Magnetospheric ULF waves driven by external sources

The multi-spacecraft missions (Cluster and THEMIS) observations allowed to collect large data base for Ultra Low Frequency (ULF) waves properties, their localization, and sources. Here we focused mainly on these recent results. Studies of the source and characteristics of ULF waves can help in the understanding of the interaction and energy transport from the solar wind to the magnetosphere. In the presented paper peculiarities of the ULF waves are presented in depends of their generation source: surface magnetopause instabilities, magnetospheric cavity modes, and solar wind sudden impulses (SI). Permanent observations of the ULF waves involve existence of the permanent source and, as the previous studies showed, the contributions to Pc4-Pc5 ULF wave power from the external sources are larger than the contribution from internal magnetosphere sources. The Kelvin-Helmholtz instability (KHI) can generate classical ULF resonant waves with spatially localized amplitude maximum on the magnetosphere flanks. As observations show the constraint satisfaction of KHI development is quite rare. SI in the solar wind dynamic pressure generate ULF waves with different polarization and frequency close to the frequency of the local field line resonance (FLR). Wide range of temporal and amplitude characteristics of the solar wind dynamics can generate magnetosphere cavity modes and magnetosonic perturbations which penetrate through the magnetosphere and can couple with the local FLR modes. The observed dependence of ULF waves properties on their localization corresponds well to these sources and their occurrence

Vortex and ULF wave structures in the plasma sheet of the Earth magnetosphere

We studied the ULF wave packet propagation in the Earth plasma sheet making use of the magnetic field measurements from FGM detector and plasma properties from CORRAL detector aboard the Interball-Tail spacecraft. The MHD vortex structures were observed simultaneously with the Pc5 ULF waves. The vortex spatial scale was found to be about 1200-3600 km and the velocity is 4-16 km/s transverse to the background magnetic field. We studied numerically the dynamics of the initial vortex perturbations in the plasma system with parameters observed in the Earth plasma sheet. The system with the vector nonlinearity was processed making use of the full reduction scheme. The good agreement of the experimental value of the vortex structure velocity with numerical results was obtained. The velocity was found to be close to the local plasma drift velocity

On the generation of probabilistic forecasts from deterministic models

Most of the methods that produce space weather forecasts are based on deterministic models. In order to generate a probabilistic forecast, a model needs to be run several times sampling the input parameter space, in order to generate an ensemble from which the distribution of outputs can be inferred. However, ensemble simulations are costly and often preclude the possibility of real-time forecasting. We introduce a simple and robust method to generate uncertainties from deterministic models, that does not require ensemble simulations. The method is based on the simple consideration that a probabilistic forecast needs to be both accurate and well calibrated (reliable). We argue that these two requirements are equally important, and we introduce the Accuracy-Reliability cost function that quantitatively measures the trade-off between accuracy and reliability. We then define the optimal uncertainties as the standard deviation of the Gaussian distribution that minimizes the cost function. We demonstrate that this simple strategy, implemented here by means of a deep neural network, produces accurate and well-calibrated forecasts, showing examples both on synthetic and real-world space weather data

Outer radiation belt electron lifetime model based on combined Van Allen Probes and Cluster VLF measurements

The flux of energetic electrons in the outer radiation belt shows a high variability. The interactions of electrons with very low frequency (VLF) chorus waves play a significant role in controlling the flux variation of these particles. Quantifying the effects of these interactions is crucially important for accurately modeling the global dynamics of the outer radiation belt and to provide a comprehensive description of electron flux variations over a wide energy range (from the source population of 30 keV electrons up to the relativistic core population of the outer radiation belt). Here, we use a synthetic chorus wave model based on a combined database compiled from the Van Allen Probes and Cluster spacecraft VLF measurements to develop a comprehensive parametric model of electron lifetimes as a function of L‐shell, electron energy, and geomagnetic activity. The wave model takes into account the wave amplitude dependence on geomagnetic latitude, wave normal angle distribution, and variations of wave frequency with latitude. We provide general analytical formulas to estimate electron lifetimes as a function of L‐shell (for L = 3.0 to L = 6.5), electron energy (from 30 keV to 2 MeV), and geomagnetic activity parameterized by the AE index. The present model lifetimes are compared to previous studies and analytical results and also show a good agreement with measured lifetimes of 30 to 300 keV electrons at geosynchronous orbit

Wave-particle interactions in the outer radiation belts

Data from the Van Allen Probes have provided the first extensive evidence of non-linear (as opposed to quasilinear) wave-particle interactions in space, with the associated rapid (fraction of a bounce period) electron acceleration, to hundreds of keV by Landau resonance, in the parallel electric fields of time domain structures (TDS) and very oblique chorus waves. The experimental evidence, simulations, and theories of these processes are discussed

