Drift Shell Research Articles

Chorus wave generation near the dawnside magnetopause due to drift shell splitting of substorm‐injected electrons

We study the relationship between the electron injection and the chorus waves during a substorm event on 23 March 2007. The chorus waves were detected at high geomagnetic latitude (∼70°S) Antarctic observatories in the range of 0600–0900 h in magnetic local time (MLT). Electrons drifting from the injection event were measured by two LANL spacecraft at 0300 and 0900 MLT. The mapping of auroral brightening areas to the magnetic equator shows that the injection occurred in an MLT range of 2200–2400. This estimate is consistent with observations by the THEMIS A, B, and D spacecraft (which were located at 2100 MLT and did not observe electron injections). Our backward model tracing from the magnetic equator near the dawnside magnetopause (which magnetically connects to the Antarctic observatories) also supports the deduced injection region. Since chorus waves are believed to be generated through the electron cyclotron instability by an anisotropic temperature distribution, we examine, by performing forward model tracing, whether the electrons injected during this substorm form a pancake‐like pitch angle distribution when they arrive near the dawn‐side magnetopause. We find that the onset time of the modeled pitch angle anisotropy is consistent with that of the observed chorus waves. We conclude that the development of the anisotropy is due to particle drift shell splitting.

Drivers of chorus in the outer dayside magnetosphere

Using ELF/VLF wave data recorded in 2007 from two high‐latitude (Λ = 69.8°, 71.8°) Antarctic ground stations, the dayside variation of chorus wave occurrence and amplitude are analyzed in conjunction with geomagnetic and solar wind driving parameters. Both stations observe chorus (defined here as discrete rising emission tones together with unstructured hiss) in a broad window of local time across the dayside when the stations are on closed magnetic field lines. Wave occurrence rates rise rapidly from ∼0.06–0.12 at dawn to their maximum value of ∼0.5–0.6 near local noon. The event amplitudes also peak near noon. Occurrence probabilities at the lower‐latitude station are consistently higher with the average difference in the rate between the two stations being 0.15. In addition, ∼80% of the time, event amplitudes are larger at the lower‐latitude site. When the stations are in the dawn local time sector (5.5 < MLT < 10), the onset of waves is clearly linked to substorms, as seen by the AE index as well as by energetic electron injections observed at geosynchronous orbit. However, as the stations rotate to noon (MLT > 10), wave occurrence rates appear to be relatively independent of geomagnetic activity as measured by Kp and AE. Chorus near noon at times appears related to substorm activity, but intense waves can also be observed during extended quiet periods. Waves across the entire dayside are more likely during higher solar wind dynamic pressure as well as during significant changes in pressure. We attribute the high occurrence rate of outer dayside chorus to several effects resulting from solar wind compression of the dayside magnetosphere; the first is electron drift shell splitting, and the second is the creation of a region of high magnetic field homogeneity which is particularly favorable for wave growth.

Trapped proton fluxes measured on board LEO satellites in comparison with models

The proton fluxes from the low-Earth orbital satellites databases (NPOES-17 and CORONAS-F) were analyzed for the quiet geomagnetic period in April 2005. The satisfactory consent was found between the experimental and the AP8 model fluxes of the trapped protons with energy more than ∼10 MeV. At the same time, trapped proton fluxes with energy less than 10 MeV measured by LEO satellites were higher than the ones predicted by the AP8 model in the region of the SAA (drift shell L < 1.5).

Variation of the trapped proton flux in the inner radiation belt of the earth as a function of solar activity

Fluxes of trapped protons with energies above 70 MeV measured onboard the NOAA-15 satellite during the 23rd solar activity cycle (from 1999 to 2006) are analyzed. Comparing to similar experimental data obtained for 1976–1996, regularities of changes in the proton flux at low drift shells (L = 1.14–1.20) of the Earths’s radiation belt caused by changes in the solar activity are discussed.

