the equinoxes and minima near the solstices. We investigate the semiannual variation (SAV) of 3.75 MeV and 3.4 MeV electron fluxes from Solar, Anomalous, and Magnetospheric Particle Explorer (SAMPEX) and Van Allen probe A (RBSP-A) data, respectively. The fluxes of both missions are binned in McIlwain’s L-shell values and in day of year (DOY). In order to obtain the SAV from the data, a superposed epoch analysis and then a 30-day smoothing is carried out for the entire L-shell range utilized. The results show clear semiannual patterns with maximum differences of ~ 1 and ~ 2 orders of magnitude between values near the equinoxes and solstices, for SAMPEX and RBSP-A fluxes, respectively. The comparison of the maxima-minima dates of the observed SAVs with corresponding dates predicted by the Axial, Equinoctial and Russell & McPherron (RM) theory shows that the latter gives the best estimations for both data sets. However, considerable delays from the theories’ predictions are found. The most important delay occurs in the Mar/Apr maximum and is found to be ~ 26.8 days on average for L ≳ 3.5 RBSP-A data. In the case of SAMPEX, this delay is found for L 3.8 with a maximum of 22.4 days. Accurately determining the Mar/Apr maximum and the Sep/Oct maximum has implications in space weather since it indicates when the SAV will affect the most particular flux enhancements capable of inducing satellite operational anomalies. .

Micro-optics for ultra-intense lasers

Table-top, femtosecond lasers provide the highest light intensities capable of extreme excitation of matter. A key challenge, however, is the efficient coupling of light to matter, a goal addressed by target structuring and laser pulse-shaping. Nanostructured surfaces enhance coupling but require “high contrast” (e.g., for modern ultrahigh intensity lasers, the peak to picosecond pedestal intensity ratio >1012) pulses to preserve target integrity. Here, we demonstrate a foam target that can efficiently absorb a common, low contrast 105 (in picosecond) laser at an intensity of 5 × 1018 W/cm2, giving ∼20 times enhanced relativistic hot electron flux. In addition, such foam target induced “micro-optic” function is analogous to the miniature plasma-parabolic mirror. The simplicity of the target—basically a structure with voids having a diameter of the order of a light wavelength—and the efficacy of these micro-sized voids under low contrast illumination can boost the scope of high intensity lasers for basic science and for table-top sources of high energy particles and ignition of laser fusion targets.

Short- and Medium-range Prediction of Relativistic Electron Flux in the Earth’s Outer Radiation Belt by Machine Learning Methods

Short- and Medium-range Prediction of Relativistic Electron Flux in the Earth’s Outer Radiation Belt by Machine Learning Methods

Formation of the Outer Radiation Belt during Geomagnetic Storms and the Adiabatic Mechanism of the Rise and Fall of Relativistic Electron Fluxes

Formation of the Outer Radiation Belt during Geomagnetic Storms and the Adiabatic Mechanism of the Rise and Fall of Relativistic Electron Fluxes

Seasonal dependence of the Earth's radiation belt – new insights

Abstract. Long-term variations in the relativistic (∼MeV) electrons in the Earth's radiation belt are explored to study seasonal features of the electrons. An L-shell dependence of the seasonal variations in the electrons is reported for the first time. A clear ∼6 month periodicity, representing one/two peaks per year, is identified for 1.5–6.0 MeV electron fluxes in the L shells between ∼3.0 and ∼5.0. The relativistic electron flux variation is strongest during solar cycle descending to minimum phases, with weaker/no variations during solar maximum. If two peaks per year occur, they are largely asymmetric in amplitude. The peaks essentially do not have an equinoctial dependence. Sometimes the peaks are shifted to solstices, and sometimes only one annual peak is observed. No such seasonal features are prominent for L<3.0 and L>5.0. The results imply varying solar/interplanetary drivers of the radiation belt electrons at different L shells. This has a potential impact on the modeling of the space environment. Plausible solar drivers are discussed.

Jovian electrons at the Earth orbit and stationary structures in the solar wind

ABSTRACT This work studies the influence of the structure of inner heliospheric magnetic field on the propagation of Jovian electrons from Jupiter to the Earth orbit. Beginning from 1974, 13-month variations of relativistic Jovian electron fluxes were recorded by spacecraft near the Earth. 22 synodic cycles are analysed. The best connection in each cycle was found within a narrow longitudinal interval with an angular divergence of the planets 230 ± 20°, when the Parker field line connecting the two planets is formed at solar wind speed 450 ± 50 km s−1. Such invariability for more than 45 yr could not be accidental. We attribute the observed phenomenon to the long-term presence of recurrent stationary structures in the solar wind generated near the Sun. This assumption is confirmed by comparing the time profiles of the solar wind speed measured over all solar rotations in the solar activity minima in 1975 and 2007–2008.

