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The most abundant neutral constituent in the exospheric region (i.e., beyond = 500 km altitude) is the atomic hydrogen (H); however, its density distributions predicted by physics-based models have been challenged by satellite-based observations of its far ultraviolet emissions. This discrepancy may impact magnetospheric ions' densities and velocities since numerous chemistry and ion-neutral coupling interactions rely sensitively on the underlying neutral hydrogen population. The Polar Wind Outflow Model a first-principled model for relevant ion species in the high-latitude ionosphere, is employed to investigate the role of neutral H on the ionospheric outflow. Specifically, variability in the outflow of ionospheric H+, He+, N+, and O+ as a response to systematic enhancement and depletion of H number densities were simulated. The altitudedependent ion density and energy partition profiles vary with neutral H density, solar activities, and ion species. These findings suggest that the exosphere plays a crucial role in controlling the production and loss of ions through ionospheric chemistry, as well as the energy contributions by altering ionneutral-electron collisions and the ambipolar electric field to the high-latitude ionospheric outflow. As a result, the escape rates of the ionospheric outflow are directly associated with exospheric distributions. This work potentially helps understand the dominant mechanisms of atmospheric escape, particularly during a hydrogen-rich early Earth's and exoplanet's atmosphere, which is known to play a significant role in understanding the evolution of Earth's atmosphere. [ABSTRACT FROM AUTHOR]

The most abundant neutral constituent in the exospheric region (i.e., beyond ≈ 500 km altitude) is the atomic hydrogen (H); however, its density distributions predicted by physics-based models have been challenged by satellite-based observations of its far ultraviolet emissions. This discrepancy may impact magnetospheric ions’ densities and velocities since numerous chemistry and ion-neutral coupling interactions rely sensitively on the underlying neutral hydrogen population. The Polar Wind Outflow Model a first-principled model for relevant ion species in the high-latitude ionosphere, is employed to investigate the role of neutral H on the ionospheric outflow. Specifically, variability in the outflow of ionospheric H+, He+, N+, and O+ as a response to systematic enhancement and depletion of H number densities were simulated. The altitude-dependent ion density and energy partition profiles vary with neutral H density, solar activities, and ion species. These findings suggest that the exosphere plays a crucial role in controlling the production and loss of ions through ionospheric chemistry, as well as the energy contributions by altering ion-neutral-electron collisions and the ambipolar electric field to the high-latitude ionospheric outflow. As a result, the escape rates of the ionospheric outflow are directly associated with exospheric distributions. This work potentially helps understand the dominant mechanisms of atmospheric escape, particularly during a hydrogen-rich early Earth’s and exoplanet’s atmosphere, which is known to play a significant role in understanding the evolution of Earth’s atmosphere.

This paper is devoted to the 80th anniversary of the discovery of Alfven waves, which play an important role in physics, radiophysics, astrophysics, and Earth physics. The emphasis is on the ponderomotive redistribution of plasma in the Earth's magnetosphere under the action of Alfven and ion-cyclotron waves. At relatively small distances from the Earth, the ponderomotive force is buoyant, i.e., is directed upwards, regardless of whether an Alfven wave propagates towards the Earth or away from it. In the near-equatorial zone of the central regions of magnetosphere, waves in the Pc 1 range push the plasma to the minimum of geomagnetic field, so that a maximum of plasma density arises on the equator at sufficiently high wave intensity. A bifurcation occurs at the magnetosphere's periphery, and the maximum is split into two maxima, the distance between which increases while moving away from the Earth. The polar wind, acceleration of heavy ions, and fictitious nonlinearity of the surface impedance of the Earth's crust are also briefly discussed. [ABSTRACT FROM AUTHOR]