LANL* V1.0: a radiation belt drift shell model suitable for real-time and reanalysis applications

Abstract. We describe here a new method for calculating the magnetic drift invariant, L*, that is used for modeling radiation belt dynamics and for other space weather applications. L* (pronounced L-star) is directly proportional to the integral of the magnetic flux contained within the surface defined by a charged particle moving in the Earth's geomagnetic field. Under adiabatic changes to the geomagnetic field L* is a conserved quantity, while under quasi-adiabatic fluctuations diffusion (with respect to a particle's L*) is the primary term in equations of particle dynamics. In particular the equations of motion for the very energetic particles that populate the Earth's radiation belts are most commonly expressed by diffusion in three dimensions: L*, energy (or momentum), and pitch angle (the dot product of velocity and the magnetic field vector). Expressing dynamics in these coordinates reduces the dimensionality of the problem by referencing the particle distribution functions to values at the magnetic equatorial point of a magnetic "drift shell" (or L-shell) irrespective of local time (or longitude). While the use of L* aids in simplifying the equations of motion, practical applications such as space weather forecasting using realistic geomagnetic fields require sophisticated magnetic field models that, in turn, require computationally intensive numerical integration. Typically a single L* calculation can require on the order of 105 calls to a magnetic field model and each point in the simulation domain and each calculated pitch angle has a different value of L*. We describe here the development and validation of a neural network surrogate model for calculating L* in sophisticated geomagnetic field models with a high degree of fidelity at computational speeds that are millions of times faster than direct numerical field line mapping and integration. This new surrogate model has applications to real-time radiation belt forecasting, analysis of data sets involving tens of satellite-years of observations, and other problems in space weather.

CORONAL RADIATION BELTS

The magnetic field of the solar corona has a large-scale dipole character, which maps into the bipolar field in the solar wind. Using standard representations of the coronal field, we show that high-energy ions can be trapped stably in these large-scale closed fields. The drift shells that describe the conservation of the third adiabatic invariant may have complicated geometries. Particles trapped in these zones would resemble the Van Allen Belts and could have detectable consequences. We discuss potential sources of trapped particles.

Radial transport of radiation belt electrons due to stormtime Pc5 waves

Abstract. During geomagnetic storms relativistic electron fluxes in the outer radiation belt exhibit dynamic variability over multiple orders of magnitude. This requires radial transport of electrons across their drift shells and implies violation of their third adiabatic invariant. Radial transport is induced by the interaction of the electron drift motion with electric and magnetic field fluctuations in the ULF frequency range. It was previously shown that solar-wind driven ULF waves have long azimuthal wave lengths and thus can violate the third invariant of trapped electrons in the process of resonant interaction with their gradient-curvature motion. However, the amplitude of solar-wind driven ULF waves rapidly decreases with decreasing L. It is therefore not clear what mechanisms are responsible for fast transport rates observed inside the geosynchronous orbit. In this paper we investigate wether stormtime Pc5 waves can contribute to this process. Stormtime Pc5s have short azimuthal wave lengths and therefore cannot exhibit resonance with the the electron drift motion. However we show that stormtime Pc5s can cause localized random scattering of electron drift motion that violates the third invariant. According to our results electron interaction with stormtime Pc5s can produce rapid radial transport even as low as L≃4. Numerical simulations show that electron transport can exhibit large deviations from radial diffusion. The diffusion approximation is not valid for individual storms but only applies to the statistically averaged response of the outer belt to stormtime Pc5 waves.

Radial transport in the outer radiation belt due to global magnetospheric compressions

Earth's outer radiation belt is populated by relativistic electrons that produce a complex dynamical response to varying geomagnetic activity. One fundamental process defining global state of the belt is radial transport of electrons across their drift shells. Radial transport is induced by resonant interaction of electron drift motion with ULF oscillations of electric and magnetic fields and is commonly believed to be a diffusive process. The goal of this paper is the analysis of radial transport due to typical ULF fluctuations in the inner magnetospheric fields. For this purpose a test-particle approach is used in the guiding center approximation. In particular we consider ULF oscillations due to global magnetospheric compressions. It is shown that typical pressure variations induce large-scale fluctuations in magnetic and inductive electric fields that produce a substantial impact on relativistic electrons. Electron motion becomes stochastic due to overlap of electron populations trapped in the vicinities of drift resonances with adjacent harmonics of the field spectrum. It is shown that in spite of the underlying stochasticity the radial diffusion limit is not fully attainable in the outer radiation belt. This is attributed to the fact that phase correlations in electron motion do not have time to decay due to finite size of the system. As a result collective motion of the outer belt electrons can exhibit large deviations from radial diffusion. Solution of the full Liouville's equation is required for accurate description of radial transport in the belt.