Structure of a quasi-parallel shock front

The aim of this study is to compare observations of the magnetic field structure of observed quasi-parallel collisionless shock fronts with the results obtained analytically. A two-fluid analytic model of the shock front structure was derived under the assumptions that the shock is stationary and planar. The ion and electron kinetic pressures were assumed to be scalar, and polytropic state equations were used. The results of this analytical approach show that the shock magnetic field has an oscillatory structure. Venus Express (VEX) observations of the Venusian bow shock have been used to validate these theoretical findings. The Venusian bow shock and corresponding foreshock are significantly smaller than those of Earth. Thus, observations of the underlying structure of the quasi-parallel shock at Venus are not masked by the presence of high-amplitude waves and nonlinear structures originating in the foreshock. It is shown that the structure of the shock front, as observed by VEX, has a very strong similarity to the structure obtained analytically

Probability of relativistic electron trapping by parallel and oblique whistler-mode waves in Earth's radiation belts

We investigate electron trapping by high-amplitude whistler-mode waves propagating at small as well as large angles relative to geomagnetic field lines. The inhomogeneity of the background magnetic field can result in an effective acceleration of trapped particles. Here, we derive useful analytical expressions for the probability of electron trapping by both parallel and oblique waves, paving the way for a full analytical description of trapping effects on the particle distribution. Numerical integrations of particle trajectories allow to demonstrate the accuracy of the derived analytical estimates. For realistic wave amplitudes, the levels of probabilities of trapping are generally comparable for oblique and parallel waves, but they turn out to be most efficient over complementary energy ranges. Trapping acceleration of 100 keV electrons

Energy repartition and entropy generation across the Earth’s bow shock: MMS observations

The evolution of plasma entropy and the process of plasma energy redistribution at the collisionless plasma shock front are evaluated based on the high temporal resolution data from the four Magnetospheric Multiscale spacecraft during the crossing of the terrestrial bow shock. The ion distribution function has been separated into the populations with different characteristic behaviors in the vicinity of the shock: the upstream core population, the reflected ions, the gyrating ions, the ions trapped in the vicinity of the shock, and the downstream core population. The values of ion and electron moments (density, bulk velocity, and temperature) have been determined separately for these populations. It is shown that the solar wind core population bulk velocity slows down mainly in the ramp with the electrostatic potential increase but not in the foot region as it was supposed. The reflected ion population determines the foot region properties, so the proton temperature peak in the foot region is an effect of the relative motion of the different ion populations, rather than an actual increase in the thermal speed of any of the ion population. The ion entropy evaluated showed a significant increase across the shock: the enhancement of the ion entropy occurs in the foot of the shock front and at the ramp, where the reflected ions are emerging in addition to the upstream solar wind ions, the anisotropy growing to generate the bursts of ion-scale electrostatic waves. The entropy of electrons across the shock does not show a significant change: electron heating goes almost adiabatically

Effects of equatorial chorus wave normal azimuthal distribution on wave propagation

The non-ducted propagation characteristics of the VLF waves in the inner magnetosphere were studied with respect to their frequency, source localization, and initial polar angle between the wave-normal and the background magnetic field and azimuthal angle. The ray tracing software based on multi-components cold plasma approach was developed by use of the Olson-Pfitzer magnetic field model and the GCPM model of plasma density. We described dynamics of the wave-normals direction during its propagation and magnetospheric reflection. We showed that whistler waves can be reflected when lower hybrid resonance frequency becomes greater than the wave frequency: ωLH > ω. It corresponds to magnetic latitude λ ∼ 50°. The simulation results confirmed the inapplicability of the quasi-longitudinal approximation to describe the propagation of magnetospheric whistlers. The simulation results of chorus emissions propagation, which use realistic distributions of waves on the initial parameters are presented. Particularly, we obtained distributions of chorus emission waves in dependence on the wave-normal directions for different magnetic latitudes, with respect to initial azimuthal angle. It is required for studying diffusive processes in the radiation belts. The results are found to be in a good agreement with the CLUSTER STAFF-SA measurements

Transverse eV ion heating by random electric field fluctuations in the plasmasphere

International audienceCharged particle acceleration in the Earth inner magnetosphere is believed to be mainly due to thelocal resonant wave-particle interaction or particle transport processes. However, the Van AllenProbes have recently provided interesting evidence of a relatively slow transverse heating of eVions at distances about 2–3 Earth radii during quiet times. Waves that are able to resonantly interactwith such very cold ions are generally rare in this region of space, called the plasmasphere. Thus,non-resonant wave-particle interactions are expected to play an important role in the observed ionheating. We demonstrate that stochastic heating by random transverse electric field fluctuations ofwhistler (and possibly electromagnetic ion cyclotron) waves could explain this weak and slowtransverse heating ofHþandOþions in the inner magnetosphere. The essential element of the pro-posed model of ion heating is the presence of trains of random whistler (hiss) wave packets, withsignificant amplitude modulations produced by strong wave damping, rapid wave growth, or asuperposition of wave packets of different frequencies, phases, and amplitudes. Such characteristicscorrespond to measured characteristics of hiss waves in this region. Using test particle simulationswith typical wave and plasma parameters, we demonstrate that the corresponding stochastic trans-verse ion heating reaches 0.07–0.2 eV/h for protons and 0.007–0.015 eV/h forOþions. This globaltemperature increase of the Maxwellian ion population from an initialTi0:3 eV could potentiallyexplain the observation