In the study of the ponderomotive action of Alfvén waves on near-Earth plasma, the general formula for ponderomotive forces, known in classical electrodynamics of continuous media, was previously used. The formula does not explicitly take into account the multi-ion composition of the plasma. Under the action of the waves, significant changes were found in macroscopic parameters — plasma density and velocity. Plasma in Earth’s magnetosphere contains ions with different charge-to-mass ratios. Besides hydrogen and helium ions, the plasma has an admixture of oxygen ions of ionospheric origin, as well as an admixture of other heavy ions. In this connection, a wide range of problems arise on the ponderomotive separation of ions of various types. To solve these problems, it is proposed to use partial ponderomotive forces and to describe the plasma not by hydrodynamic, but by quasi-hydrodynamic equations. In this paper, we discuss the derivation of partial forces for a traveling monochromatic Alfvén wave, and also suggest a method for deriving more general formulas by expanding the classical formula, known in macroscopic electrodynamic, into the sum of partial forces. The ponderomotive separation of ions is illustrated by the example of the problem for diffusion equilibrium of magnetospheric plasma. We propose a hypothesis that Alfvén waves redistribute plasma along geomagnetic field lines in such a way that the plasma at the magnetic field minima is characterized by an increased content of heavy ions. We suggest that a small admixture of heavy ions exists in the polar wind jet stream. The article is dedicated to the 80th anniversary of the discovery of Alfvén waves.

The polar wind, consisting of low‐energy ions and electrons, is an outflow along the open magnetic field lines from the polar cap ionosphere to the magnetosphere. Previous studies found that both solar radiation and solar wind electromagnetic energy are the two main energy sources for the polar wind. The polar rain, being field‐aligned precipitating electrons from the solar wind to the polar cap, may provide additional energies for the polar wind. This scenario is complicated as simulation studies show that polar rain changes the electric potential structures over the polar cap ionosphere. It is unclear how the polar rain affects the polar wind ion outflow. In this study, we show a positive correlation between the polar wind and the polar rain. Meanwhile, the polar wind is generally diminished in regions with strong Earth's magnetic field, suggesting the |B| modulates the penetration depth of the polar rain through the magnetic mirror force and thus the energy dissipation of the polar rain. Therefore, the polar rain can be an additional energy source for the polar wind although the polar rain has generally smaller energies and intensities than the particle precipitations in the auroral regions. Key Points: Both the density and the particle flux of the polar wind ion outflow are positively correlated with the energy flux of the polar rainDensity, velocity, and particle flux of the polar wind ion outflow are higher in regions with smaller Earth's magnetic strengthThe polar rain is an energy source for the polar wind from the nightside ionosphere during geomagnetic quiet times [ABSTRACT FROM AUTHOR]

In the past decade, many observations of transversely heated low energy protons were reported in the inner magnetosphere. Interestingly, most of the time heated protons were observed along with magnetosonic waves. Due to the strong correlation, it was often assumed that magnetosonic waves were responsible for the heating of low energy protons. By performing a case study under unusually disturbed geomagnetic conditions, this paper unravels the controversial relationship between the observed pitch angle anisotropy of warm protons and the accompanying magnetosonic waves in the inner magnetosphere. We perform a comparative analysis involving two nearly identical cases of pitch angle anisotropy of warm protons in low L-shell region–one with magnetosonic waves and one without them. It is found that magnetosonic waves are not responsible for primary heating of low-energy protons and may just marginally alter the shape of the distribution of heated protons in the events analyzed. Based on the recent Cluster and POLAR observations, we also show how the recirculated polar wind plasma in the Earth’s magnetosphere can cause the concurrent appearance of heated protons and magnetosonic waves.

Ionospheric molecular ions, such as NO+, N2+ and O2+, are gravitationally bound, and are expected to undergo recombination to form a pair of neutral atoms, due to short dissociative recombination lifetime. Therefore, they are expected to be relatively cold in the Earth’s atmosphere, compared with light ions such as H+ and He+, or even heavier ions such as N+ or O+. However, several spacecraft missions observed their presence in the high-altitude ionosphere and the magnetosphere, predominantly during the geomagnetically active times. This hints to the possibility that molecular ions have the ability to acquire sufficient energy in a very short time, and can be used as tracers of mass differentiated vertical transport to understand the mechanisms responsible for “fast ionospheric outflow.” In this letter, we review the observational data sets that reported on the abundances of molecular ions in the Earth’s magnetosphere-ionosphere system, starting from their first observations by the Sputnik III mission, to the current Arase (ERG) satellite and Enhanced Polar Outflow Probe (e-POP) missions. The available data suggests that molecular ions are quite abundant in the lower atmosphere at all times, but are only seen in the high-altitude ionosphere and magnetosphere during the times of increased geomagnetic activity.

