Particles are accelerated to very high, non-thermal energies in solar and space plasma environments. While energy spectra of accelerated electrons often exhibit a power law, it remains unclear how ...electrons are accelerated to high energies and what processes determine the power-law index
δ
. Here, we review previous observations of the power-law index
δ
in a variety of different plasma environments with a particular focus on sub-relativistic electrons. It appears that in regions more closely related to magnetic reconnection (such as the ‘above-the-looptop’ solar hard X-ray source and the plasma sheet in Earth’s magnetotail), the spectra are typically soft (
δ
≳
4
). This is in contrast to the typically hard spectra (
δ
≲
4
) that are observed in coincidence with shocks. The difference implies that shocks are more efficient in producing a larger non-thermal fraction of electron energies when compared to magnetic reconnection. A caveat is that during active times in Earth’s magnetotail,
δ
values seem spatially uniform in the plasma sheet, while power-law distributions still exist even in quiet times. The role of magnetotail reconnection in the electron power-law formation could therefore be confounded with these background conditions. Because different regions have been studied with different instrumentations and methodologies, we point out a need for more systematic and coordinated studies of power-law distributions for a better understanding of possible scaling laws in particle acceleration as well as their universality.
Context. Current solar energetic particle (SEP) propagation models describe the effects of interplanetary plasma turbulence on SEPs as diffusion, using a Fokker-Planck (FP) equation. However, FP ...models cannot explain the observed fast access of SEPs across the average magnetic field to regions that are widely separated in longitude within the heliosphere without using unrealistically strong cross-field diffusion. Aims. We study whether the recently suggested early non-diffusive phase of SEP propagation can explain the wide SEP events with realistic particle transport parameters. Methods. We used a novel model that accounts for the SEP propagation along field lines that meander as a result of plasma turbulence. Such a non-diffusive propagation mode has been shown to dominate the SEP cross-field propagation early in the SEP event history. We compare the new model to the traditional approach, and to SEP observations. Results. Using the new model, we reproduce the observed longitudinal extent of SEP peak fluxes that are characterised by a Gaussian profile with σ = 30−50°, while current diffusion theory can only explain extents of 11° with realistic diffusion coefficients. Our model also reproduces the timing of SEP arrival at distant longitudes, which cannot be explained using the diffusion model. Conclusions. The early onset of SEPs over a wide range of longitudes can be understood as a result of the effects of magnetic field-line random walk in the interplanetary medium and requires an SEP transport model that properly describes the non-diffusive early phase of SEP cross-field propagation.
Context. The acceleration and transport of energetic particles in astrophysical plasmas can be described by the so-called Parker equation, which is a kinetic equation comprising diffusion terms both ...in coordinate space and in momentum space. In the past years, it has been found that energetic particle transport in space can be anomalous, for instance, superdiffusive rather than normal diffusive. This requires a revision of the basic transport equation for such circumstances. Aims. Here, we extend the Parker equation to the case of anomalous diffusion by means of fractional derivatives that generalize the usual second-order spatial diffusion operator. Methods. We introduce the left and right Caputo fractional derivatives in space. These derivatives are one of the tools used to describe anomalous transport. We consider the case of steady-state solutions upstream and downstream of a planar shock. Results. We obtain an estimate of the particle acceleration time at shocks in the case of superdiffusion. An analytical solution of the steady-state fractional Parker equation is given by the Mittag-Leffler functions, which correspond to a power-law profile for the energetic particle intensity far upstream of the shock, in agreement with the results obtained from a probabilistic approach to superdiffusion. These functions also correspond to a stretched exponential close upstream of the shock. Conclusions. These results can help to model more precisely the measured fluxes of energetic particles that are accelerated at both interplanetary shocks and supernova remnant shocks.
Modelling the transport of cosmic rays (CRs) in the heliosphere represents a global challenge in the field of heliophysics, in that such a study, if it were to be performed from first principles, ...requires the careful modelling of both large scale heliospheric plasma quantities (such as the global structure of the heliosphere, or the heliospheric magnetic field) and small scale plasma quantities (such as various turbulence-related quantities). Here, recent advances in our understanding of the transport of galactic cosmic rays are reviewed, with an emphasis on new developments pertaining to their transport coefficients, with a special emphasis on novel theoretical and numerical simulation results, as well as the CR transport studies that employ them. Furthermore, brief reviews are given of recent progress in CR focused transport modelling, as well as the modelling of non-diffusive CR transport.
During geomagnetic storms, the rapid depletion of the high‐energy (several MeV) outer radiation belt electrons is the result of loss to the interplanetary medium through the magnetopause, outward ...radial diffusion, and loss to the atmosphere due to wave‐particle interactions. We have performed a statistical study of 110 storms using pitch angle resolved electron flux measurements from the Van Allen Probes mission and found that inside of the radiation belt (L* = 3 − 5) the number of storms that result in depletion of electrons with equatorial pitch angle αeq = 30∘ is higher than number of storms that result in depletion of electrons with equatorial pitch angle αeq = 75∘. We conclude that this result is consistent with electron scattering by whistler and electromagnetic ion cyclotron waves. At the outer edge of the radiation belt (L* ≥ 5.2) the number of storms that result in depletion is also large (~40–50%), emphasizing the significance of the magnetopause shadowing effect and outward radial transport.