3-Dimensional Drift Shell Splitting During the Geomagnetic Disturbance

基于磁层粒子动力学理论,首先对比了计算漂移壳分离的引导中心法和磁力线追踪法,计算表明两种方法的计算结果一致.然后分别采用T89c和T96磁层磁场模式,用磁力线追踪法数值计算了不同初始位置(≤9Re)、不同初始投掷角、不同Kp指数和不同太阳风压力下,带电粒子的漂移壳分离.计算结果揭示了漂移壳分离随初始位置、投掷角、Kp指数和太阳风压力的变化.其具体特征如下. (1)随着径向距离的增大,漂移壳分离效应愈加显著,由正午出发的粒子将被稳定捕获,而午夜出发的径向距离≥7Re的部分大投掷角粒子将沿磁层顶逃逸. (2)正午出发的粒子,漂移到午夜时其漂移壳随投掷角减小向外排列;午夜出发的粒子,漂移到正午时其漂移壳随投掷角增大排列; 90°投掷角粒子在磁赤道面的漂移壳沿着磁场等值线排列. (3)漂移壳分离随Kp指数和太阳风压力增大变得显著,且随这两种扰动参数的变化特征和趋势是基本相似的.

Bifurcation of drift shells near the dayside magnetopause

Close to the dayside magnetopause, there is a region of space where each field line has two magnetic field minima, one near each cusp. That region is located around local noon, and extends about 1–2 Re from the magnetopause. Particles that enter this region with equatorial pitch angles sufficiently close to 90° will cross the dayside not along an equatorial path, but along one of the two branches on either side of the equatorial plane. The two branches are joined again past local noon. This process of drift‐shell bifurcation (DSB) is nonadiabatic even under static conditions. Two physical mechanisms can cause this nonadiabaticity: one that is operative for nearly all magnetospheric magnetic field configurations and another that depends on a particular combination of north‐south and east‐west asymmetry in the magnetic field. This paper deals only with the first mechanism. For configurations with north‐south and east‐west symmetry, DSB changes the second invariant I of the motion by a small amount that is of the order of the gyroradius (the first invariant is intact). For near‐equatorial particles (I ≈ 0) the change can be significantly larger. Assuming north‐south and dawn‐dusk symmetry, we present general theoretical expressions for the second‐invariant jump ΔI, which can be applied to a variety of magnetic field models. The results show that ΔI is sensitively dependent on the bounce phase of the particle at the bifurcation line. The RMS value of ΔI over a bounce‐phase ensemble increases with decreasing mirror field and with increasing kinetic energy. We verify these results with test‐particle simulations using model magnetic fields.

Electron microdiffusion in the Saturnian radiation belts: Cassini MIMI/LEMMS observations of energetic electron absorption by the icy moons