Catalogue of events with cumulative fluxes below as well as comparable and exceeding those for RBSP discovered third radiation belt

The formation of a temporary third radiation belt in the slot region of Earth’s magnetosphere was reported (Baker et al. in Science 340:186-190, 2013a) from the early data of the radiation belt storm probes (RBSP) mission. The cumulative flux of relativistic electrons in L = 3-3.5 for the third radiation belt of that study is calculated here and defined as threshold flux (TF) (105 cm−2 s−1 sr−1 MeV−1). A catalogue of 133 events during Sep 2012 – Feb 2019 is presented. Events are distributed into, below threshold flux (BTF), of the order of, one hundred and one thousand times the threshold flux, (OTF), (HTF), and (TTF) categories respectively. Finding high 2 MeV flux threshold at L = 3-3.5 is a way to find ideal condition for the possible formation of a third radiation belt, aware that attaining TF does not necessarily mean formation of the third radiation belt. It is found that BTF occurred 29 times and 105 times cumulative flux exceeded TF but TTF occurred very rarely. The effects of large scale solar wind structures (LSSS) and number of main phase Dst dips on BTF-TTF events are also studied. The findings of this study may be helpful for understanding the third radiation belt formation in the slot region of Earth’s magnetosphere.

Краткосрочное и среднесрочное прогнозирование потоков релятивистских электронов внешнего радиационного пояса Земли методами машинного обучения

The ways are studied to improve the quality of prediction of the time series of hourly mean fluxes and daily total fluxes (fluences) of relativistic electrons in the outer radiation belt of the Earth 1 to 24 hours ahead and 1 to 4 days ahead, respectively. The prediction uses an approximation approach based on various machine learning methods, namely, artificial neural networks (ANNs), decision tree (random forest), and gradient boosting. A comparison of the skill scores of short-range forecasts with the lead time of 1 to 24 hours showed that the best results were demonstrated by ANNs. For medium-range forecasting, the accuracy of prediction of the fluences of relativistic electrons in the Earth’s outer radiation belt three to four days ahead increases significantly when the predicted values of the solar wind velocity near the Earth obtained from the UV images of the Sun of the AIA (Atmospheric Imaging Assembly) instrument of the SDO (Solar Dynamics Observatory) are included to the list of the input parameters.

Van Allen Belt Punctures and Their Correlation With Solar Wind, Geomagnetic Activity, and ULF Waves

AbstractWe investigate the rare events of sudden appearances of relativistic electrons (>700 keV), which are normally confined to the Van Allen belts, in the slot region. The frequency of occurrence of these events is on average 1–2 per year. To cope with the scarcity of events, in this study, we examine 21 years of trapped relativistic electron fluxes available from the POES and MetOp Space Environment Monitor (SEM‐2). Our statistical analysis shows that these events can occur even during moderate geomagnetic activity. Occurrence of these events correlates with high‐speed solar winds or interplanetary coronal mass ejections depending on the phase of the solar cycle. A strong correlation of these events is found with ultra‐low frequency (ULF) wave activity, which can be used to predict these events with more than 75% accuracy.

Wavelet and Cross-Correlation Analysis of Relativistic Electron Flux with Sunspot Number, Solar Flux, and Solar Wind Parameters

The Geostationary Operational Environmental Satellites (GOES) have been monitoring the Earth's radiation environment and is providing the electron flux data (of energy >0.8 MeV, >2 MeV, and >4 MeV) by means of a connected sensor subsystem. Relativistic electron flux is one of the components of the radiation belt which not only affects the electrical system in satellites but also has an impact on Earth’s upper atmospheric climatic variation. We have carried out a study to determine the relation of sunspot number (R), solar flux (F10.7), and solar wind parameters i.e., solar wind velocity (Vsw), plasma density Nsw), the southern component of the interplanetary magnetic field (IMF-Bz), Plasma temperature (Tsw) with relativistic electron flux of energy >0.8 MeV, >2 MeV, and >4 MeV in outer radiation belt using the data of 24 years (1996-2020) covering solar cycle 23 and 24. Time series analysis, Cross-correlation and wavelet analysis techniques have been used in this study. The time series plot displayed that the radiation is occupied mostly by electron flux of energy less than 4 Mev and solar cycle 23 (1996-2008) was strong to produce more intensity of relativistic electron flux of all energy in comparison to cycle 24 (2008-2019). Results from cross-correlation analysis illustrated that Bz has no significant impact on the enhancement of relativistic electron flux of any energy range in the radiation belt. Whereas other studied parameters have a positive correlation with relativistic electron flux, but with significantly different coefficient values for different energy. We found that electron flux >0.8 MeV and >2 MeV has a strong positive association with sunspot number, solar flux, solar wind velocity, plasma density and temperature whereas weak correlation with electron flux of energy >4 MeV. This result leads us to conclude that solar activity and solar parameters have greater influence in producing relativistic electron flux of energy ~ 0.8-4 MeV, than of flux > 4 MeV. The study made to observe the distribution of relativistic electrons in radiation belt with time through continuous wavelet analysis showed that electron flux of energy >0.8 has a higher periodicity in comparison to the flux of other energy ranger.

