Exterior Cusp Research Articles

Evidence of the Alfvén Transition Layer and Particle Precipitation in the Cusp Region: 3D Global PIC Simulation of the Solar Wind–Earth Magnetosphere Interaction

A transition layer, named the Alfvénic transition layer (or ATL), has been clearly evidenced near the outer boundary of the cusp by experimental observations from the Cluster mission. This layer characterized by a local value of Log M A ∼ 1, where M A is the Alfvén Mach number, allows the bulk flow to transit from super-Alfvénic to sub-Alfvénic from the exterior to the interior side of the outer cusp. The ATL has been observed during northward interplanetary magnetic field orientation, and mainly within the meridian plane. Currently, 3D Particle In Cell (PIC) global simulations of the solar wind–magnetosphere interaction are being performed in order to analyze the cusp region and this layer in detail. Present results stress the following points: (i) the ATL has a 3D structure; (ii) within the meridian plane, the ATL appears as a sublayer within a much more extended slow-mode pattern, and it is almost adjacent and located above the upper edge of the stagnant exterior cusp (SEC); and (iii) the plasma deceleration through the ATL is not uniform in the region located above the cusp. In addition, present preliminary results stress that (a) the spiraled streamlines of ion/electron fluxes converge when approaching the cusp, and their intensity strongly increases; and (b) ion and electron energetic fluxes penetrating the cusp region strongly differ in terms of their penetration depths and are issued from different regions of the magnetosphere/magnetosheath. Our results illustrate the importance of 3D effects used with a PIC simulation approach allowing the analysis of each population simultaneously.

On the behaviour of derivative of algebraic polynomials in the regions with cusps

ABSTRACT In this paper, we study the behavior of derivatives of algebraic polynomials in bounded and unbounded regions of the complex plane. At the same time, both interior and exterior cusp points are allowed on the boundary of such regions. Bernstein-Walsh-type estimates are obtained for derivatives of algebraic polynomials in the specified region with corners for exterior points, as well as Markoff-type estimates for closure of the region. As a result, estimates are found for the derivatives of algebraic polynomials in the whole complex plane. It is also shown that the inequality for the closed region is exact in order for the given region.

The Polar Cusp Seen by Cluster

AbstractThe investigation of the magnetospheric polar cusps was one of the main objectives of the Cluster mission. The four satellites have crossed those regions numerous times over the years and, with their suitable instrumentation, favorable orbits, and unique multipoint measurements, many aspects of the cusp have been unveiled. The first of those is its highly dynamic nature. With four satellites, whatever their altitude and thus their configuration, the spatial/temporal ambiguity has been lifted and a completely new insight into the motion of the cusp and evolution of the transient small‐scale structures within it was given. Second, the high altitude or exterior cusp, its properties and dynamics, magnetic configuration, the energetic particles observed within, and its boundary with the magnetosheath were characterized in a number of case studies and on a statistical basis. Third, the Cluster cusp observations brought a fresh eye on the reconnection process at the magnetopause, including its location and spatio‐temporal variability. Finally, the complete payload with particle, field and wave detectors have made it possible to treat cusp as a plasma physics laboratory to progress our understanding of wave‐particle interaction and turbulence within the cusp. We have no choice but to note that Cluster has been extremely successful for all these matters.

MMS Observations of the Multiscale Wave Structures and Parallel Electron Heating in the Vicinity of the Southern Exterior Cusp

AbstractUnderstanding the physical mechanisms responsible for the cross‐scale energy transport and plasma heating from solar wind into the Earth's magnetosphere is of fundamental importance for magnetospheric physics and for understanding these processes in other places in the universe with comparable plasma parameter ranges. This paper presents observations from the Magnetosphere Multiscale (MMS) mission at the dawn‐side high‐latitude dayside boundary layer on February 25, 2016 between 18:55 and 20:05 UT. During this interval, MMS encountered both the inner and outer boundary layers with quasiperiodic low frequency fluctuations in all plasma and field parameters. The frequency analysis and growth rate calculations are consistent with the Kelvin‐Helmholtz instability (KHI). The intervals within the low frequency wave structures contained several counter‐streaming, low‐ (0–200 eV) and mid‐energy (200 eV–2 keV) electrons in the loss cone and trapped energetic (70–600 keV) electrons in alternate intervals. The counter‐streaming electron intervals were associated with large‐magnitude field‐aligned Poynting fluxes. Burst mode data at the large Alfvén velocity gradient revealed a strong correlation between counter streaming electrons, enhanced parallel electron temperatures, strong anti‐field aligned wave Poynting fluxes, and wave activity from sub‐proton cyclotron frequencies extending to electron cyclotron frequency. Waves were identified as Kinetic Alfvén waves but their contribution to parallel electron heating was not sufficient to explain the >100 eV electrons.