Cold ions with low (a few eV) thermal energies and also often low bulk drift energies, dominate the ion population in the Earth’s magnetosphere. These ions mainly originate from the ionosphere. Here we concentrate on cold ions in the high latitude polar regions, where magnetic field lines are open and connected to the magnetotail. Outflow from the ionosphere can modify the dynamics of the magnetosphere. In-situ observations of low energy ions are challenging. In the low-density polar regions the equivalent spacecraft potential is often large compared to cold ion energies and the ions cannot reach the spacecraft. Rather, a supersonic ion flow creates an enhanced wake. The local electric field associated with this wake can be used to detect the drifting cold ions, and this wake technique can be used for statistical studies. In this paper, we review some of the key results obtained from this technique. These results help us to understand how cold ionospheric outflow varies with various conditions of solar activities and the Earth’s intrinsic magnetic field.

Abstract Significant polar topside total electron content (topTEC) enhancement (PTTE) above 1,336 km altitude is reported for the first time. The results are based on GPS measurements during 2008–2019 from NASA's Jason‐2 satellite with zenith‐oriented antennas. The observations show increasing topTEC toward the southern polar cap at geomagnetic latitudes poleward of 65°S, where TEC values are normally very low. A case study for the 2013 St. Patrick's Day storm indicates that the enhancement can exceed 5.5 TEC units above the dayside ambient state, corresponding to 78% increase. Comparisons with COSMIC/FORMOSAT‐3 topTEC measurements above 800 km altitude confirm that PTTE events are observed from both Jason‐2 and COSMIC on the same day. Our statistical analysis of the Jason‐2 data in the southern polar region reveals that PTTE mostly occurs on the dayside, with a seasonal preference of southern summer, and preferentially during geomagnetically disturbed days but can also occur during quiet days. PTTE during storm days shows increased occurrence, magnitude, and deviation from the mean in the cusp region compared with quiet days. Our case analysis indicates that PTTE is observed simultaneously with the effect of tongue of ionization. This suggests that the during storms, dayside F region plasma moving poleward following the antisunward plasma convection may also be part of the PTTE source, and the plasma upflow driven by the polar wind may act to cause PTTE.

Significant polar topside total electron content (topTEC) enhancement (PTTE) above 1,336 km altitude is reported for the first time. The results are based on GPS measurements during 2008–2019 from NASA's Jason‐2 satellite with zenith‐oriented antennas. The observations show increasing topTEC toward the southern polar cap at geomagnetic latitudes poleward of 65°S, where TEC values are normally very low. A case study for the 2013 St. Patrick's Day storm indicates that the enhancement can exceed 5.5 TEC units above the dayside ambient state, corresponding to 78% increase. Comparisons with COSMIC/FORMOSAT‐3 topTEC measurements above 800 km altitude confirm that PTTE events are observed from both Jason‐2 and COSMIC on the same day. Our statistical analysis of the Jason‐2 data in the southern polar region reveals that PTTE mostly occurs on the dayside, with a seasonal preference of southern summer, and preferentially during geomagnetically disturbed days but can also occur during quiet days. PTTE during storm days shows increased occurrence, magnitude, and deviation from the mean in the cusp region compared with quiet days. Our case analysis indicates that PTTE is observed simultaneously with the effect of tongue of ionization. This suggests that the during storms, dayside F region plasma moving poleward following the antisunward plasma convection may also be part of the PTTE source, and the plasma upflow driven by the polar wind may act to cause PTTE. Plain Language Summary: Significant polar topside total electron content (topTEC) enhancement (PTTE) above 1,336 km altitude is reported for the first time. The results are based on GPS measurements from NASA's Jason‐2 satellite during 2008–2018. The observations show increasing topside TEC toward the southern polar cap where TEC values are normally very low. Comparisons with COSMIC/FORMOSAT‐3 topside TEC measurements confirm that PTTE events are observed from both Jason‐2 and COSMIC on the same day. Our statistical analysis reveals that PTTE mostly occurs in the southern cusp and dayside polar cap, with a seasonal preference of summer, and preferentially during geomagnetically disturbed days but can also occur during quiet days. PTTE during storm days shows increased occurrence, magnitude, and deviation from the mean in the cusp region compared with quiet days. Our case analysis indicates that PTTE is observed simultaneously with the effect of tongue of ionization. This suggests that the during storms, dayside F region plasma moving poleward following the antisunward plasma convection may also be part of the PTTE source, and the plasma upflow driven by the polar wind may act to cause PTTE. Key Points: NASA's Jason‐2 satellite zenith‐viewing GPS total electron content (TEC) measurements spanning 2008–2018 are analyzedSignificant increases of TEC above 1,336 km altitude in the southern polar region are reported for the first timeThe polar topside TEC enhancement (PTTE) appears preferentially during geomagnetic storms and during summer [ABSTRACT FROM AUTHOR]