Since Saturn orbit insertion (SOI), Cassini has performed numerous crossings of Saturn's inner moons' L shells. The Low‐Energy Magnetospheric Measurement System (LEMMS) has detected a large number of microsignatures in its lowest‐energy electron channels (20–100 keV) as well as in the MeV energy range. We have catalogued and analyzed more than 70 microsignatures in the LEMMS data from the first 22 Cassini orbits and have correlated their evolution with electron diffusive processes. Our results on the L‐dependence of the radial diffusion coefficients, DLL, show that radial microdiffusion driven by magnetic field impulses is the dominant mechanism to account for their refilling. The dependency of DLL from equatorial pitch angles also points toward this mechanism. The large scattering of the DLL values at Tethys and Dione suggest that these field impulses might be related to injections. Our analysis also supports the, inferred from pre‐Cassini studies, filtering effect by the icy moons on radially diffusing electrons, which starts at the orbit of Dione, at 6.28 Saturn radii, Rs. This is suggested primarily by the very low radial diffusion speeds and by the characteristics of four microsignatures attributed to the moons Mimas and Epimetheus that all seem to have been formed in energies between 1.6 and 3.5 MeV. Despite the low DLL, diffusing electrons can escape absorption and be transported in the inner magnetosphere due to nonaxisymmetric drift shells, which can be detected even along the orbit of Enceladus. We estimate that a significant contribution to the filtering comes from the core of the E ring. Our results also show that L displacements due to the nonaxisymmetric drift shells are orders of magnitude higher than the icy moon L shell variability due to the nonzero eccentricities and inclinations, and total plasma losses on the moon surfaces should be reevaluated. We also examine the energy dependence of DLL and we present a series of possible explanations for the faster depletion of microsignatures at MeV energies. Using the high‐energy resolution PHA channels we assess that this faster depletion could result partly from an increase of DLL with energy. The larger passbands of the high‐energy electron detectors could amplify the erosion of the microsignature signal.

A theoretical model of the inner proton radiation belt

A theoretical calculation provides inner radiation belt proton intensities as a function of time and of the three adiabatic invariants, M, K, and L, in the kinetic energy range from ∼10 MeV to ∼4 GeV and the L range from 1.1 to 2.4. Long residence times for trapped protons of up to several thousand years require similarly long input time series for the geomagnetic field, solar activity, and solar proton fluences. Additional inputs include galactic cosmic ray spectra, nuclear scattering cross sections, and the neutral and plasma densities in the atmosphere, ionosphere, and plasmasphere. Trapped proton sources are cosmic ray albedo neutron decay (CRAND), calculated from a Monte Carlo particle transport simulation, and solar proton injection using a derived empirical injection efficiency that is ∼10−4 at 10 MeV. Radial diffusion provides inward transport of injected solar protons. Calculated intensities at energies ≲100 MeV and for L ≳ 1.3 are dominated by solar protons, CRAND being the dominant source otherwise. Losses are by ionization of the neutral atmosphere, energy transfer to plasma electrons, and inelastic nuclear scattering. Numerical trajectory tracing determines trapping limits and drift shell averages of the albedo neutron intensity and of neutral and plasma densities for loss rate calculations. Geomagnetic secular variations cause adiabatic energy and drift shell changes. Intensities are greater than they would be in a constant geomagnetic field by factors up to ∼10, a result of long proton residence times and the presently decreasing geomagnetic dipole moment.

Using invariant altitude (hinv) for mapping of the radiation belt fluxes in the low‐altitude environment

Mapping of the radiation belt environment in the classical (B, L) invariant coordinates is rather poorly resolved at low altitudes where the SAMPEX and DEMETER missions are collecting scientific data. This lack of adequate spatial resolution at low altitudes has been pointed out since 1986. A simple solution to this standing problem is proposed in this article. We recall alternative coordinates that were proposed in the 90s to improve the spatial resolution of binning meshes and radiation belt maps in the low‐altitude region, i.e., near the atmospheric cutoff. Next, we define a new coordinate: the “invariant altitude,” hinv, that we recommend instead of B or other invariant drift shell coordinates like B/B0 or α0, the equatorial pitch angle. In McIlwain's reference dipole, the new coordinate, hinv, corresponds to the altitude (in units of km) of mirror points of particles which have given values of B and I or L, calculated by using a geomagnetic field model like the International Geomagnetic Reference Field. The advantages and limitations of the new hinv coordinate are presented. For illustration, the distributions of the omnidirectional fluxes of electrons and protons predicted by the standard AE8 and AP8 radiation belt models are displayed using this new invariant coordinate, as well as by using alternative invariant coordinates like B/B0 or α0. A set of orbits of the SAMPEX, DEMETER, and CRRES spacecraft are displayed in these different coordinate systems to illustrate the advantage of using the invariant altitude hinv to map the radiation belt environment at low altitudes.