Energy conversion through mass loading of escaping ionospheric ions for different Kp values

Abstract. By conserving momentum during the mixing of fast solar wind flow and slow planetary ion flow in an inelastic way, mass loading converts kinetic energy to other forms – e.g. first to electrical energy through charge separation and then to thermal energy (randomness) through gyromotion of the newly born cold ions for the comet and Mars cases. Here, we consider the Earth's exterior cusp and plasma mantle, where the ionospheric origin escaping ions with finite temperatures are loaded into the decelerated solar wind flow. Due to direct connectivity to the ionosphere through the geomagnetic field, a large part of this electrical energy is consumed to maintain field-aligned currents (FACs) toward the ionosphere, in a similar manner as the solar wind-driven ionospheric convection in the open geomagnetic field region. We show that the energy extraction rate by the mass loading of escaping ions (ΔK) is sufficient to explain the cusp FACs, and that ΔK depends only on the solar wind velocity accessing the mass-loading region (usw) and the total mass flux of the escaping ions into this region (mloadFload), as ΔK ∼ −mloadFloadu2sw∕4. The expected distribution of the separated charges by this process also predicts the observed flowing directions of the cusp FACs for different interplanetary magnetic field (IMF) orientations if we include the deflection of the solar wind flow directions in the exterior cusp. Using empirical relations of u0 ∝ Kp + 1.2 and Fload ∝ exp(0.45Kp) for Kp = 1–7, where u0 is the solar wind velocity upstream of the bow shock, ΔK becomes a simple function of Kp as log10(ΔK) = 0.2 ⋅ Kp + 2 ⋅ log10(Kp + 1.2) + constant. The major contribution of this nearly linear increase is the Fload term, i.e. positive feedback between the increase of ion escaping rate Fload through the increased energy consumption in the ionosphere for high Kp, and subsequent extraction of more kinetic energy ΔK from the solar wind to the current system by the increased Fload. Since Fload significantly increases for increased flux of extreme ultraviolet (EUV) radiation, high EUV flux may significantly enhance this positive feedback. Therefore, the ion escape rate and the energy extraction by mass loading during ancient Earth, when the Sun is believed to have emitted much higher EUV flux than at present, could have been even higher than the currently available highest values based on Kp = 9. This raises a possibility that the ion escape has substantially contributed to the evolution of the Earth's atmosphere.

Cusp dynamics under northward IMF using three‐dimensional global particle‐in‐cell simulations

AbstractThe interaction of the solar wind with the terrestrial magnetosphere is analyzed with the help of three‐dimensional (3‐D) global, full‐electromagnetic particle‐in‐cell (PIC) simulations, in the configuration where the interplanetary magnetic field (IMF) is steadily northward. The present study is mainly focused on the cusp region and associated particle momenta dynamics. Within the present context and to the best of our knowledge, this work represents the first numerical simulation for analyzing the cusp dynamics using a fully self‐consistent 3‐D kinetic and electromagnetic approach. The main goals of the study are the following: (i) to retrieve the main known features of the cusp to validate the use of 3‐D PIC “global” simulations, (ii) to compare with previous results obtained with 3‐D MHD simulations, (iii) to create an updated global view of the cusp based on use of 3‐D PIC simulation, which cannot be obtained from a MHD approach, and (iv) to compare with statistical results from the Cluster mission. In particular, the stagnant exterior cusp (SEC) identified in previous statistical analysis of experimental data is retrieved, and it is possible to more precisely define the edges of the SEC region. In addition, we will focus on cusp features recently observed by the Cluster mission, for example, the Alfvén Transition Layer or ATL and on the features not reproduced by either MHD or the hybrid approach, which have been used to characterize the outer edges of the cusp more clearly.