The escape of heavy ions from the Earth atmosphere is a consequence of energization and transport mechanisms, including photoionization, electron precipitation, ion‐electron‐neutral chemistry, and collisions. Numerous studies considered the outflow of O+ ions only, but ignored the observational record of outflowing N+. In spite of 12% mass difference, N+ and O+ ions have different ionization potentials, ionospheric chemistry, and scale heights. We expanded the Polar Wind Outflow Model (PWOM) to include N+ and key molecular ions in the polar wind. We refer to this model expansion as the Seven Ion Polar Wind Outflow Model (7iPWOM), which involves expanded schemes for suprathermal electron production and ion‐electron‐neutral chemistry and collisions. Numerical experiments, designed to probe the influence of season, as well as that of solar conditions, suggest that N+ is a significant ion species in the polar ionosphere and its presence largely improves the polar wind solution, as compared to observations. Plain Language Summary: Nitrogen is the most abundant element in the Earth's atmosphere. Around 78% N2 and 21% O2 form the air we breathe and expand into high‐altitude atmosphere, the thermosphere, and eventually the ionosphere. The neutral molecules in the ionosphere are ionized by solar radiation, and some of them break up into atoms, and others become charged particles. The ionospheric ions with sufficient energy can flow out into space, and the abundances of these outflowing ionospheric ions highly impact the near‐Earth plasma properties. Studies focused on outflowing O+ ions have been conducted for several years. However, the contribution of N+ ions to the outflow solution is still largely unknown due to the instrumental limitations. This letter addresses the transport and energization of ionospheric N+ ions based on theoretical predictions, and examines the role of N+ ions to the collision and chemistry in the topside ionosphere. This study shows that N+ ions are important components in the high‐altitude polar ionosphere and their abundances can be affected by the sunlight and seasonal variations. Key Points: We developed a seven‐ion polar wind model (7iPWOM), which solves for the outflowing N+ ionsN+ ions are the second most abundant ionospheric species, up to 1,200 kmThe presence of N+ ions improves the overall polar wind solution, when compared with observations [ABSTRACT FROM AUTHOR]

Ionospheric outflow is the flow of plasma initiated by a loss of equilibrium along a magnetic field line, which induces an ambipolar electric field due to the separation of electrons and ions in a gravitational field and other mass‐dependent sources. We have developed an ionospheric outflow model using the transport equations to determine the number of particles that flow into the outer magnetosphere of Jupiter. The model ranges from 1,400 km in altitude above the 1 bar level to 2.5 RJ along the magnetic field line and considers H+ and H3+ as the main ion constituents. Previously, only pressure gradients and gravitational forces were considered in modeling polar wind. However, at Jupiter we need to evaluate the effect of field‐aligned currents present in the auroral regions due to the breakdown of corotation in the magnetosphere, along with the centrifugal force exerted on the particles due to the fast planetary rotation rate. The total number flux from both hemispheres is found to be 1.3–1.8 × 1028 s−1 comparable in total number flux to the Io plasma source. The mass flux is lower due to the difference in ion species. This influx of protons from the ionosphere into the inner and middle magnetosphere needs to be included in future assessments of global flux tube dynamics and composition of the magnetosphere system. Key Points: An ionospheric outflow model is developed for use at Jupiter's auroral regionsThe model evaluates the effect of field‐aligned currents and centrifugal forcesA total number flux of 1.3 – 1.8 × 1028 s−1 is found, which is comparable to number flux from Io [ABSTRACT FROM AUTHOR]