Key Points
Up to 49% of the studied storms result in a depletion of multi‐MeV electrons, with most depletions at L* < 5.2 are consistent with EMIC waves
The percentage of storms that result in multi‐MeV electron depletions is dependent upon pitch angle
The number of storm depletions at small pitch angles is higher (increase up to 19%) than the number of depletions at large pitch angles
Plain Language Summary
Protons and electrons form a radiation environment around Earth that can change drastically during so called geomagnetic storms. In this study, we looked at 110 storms to understand how high‐energy electrons can disappear due to different phenomena. We found that it is very common to observe a loss of high‐energy electrons after storms. More often such a loss happens far away from the Earth as the electrons cross the boundary of the magnetosphere. However, closer to Earth the electrons are lost most likely due to the interaction with whistler and electromagnetic ion cyclotron waves, which play an important role in the dynamics of the radiation environment.
Galactic transport models for cosmic rays involve the diffusive motion of these particles in the interstellar medium. Owing to the large-scale structured Galactic magnetic field, this diffusion is ...anisotropic with respect to the local field direction. We included this transport effect along with continuous loss processes in a quantitative model of Galactic propagation for cosmic ray protons that is based on stochastic differential equations. We calculated energy spectra at different positions along the Sun’s Galactic orbit and compared them to the isotropic diffusion case. The results show that a larger amplitude of variation and different spectral shapes are obtained in the introduced anisotropic diffusion scenario, which in turn emphasizes the need for accurate Galactic magnetic field models.
The radiation belts of the Earth, filled with energetic electrons, comprise complex and dynamic systems that pose a significant threat to satellite operation. While various models of electron flux ...both for low and relativistic energies have been developed, the behavior of medium energy (120–600 keV) electrons, especially in the MEO region, remains poorly quantified. At these energies, electrons are driven by both convective and diffusive transport, and their prediction usually requires sophisticated 4D modeling codes. In this paper, we present an alternative approach using the Light Gradient Boosting (LightGBM) machine learning algorithm. The Medium Energy electRon fLux In Earth's outer radiatioN belt (MERLIN) model takes as input the satellite position, a combination of geomagnetic indices and solar wind parameters including the time history of velocity, and does not use persistence. MERLIN is trained on >15 years of the GPS electron flux data and tested on more than 1.5 years of measurements. Tenfold cross validation yields that the model predicts the MEO radiation environment well, both in terms of dynamics and amplitudes o f flux. Evaluation on the test set shows high correlation between the predicted and observed electron flux (0.8) and low values of absolute error. The MERLIN model can have wide space weather applications, providing information for the scientific community in the form of radiation belts reconstructions, as well as industry for satellite mission design, nowcast of the MEO environment, and surface charging analysis.
Plain Language Summary
The radiation belts of the Earth, which are the zones of charged energetic particles trapped by the geomagnetic field, comprise complex and dynamic systems posing a significant threat to a variety of commercial and military satellites. While the inner belt is relatively stable, the outer belt is highly variable and depends substantially on solar activity; therefore, accurate and improved models of electron flux in the outer radiation belt are essential to understand the underlying physical processes. Although many models have been developed for the geostationary orbit and relativistic energies, prediction of electron flux in the 120–600 keV energy range still remains challenging. We present a data‐driven model of the medium energies (120–600 keV) differentialelectron flux in the outer radiation belt based on machine learning. We use 17 years of electron observations by Global Positioning System (GPS) satellites. We set up a 3D model for flux prediction in terms of L‐values, MLT, and magnetic latitude. The model gives reliable predictions of the radiation environment in the outer radiation belt and has wide space weather applications.
Key Points
A machine learning model is created to predict electron flux at MEO for energies 120–600 keV
The model requires solar wind parameters and geomagnetic indices as input and does not use persistence
MERLIN model yields high accuracy and high correlation with observations (0.8)
Common bean plants were grown in soil and irrigated with water solutions containing different concentrations of
Fe
3
O
4
nanoparticles (NPs) with a mean diameter close to 10 nm. No toxicity on plant ...growth has been detected as a consequence of Fe deficiency or excess in leaves. In order to track the
Fe
3
O
4
NPs, magnetization measurements were performed in soils and in three different dried organs of the plants: roots, stems, and leaves. Some magnetic features of both temperature and magnetic field dependence of magnetization
M
(
T
,
H
) arising from
Fe
3
O
4
NPs were identified in all the three organs of the plants. Based on the results of saturation magnetization
M
s
at 300 K, the estimated number of
Fe
3
O
4
NPs was found to increase from 2 to 3 times in leaves of common bean plants irrigated with solutions containing magnetic material. The combined results indicated that
M
(
T
,
H
) measurements, conducted in a wide range of temperature and applied magnetic fields up to 70 kOe, constitute a useful tool through which the uptake, translocation, and accumulation of magnetic nanoparticles by plant organs may be monitored and tracked.
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