Studies of substorm on March 12, 1991: 2. Auroral electrons. Acceleration, injection, and dynamics

In the first part of this study of the substorm of March 12, 1991, the space-time structure of substrorm disturbance and dynamics of auroral ions were considered. This second part presents an analysis of measurements of auroral electrons onboard the CRRES satellite. It is demonstrated that enhancements of the electron flux (injections) during large-scale and local dipolarizations of the magnetic field are determined by a combination of field-aligned, induction, and betatron mechanisms of acceleration with an effect of displacement of the drift shells of particles. The relative contributions of these mechanisms in relation to the energy of auroral electrons are determined.

Short increases of the fluxes of electrons with energies &gt; 0.08 MeV at low-latitude (L &lt; 2) regions of near-Earth space

We present the characteristics of short (duration less than 1 min) increases of the counting rate of electrons with energies >0.08 MeV observed in low-latitude (L < 2.0) regions of near-Earth space in the course of the GRIF experiment on the Spektr module of the Mir orbital station. The measurements were carried out using a set of instruments including X-ray and gamma-ray spectrometers, as well as detectors of electrons, protons, and nuclei with large and small geometrical factors, which allowed one to detect the fluxes of charged particles both in the region of the Earth’s radiation belts and in regions close to the geomagnetic equator. As a result of more than 1.5 years of observation, it is demonstrated that short increases in the intensity of electrons of subrelativistic energies are detected not only in the regions of the near-Earth space known as “precipitation zones” (1.7 < L < 2.5), but in high-latitude regions (up to the geomagnetic equator, L < 1.1) as well. Two types of increases of the electron counting rate are found: either fairly regular increases repeating on successive orbits or increases local in time. The latter type of increases can be caused by a short enhancement of electron flux on a given drift shell. The results of our measurements have shown that the duration of the detected increases in intensity can be rather short, as little as 20–30 s. Therefore, in the case of large amplitudes, such increases of the counting rate of electrons can imitate astrophysical events of the type of cosmic gamma-ray bursts in the detectors of hard X-ray and gamma radiation.

Radial diffusion and MHD particle simulations of relativistic electron transport by ULF waves in the September 1998 storm

In an MHD particle simulation of the September 1998 magnetic storm the evolution of the radiation belt electron radial flux profile appears to be diffusive, and diffusion caused by ULF waves has been invoked as the probable mechanism. In order to separate adiabatic and nonadiabatic effects and to investigate the radial diffusion mechanism during this storm, in this work we solve a radial diffusion equation with ULF wave diffusion coefficients and a time‐dependent outer boundary condition, and the results are compared with the phase space density of the MHD particle simulation. The diffusion coefficients include contributions from both symmetric resonance modes (ω ≈ mωd, where ω is the wave frequency, m is the azimuthal wave number, and ωd is the bounce‐averaged drift frequency) and asymmetric resonance modes (ω ≈ (m ± 1)ωd). ULF wave power spectral densities are obtained from a Fourier analysis of the electric and magnetic fields of the MHD simulation and are used in calculating the radial diffusion coefficients. The asymmetric diffusion coefficients are proportional to the magnetic field asymmetry, which is also calculated from the MHD field. The resulting diffusion coefficients vary with the radial coordinate L (the Roederer L‐value) and with time during different phases of the storm. The last closed drift shell defines the location of the outer boundary. Both the location of the outer boundary and the value of the phase space density at the outer boundary are time‐varying. The diffusion calculation simulates a 42‐hour period during the 24–26 September 1998 magnetic storm, starting just before the storm sudden commencement and ending in the late recovery phase. The differential flux calculated in the MHD particle simulation is converted to phase space density. Phase space densities in both simulations (diffusion and MHD particle) are functions of Roederer L‐value for fixed first and second adiabatic invariants. The Roederer L‐value is calculated using drift shell tracing in the MHD magnetic field, and particles have zero second invariant. The radial diffusion calculation reproduces the main features of the MHD particle simulation quite well. The symmetric resonance modes dominate the radial diffusion, especially in the inner and middle L region, while the asymmetric resonances are more important in the outer region. Using both symmetric and asymmetric terms gives a better result than using only one or the other and is better than using a simple power law diffusion coefficient. We find that it is important to specify the value of the phase space density on the outer boundary dynamically in order to get better agreement between the radial diffusion simulation and the MHD particle simulation.