Ionospheric outflow is driven by an ambipolar electric field induced due to the separation of electrons and ions in a gravitational field when equilibrium along a magnetic field line is lost. A model of ionospheric outflow at Saturn was developed using transport equations to estimate the number of charged particles that flow from the auroral regions into the magnetosphere. The model evaluates the outflow from 1,400 km in altitude above the 1 bar level, to 3 RS along the field line. The main ion constituents evaluated are R+ and R3+. We consider the centrifugal force exerted on the particles due to a fast rotation rate, along with the effects of field‐aligned currents present in the auroral regions. The total number flux from both auroral regions is found to be 5.5–13.0×1027 s−1, which relates to a total mass source of 5.5–17.7 kg s−1. These values are on average an order of magnitude higher than expected without the additional effects of centrifugal force and field‐aligned currents. We find the ionospheric outflow rate to be comparable to the lower estimates of the mass loading rate from Enceladus and are in agreement with recent Cassini observations. This additional mass flux into the magnetosphere can substantially affect the dynamics and composition of the inner and middle magnetosphere of Saturn. Key Points: An ionospheric outflow model is developed for use at Saturn's auroral regionsThe presence of field‐aligned currents and centrifugal forces enhances outflow by an order of magnitudePredicted total outflow flux rate of 5.5–13.0×1027 s−1 is comparable to flux calculated from Cassini data [ABSTRACT FROM AUTHOR]

When the geomagnetic field is weak, the small mirror force allows precipitating charged particles to deposit energy in the ionosphere. This leads to an increase in ionospheric outflow from the Earth's polar cap region, but such an effect has not been previously observed because the energies of the ions of the polar ionospheric outflow are too low, making it difficult to detect the low‐energy ions with a positively charged spacecraft. In this study, we found an anticorrelation between ionospheric outflow and the strength of the Earth's magnetic field. Our results suggest that the electron precipitation through the polar rain can be a main energy source of the polar wind during periods of high levels of solar activity. The decreased magnetic field due to spatial inhomogeneity of the Earth's magnetic field and its effect on outflow can be used to study the outflow in history when the magnetic field was at similar levels. Plain Language Summary: Earth, Venus, and Mars have very different atmospheres although they are thought to possess similar atmospheres about 4.5 billion years ago. One of the main reasons considered for the losses of H2O and O2 is dramatic decreases in the dipole magnetic field on Venus and Mars. Although the Earth has kept its intrinsic magnetic field, there are variations in both orientation and strength. Previous observations have confirmed that atmospheric loss is controlled by the orientation of the geomagnetic dipole. However, the effect of variations in the strength of the Earth's magnetic field on atmospheric outflow has not been addressed. In this study, we have focused on the polar wind, the dominant ionospheric outflow from the polar regions. Our results reveal an anticorrelation between the outflow and the strength of the Earth's magnetic field, offering us a clue on the ionospheric and atmospheric evolution with a changing magnetic field. Key Points: The density and the particle flux of the polar wind are revealed to be anticorrelated with the strength of the Earth's magnetic fieldThe polar rain can be the main energy source of the polar wind in the southern hemisphere during periods of high solar activity levelsA strong magnetic field diminishes energy depositions in the polar cap and thus controls the density and particle flux of the polar wind [ABSTRACT FROM AUTHOR]

The theory of plasma density redistribution and polar wind acceleration acceleration under the affect on the magnetosphere of the ponderomotive forces induced by the ultra-low frequency electromagnetic waves is presented. Our attention is focused mainly on the important question about the necessity of experimental verification of fairly certain theoretical predictions. It is pointed out that experimental validation is not only necessary for the development of the theory but also for replenishing the knowledge about the structure and dynamics of the near-Earth space. An original method for indirect verification is presented. The idea of this method is based on the dependence of the foreshock locations on the orientation of the field lines of the interplanetary magnetic field (IMF) in front of the magnetosphere relative to the plane of the geomagnetic equator. [ABSTRACT FROM AUTHOR]

Ionospheric outflow from the polar cap through the polar wind plays an important role in the evolution of the atmosphere and magnetospheric dynamics. Both solar illumination and solar wind energy input are known to be energy sources of the polar wind. However, observational studies of the energy transfer from these two energy sources to the polar wind are difficult. Because of their low energy, polar wind ions are invisible to regular ion detectors onboard a positively charged spacecraft. Using a new technique that indirectly measures these low‐energy ions, we are able to estimate the energy budget of the polar wind. Our results show that solar illumination provides about 107 W of the kinetic energy of the polar wind, in addition to the energy transferred from the solar wind with a maximum rate of about 108 W. The energy transfer efficiency of solar illumination to the kinetic energy of the polar wind is about 6 to 7 orders of magnitude lower than that of the solar wind. Moreover, daily and seasonal changes in the orientation of the geomagnetic dipole axis control solar illumination over the polar cap, modulating both energies of the polar wind and energy transfer efficiencies from the two energy sources. Key Points: Quantitative energy budget of the polar wind outflow has been estimatedSolar wind energy input is the dominant energy source when the ε parameter is higher than 1010 WSolar illumination provides the kinetic energy of the polar wind outflow at a rate of about 107 W, which is lower than the solar wind [ABSTRACT FROM AUTHOR]