Turbulence in the Earth's cusp region: The k‐filtering analysis

AbstractOn 13 April 2002, four Cluster spacecraft with separations up to 127 km measured similar turbulence in the exterior cusp during northward interplanetary magnetic field (IMF) Bz. Both the power spectra of magnetic and electric field fluctuations resemble the classical Kolmogorov power law, with the scaling f−1.7 under the proton gyrofrequency fcp (~0.3 Hz), breaks near fcp, and then steepens with the scalings f−2.8 and f−2.0 up to 10 Hz, respectively. The observed ratio of the electric to magnetic field is in agreement with the theoretical values of |δE/δB| for the quasi‐perpendicular kinetic Alfvén waves (KAWs), which reflects the features of Alfvén turbulence. The wave vector and dispersion relation of the turbulence are obtained using k‐filtering technique. The results show that the waves propagate quasi‐perpendicularly to the background magnetic field. The similarity between the experimental and the theoretical dispersion relations indicates that the measured waves are kinetic Alfvén wave. The waves have right‐handed elliptical polarization in the plane perpendicular to k. The main axis of polarization ellipse is perpendicular to the average magnetic field. These features furthermore indicate that the turbulence properties agree well with those of KAW mode. The observed KAW is much possibly produced through resonance mode conversion. We calculate the density gradient vector using multipoint density data and found that the waves propagate basically toward high‐density region. The density gradient in the exterior cusp provides a favorable condition for the resonance converted KAW.

Energetic electrons along the high-latitude magnetopause

Abstract. A case study is presented to determine the source of the energetic electron layer frequently observed along the high-latitude magnetopause. Measurements by the Cluster spacecraft show bursts of field-aligned electrons occurring during time periods with high potential for dayside reconnection. These properties are compared with the expected signatures from several sources including escape from the exterior cusp, acceleration in a reconnection region, and release from the dayside trapping region through reconnection. The observed properties are most consistent with the electrons being released from the magnetosphere due to reconnection. In this model the electrons would flow along the newly reconnected IMF draped along the magnetopause and propagate along the high-latitude magnetopause. These observations demonstrate an active source for populating the energetic particle layer frequently observed along and just outside the high-latitude magnetopause.

Upstream‐generated Pc3 ULF wave signatures observed near the Earth's cusp

Pc3 pulsations (frequency ∼20–100 mHz) which originate in the ion foreshock upstream of the Earth's bow shock due to the interaction between reflected ions and the solar wind are frequently observed in ground‐based pulsation magnetometer data. Previous studies have noted increased Pc3 wave power in the vicinity of the dayside cusp and inferred that the upstream waves gained entry via the cusp, although more recent studies have revealed a more complex picture. Here, we examine Pc3 wave power near local noon observed by search coil magnetometers at three closely‐spaced stations on Svalbard, during times when an extended interval of HF radar backscatter indicative of the cusp is detected by the Hankasalmi SuperDARN radar. The location of the equatorward edge of the HF radar cusp may then be directly compared with the Pc3 wave power measured at three latitudes as the cusp migrates across the stations on a statistical basis. These observations are more consistent with wave entry to the magnetosphere along closed field lines equatorward of the cusp via the ionospheric transistor mechanism of Engebretson et al. (1991a), or weakly coupled fast and Alfvén wave modes, which then map to the low‐latitude boundary layer or outer magnetosphere, rather than with wave entry into the magnetosphere via the cusp proper or exterior cusp.

Cluster energetic electron survey of the high-altitude cusp and adjacent regions

[1] A statistical study of the energetic electron population (E > 37 keV) in the high-altitude cusp and surrounding regions is conducted with 7 years of data from the Cluster spacecraft. The progression of Cluster's orbit during this period allows for a wide range of latitude on the dayside magnetosphere to be surveyed. Locations of the spacecraft are adjusted to account for changes in the solar wind and geomagnetic activity measurements. The survey shows (1) frequent presence of energetic electrons within the high latitude trapping region and exterior cusp, (2) energetic electron flux dropping off rapidly with distance from the magnetosphere into the magnetosheath, (3) a similar spectral power law for the electrons in the outer high latitude trapping region as the exterior cusp, and (4) a pitch angle distribution in the cusp peaking at 90°. These findings indicate the energetic electron population on potentially open field lines in the exterior cusp likely is fed by both the high latitude trapping region as well as local acceleration.