Adiabatic and non-adiabatic evolution of relativistic electrons in the heart of the outer radiation belt during the 1 June 2013 geomagnetic storm

The adiabatic and non-adiabatic behavior of relativistic electrons in the outer radiation belt during the 1 June 2013 geomagnetic storm is studied using data from the Van Allen Probes and THEMIS missions. Analysis of the evolution of the plasma pressure shows that the pressure increased by one order of magnitude during the storm reaching a maximum value towards the end or slightly after the main phase of the storm. At the same time, the location of the maximum pressure moved towards the Earth, reaching the closest distance at L∼3.7. Relativistic electron fluxes show that the location of the peak fluxes also move closer to the Earth reaching the same L as the maximum of plasma pressure. In order to study whether the adiabatic mechanisms are relevant to explain the behavior of relativistic electrons, we analyzed the electron fluxes in the energy range from 1.8 to 4.2 MeV and found that the electron spectra fits well to a power law function. For a fixed L−shell, the power law index is conserved during the pre-storm time, increases during the main phase, and presents little variation again during the recovery phase, but the power law index calculated during the recovery phase is larger than during pre-storm phase. A strong depletion of electron fluxes during the main phase of the storm is also measured, with fluxes returning to the pre-storm level afterwards. The conservation of the slope of the electron spectra during a long time can be considered as an evidence of a dominant contribution of adiabatic processes, as it is difficult to explain this effect as other processes such acceleration and losses of relativistic electrons. An increase of the power law index towards the end or right after the main phase of the storm can be related to the increase of the losses with the electron energy, and/or to the processes of thermalization (relaxation) of the electron distribution functions.

Prolonged, Weak C1.2 Flares: A Source of Protons and Electrons

Two proton events (>100 MeV; GOES, ACS SPI) associated with weak flares (C1.2, GOES class) in the soft X-ray range that occurred on November 26, 2011, and September 29, 2013, are analyzed. These events were accompanied by significant fluxes of relativistic electrons (>1 MeV; SOHO EPHIN) in the interplanetary space. The time profiles of these protons and electron fluxes were similar during the growth phase, which suggested a common mechanism of their acceleration and propagation. The gradual increase in the flux intensities, in our opinion, shows a prolonged and gradual injection of particles into the interplanetary space, which may be the result of prolonged acceleration or capture. Since prolonged electron capture is unlikely, it is most probable that a prolonged acceleration took place. The prolonged proton acceleration is realized at the post-eruptive phase of solar flares or shock-wave coronal mass ejection. According to the existing theoretical concepts, the acceleration of solar electrons to ~10 MeV by a shock wave is hardly possible. In this case, relativistic electrons and protons were apparently accelerated in the post-eruptive phase of solar flares, where the stochastic acceleration by magnetohydrodynamic turbulence is considered the most probable mechanism.

Long‐Term Dropout of Relativistic Electrons in the Outer Radiation Belt During Two Sequential Geomagnetic Storms

AbstractOn 31 January 2016, the flux of >2 MeV electrons observed by Geostationary Operational Environmental Satellite (GOES)‐13 dropped to the background level during a minor storm main phase (−48 nT). Then, a second storm (−53 nT) occurred on 2 February; during the 3 days after its main phase, the flux remained at background level. Using data from various instruments on the GOES, Polar Operational Environmental Satellites (POES), Radiation Belt Storm Probes (RBSP), Meteor‐M2, and Fengyun‐series spacecraft, we study this long‐term dropout of MeV electrons during two sequential storms of similar magnitude under lightly disturbed solar wind conditions. Observations from low‐altitude satellites show that the fluxes decreased first at higher L‐shells and then gradually propagated inward. Moreover, the fluxes were almost completely lost and dropped to the background level at L > 5, while the fluxes at 4 < L < 5 were partly lost, as observed by RBSP and low‐altitude satellites. Finally, observations show that on 5 February, only the fluxes at L > 5.5 recovered, while the fluxes at 4 < L < 5 did not return to the prestorm levels. These observations indicate that the loss and recovery processes developed first at higher L‐shells. Phase space density (PSD) analysis shows that radial outward diffusion was the main reason for the dropout at higher L‐shells. Regarding electron enhancement, stronger inward diffusion was accompanied by ultra‐low‐frequency (ULF) wave activities at higher L‐shells, and chorus waves observed at outer L‐shells provided conditions for relativistic electron flux recovery to the prestorm levels.