The problem of the outflow of ionospheric plasma into the magnetosphere is considered. In particular, the phenomenon of the polar wind observed in the polar cap is studied. The study of this phenomenon is complicated by the fact that the field-alined velocities of individual ions are small, and therefore, the electric field of the positively charged satellite prevents their measurement. This paper examines the measurements carried out on the Interball-2 satellite at altitudes of ~20000 km and compares them with the results of simulations within the framework of the GSM TIP model. It has been demonstrated the GSM TIP model well describes the outflow of H+ ions from the ionosphere to the magnetosphere in the polar cap. [ABSTRACT FROM AUTHOR]

The Naval Research Laboratory Sami3 is Also a Model of the Ionosphere (SAMI3) ionosphere/plasmasphere code is used to examine the physics of a long-lived plasmasphere plume. The May 1994 storm is simulated. Here a plasma density peak was observed in the afternoon sector by multiple spacecraft at geosynchronous orbit on each of 11 continuous days. The storm is modeled by adding a Kp>-driven Volland/Stern-Maynard/Chen analytic convection potential to the self-consistent electric potential that is driven by thermosphere winds. Results are compared to measurements of the cold-ion density from the 1989-046 spacecraft in geosynchronous orbit. We find that many observed features are reproduced by SAMI3 and that high-speed, field-aligned plasma flows from the ionosphere contribute significantly to [ABSTRACT FROM AUTHOR]

Polar wind outflow is an important process through which the ionosphere supplies plasma to the magnetosphere. The main source of energy driving the polar wind is solar illumination of the ionosphere. As a result, many studies have found a relation between polar wind flux densities and solar EUV intensity, but less is known about their relation to the solar zenith angle at the ionospheric origin, certainly at higher altitudes. The low energy of the outflowing particles and spacecraft charging means it is very difficult to measure the polar wind at high altitudes. We take advantage of an alternative method that allows estimations of the polar wind flux densities far in the lobes. We analyze measurements made by the Cluster spacecraft at altitudes from 4 up to 20 R E. We observe a strong dependence on the solar zenith angle in the ion flux density and see that both the ion velocity and density exhibit a solar zenith angle dependence as well. We also find a seasonal variation of the flux density. [ABSTRACT FROM AUTHOR]

Wave-particle interaction is a very important mechanism in describing the outflow of ions at high latitudes and high altitudes. Quasi-linear perpendicular velocity diffusion coefficients are used to describe the effect of wave-particle interactions, therefore it is essential to determine the correct diffusion coefficients that must be used to model the outflow of ions. In this study a Monte Carlo method is used to assess the role of different diffusion coefficients for O+ and H+ ions at high altitudes above the polar cap. Two different sets of diffusion coefficients obtained from Barghouthi [1997]; Barghouthi et al. [1998] and Nilsson et al. [2013] are used. Barghouthi [1997]; Barghouthi et al. [1998] used spectral density measurements from Dynamic Explorer 1 spacecraft (DE-1) observations to calculate the diffusion coefficients, while Nilsson et al. [2013] used spectral density measurements from the Cluster spacecraft to obtain the diffusion coefficients. It was found that diffusion coefficients from Barghouthi [1997]; Barghouthi et al. [1998] in the cusp (aurora) and central polar cap (polar wind) respectively, describe well the observations of ion outflow at altitudes lower than 5 RE, but yield unreasonably high parallel velocities and temperatures at higher altitudes. Also diffusion coefficients from Cluster spectral density measurements produce reasonable results for high altitudes and unreasonably low parallel velocities and temperatures for the low altitude region. Therefore it is suggested that a combination of these diffusion coefficients is used where the diffusion coefficients given by Barghouthi [1997]; Barghouthi et al. [1998] are used at low altitudes and the diffusion coefficients obtained from Cluster measurements are used at high altitudes.