Simultaneous observations of the exterior cusp region

A case study is presented analyzing the properties and spatial extent of the exterior cusp region. The dynamic nature of the exterior cusp makes the large scale properties difficult to measure using a single spacecraft. We use simultaneous cusp observations of the four Cluster spacecraft as well as the Polar spacecraft to monitor the region. On 10–11 March 2006 all five spacecraft observed the exterior cusp in the southern hemisphere mapping out an extended region in latitude spanning 4.5 RE (and possibly up to 9 RE) along the magnetopause. The depth, or dimension of the diamagnetic exterior cusp perpendicular to the magnetopause is measured to be 1.3 RE with simultaneous measurements from the Cluster spacecraft. The multipoint observations provide a unique view of the diamagnetic exterior cusp showing a spatially extended region.

Energetic electrons in the exterior cusp: identifying the source

Abstract. A case study is presented to test the role several different sources may play in populating the exterior cusp with energetic (E>40 keV) electrons. The properties of the electrons measured in the exterior cusp are compared with the expected signatures of three sources in order to weigh the role each source may contribute in populating this region. The potential sources probed are: (1) solar energetic electrons entering the cusp from the solar wind; (2) an equatorial magnetospheric source with particles drifting to high latitudes on the dayside; and (3) a local source accelerating the electrons in situ. From the observations it is likely that local acceleration is the primary source of the energetic electrons in the exterior cusp during this event.

Cluster observations of high-altitude cusp during multiple fast-turning IMF

Using coordinated observations from the Cluster, DMSP and ESR radar, high-altitude cusp was investigated for a time period characterized by four fast reversals of the IMF B Z. On February 12, 2003, Cluster was flying sunward at duskside over the Northern Hemisphere, across the high-altitude northern cusp twice. Both the two crossings are during steady northward IMF interval, whereas ion fluxes detected during the time period are quite different. The cusp in the first crossing is a “typical” northward-IMF one, with short-lived ion injections of evident “reversed” dispersion signatures. In the second crossing, however, the cusp appears to be a region reminiscent of the Stagnant Exterior Cusp (SEC). In addition, evident upward-flowing O+ ion bursts, possibly original from polar ionosphere, are also detected during the second cusp crossing, together with enhancement of trapped magnetospheric-like electron fluxes. We suggest that the SEC-like cusp is likely on newly closed field lines, which were first reconnected (being opened) at low latitudes and later reconnected again (being closed) poleward of the northern cusp.

Transverse‐scale size of Pc3 ULF waves near the exterior cusp

The concept of a geomagnetic field line has been widely used in the study of magnetospheric physical phenomena. For example, the mode in which ULF waves propagate relates to the direction of the field, with the Alfven wave mode propagating along the field direction. Very little is known about the perpendicular extent of the propagating wave. In this paper, wave coherency methods are utilized to analyze ULF waves in the Pc3 band that were simultaneously observed by the Cluster satellites near the exterior cusp and by ground stations at local magnetic noon near the footprint of the cusp. The results show that the coherency of waves observed at the ground on the H component is much larger than that on the D component, which is opposite to that seen by Cluster in space. The coherency between the H component on the ground and the y component in space was higher than the other combination of pairs, with the coherency between the satellite and the Daneborg (DNB) station having the maximum value. These results suggest that the polarization of the waves are rotated by 90° after propagating through the ionosphere, and the magnetic footprint of Cluster is closest to the DNB station at this time. The coherency of the Pc3 waves between the satellites is highly related to the alignment of satellite pairs with respect to the geomagnetic field direction. This alignment may provide a transverse‐scale size of the geomagnetic Pc3 ULF waves near the exterior cusp at ∼900 km with a coherency of 0.65.