Impact of ULF oscillations in solar wind dynamic pressure on the outer radiation belt electrons

This work addresses radial transport of outer radiation belt electrons due to ULF disturbances of geomagnetic field. A new approach to calculating inductive electric field is developed and implemented using a dynamical model of the storm‐time geomagnetic field. The approach is used to analyze the effects associated with solar wind dynamic pressure (Pdyn). It is found that Pdyn produces large‐scale electric fields with maximum intensity at noon and midnight local time. Derived fields are used in test particle calculations of relativistic electron dynamics. The results show that even moderate oscillations of Pdyn typical for quiet‐time magnetosphere can result in rapid electron scattering across the drift shells, which identifies Pdyn as one of the primary mechanisms of radial transport in the belt. Calculations show that electron motion is inconsistent with radial diffusion, and hence a more detailed description is required for accurate predictions of electron fluxes in the belt.

Low energy electron microsignatures at the orbit of Tethys: Cassini MIMI/LEMMS observations

We report on low energy electron microsignature observations by the Low Energy Magnetospheric Measurement System (LEMMS) in the vicinity of Tethys's L‐shell, during the first seven orbits of the Cassini mission. Tethys, due to its large size, is the source of strong microsignatures. Shallower absorption features seen are the result of aged Tethys microsignatures rather than the effect of its small Lagrangian moons. Several remarkable observations are also discussed: the displacement of the microsignatures indicates that the drift shell deviation from axisymmetry is greater than previously expected. Midnight to dawn wakes have drifted toward the planet whereas noon to dusk ones have drifted outward, revealing possible magnetospheric convection effects. Double microsignatures seen for the first time, suggest low radial diffusion coefficients and point to dynamic events in the magnetosphere.

Multisatellite determination of the relativistic electron phase space density at geosynchronous orbit: Methodology and results during geomagnetically quiet times

We develop and test a methodology to determine the relativistic electron phase space density distribution in the vicinity of geostationary orbit by making use of the pitch‐angle resolved energetic electron data from three Los Alamos National Laboratory geosynchronous Synchronous Orbit Particle Analyzer instruments and magnetic field measurements from two GOES satellites. Owing to the Earth's dipole tilt and drift shell splitting for different pitch angles, each satellite samples a different range of Roederer L* throughout its orbit. We use existing empirical magnetic field models and the measured pitch‐angle resolved electron spectra to determine the phase space density as a function of the three adiabatic invariants at each spacecraft. Comparing all satellite measurements provides a determination of the global phase space density gradient over the range L* ∼ 6–7. We investigate the sensitivity of this method to the choice of the magnetic field model and the fidelity of the instrument intercalibration in order to both understand and mitigate possible error sources. Results for magnetically quiet periods show that the radial slopes of the density distribution at low energy are positive, while at high energy the slopes are negative, which confirms the results from some earlier studies of this type. We further show that the observed gradients near geosynchronous are generally small, making them very sensitive to both calibration and magnetic field model choice. This paper lays the foundation for this method for future applications to disturbed periods and for future inclusion of additional satellite data.

Fluxes of Quasi-trapped Electrons with Energies &gt;0.08 MeV in the Near-Earth Space on Drift Shells L &lt; 2

We study the characteristics of fluxes of electrons with energy >80 keV in the near-Earth space regions corresponding to the drift shells L = 1.7, 1.4, and 1.1 observed during the entire period of the GRIF experiment onboard the Spectr module of the Mir orbital station from October 1995 to June 1997. The obtained geographic maps of the distribution of electron fluxes at the height of the station flight (400 km) and, also, the estimates of the spectra indicate that the South-Atlantic Anomaly provides for a mechanism of stable replenishment for shells with L < 1.5. The mechanism of stable replenishment of shells with L < 1.5 may be due to the scattering, in the residual atmosphere, of electrons from the inner radiation belt precipitating into the region of the South-Atlantic Anomaly.