Pc3–4 ULF waves at polar latitudes

A search for Pc3–4 wave activity was performed using data from a trans-Antarctic profile of search-coil magnetometers extending from the auroral zone through cusp latitudes and deep into the polar cap. Pc3–4 pulsations were found to be a ubiquitous element of ULF wave activity in all these regions. The diurnal variations of Pc3 and Pc4 pulsations at different latitudes have been statistically examined using discrimination between wave packets (pulsations) and noise. Daily variations of the Pc3–4 wave power differ for the stations at the polar cap, cusp, and auroral latitudes, which suggests the occurrence of several channels of propagation of upstream wave energy to the ground: via the equatorial magnetosphere, cusp, and lobe/mantle. An additional maximum of Pc3 pulsations during early-morning hours in the polar cap has been detected. This maximum, possibly, is due to the proximity of the geomagnetic field lines at these hours to the exterior cusp. The statistical relation between the occurrence of Pc3–4 pulsations and interplanetary parameters has been examined by analyzing normalized distributions of wave occurrence probability. The dependences of the occurrence probability of Pc3–4 pulsations on the IMF and solar wind parameters are nearly the same at all latitudes, but remarkably different for the Pc3 and Pc4 bands. We conclude that the mechanisms of high-latitude Pc3 and Pc4 pulsations are different: Pc3 waves are generated in the foreshock upstream of the quasi-parallel bow shock, whereas the source of the Pc4 activity is related to magnetospheric activity. Hourly Pc3 power has been found to be strongly dependent on the season: the power ratio between the polar summer and winter seasons is ∼8. The effect of substantial suppression of the Pc3 amplitudes during the polar night is reasonably well explained by the features of Alfven wave transmission through the ionosphere. Spectral analysis of the daily energy of Pc3 and Pc4 pulsations in the polar cap revealed the occurrence of several periodicities. Periodic modulations with periods 26, 13 and 8–9 days are caused by similar periodicities in the solar wind and IMF parameters, whereas the 18-day periodicity, observed during the polar winter only, is caused, probably, by modulation of the ionospheric conductance by atmospheric planetary waves. The occurrence of the narrow-band Pc3 waves in the polar cap is a challenge to modelers, because so far no band-pass filtering mechanism on open field lines has been identified.

Response of the magnetosheath‐cusp region to a coronal mass ejection

Cluster made an unusual magnetosheath‐exterior cusp crossing during the first 2.5 hours of a coronal mass ejection (CME) that flowed past Earth for about 7 hours on 24 October 2003. During the first 2.5 hours (1525–1802 UT) the solar wind dynamic pressure remained high and stable though the CME had a discontinuity after 40 min (1605 UT), when the azimuthal flow turned dawnward up to −100 km s−1 and IMF By and Bz changed from highly negative to positive up to 25 nT. The responses of the magnetosheath‐cusp region during the unusual event are presented using Cluster and ground‐based (EISCAT VHF radar; 69.6°N, 19.2°E) observations. The unusual Cluster crossing (compared to the usual midaltitude cusp crossing at this time of the year) occurred owing to a large compression of the magnetosphere. Cluster, which was in the southern magnetospheric lobe, suddenly found itself in the magnetosheath at the arrival of the CME at 1524:45 UT. Cluster then crossed through the compressed magnetosheath (highly compressed after the discontinuity in the CME) for about 1.5 hours (1525–1655 UT), magnetopause with strong signatures of lobe reconnection (≈1655 UT), stagnant but compressed exterior cusp for about an hour (1700–1802 UT), and then entered the dayside magnetosphere. The observations also show strong signatures of magnetosphere‐ionosphere coupling through a late afternoon (≈17 MLT) cusp during the first 40 min (1525–1605 UT) of the event when IMF Bz remained negative. Strong magnetic waves are also generated in the magnetosheath‐cusp region.

Energy input from the exterior cusp into the ionosphere: Correlated ground‐based and satellite observations

The energy transport from the exterior cusp into the ionosphere is investigated using coordinated ground‐based (EISCAT and MIRACLE) and satellite (Cluster) observations. EISCAT and MIRACLE data are used to estimate the plasma heating in the F‐region and the Joule heating in the E‐region. Cluster measurements are used to derive the electromagnetic and particle energy fluxes at the high altitudes. These fluxes are then compared with the energy deposition into the ionospheric cusp during a 30 minutes long time interval in which Cluster and EISCAT are nearly conjugated. It is shown that the particles seen at about 9 Re in the exterior cusp carry an earthward energy flux that corresponds to the observed heating of the F‐region. The estimated earthward Poynting flux is more than enough to account for the Joule heating in the E‐region.

Reconnection and energetic particles at the edge of the exterior cusp

Abstract. In this paper we study flux transfer events (FTE) observed at the post-noon edge of the exterior cusp region by Cluster satellites. During the outbound dayside orbit on 2 February 2003, intense bursts of energetic particles were observed in close conjuction with magnetic field FTE signatures by the RAPID instrument onboard the Cluster 4. The pitch-angle distribution of the particles showed that the enhancements consist of particles flowing antiparallel to the magnetosheath field lines away from the expected reconnection site to the exterior cusp. At the same time Cluster 3 observed enhancements of energetic particles deeper in the exterior cusp with a delay of about 40 s to the Cluster 4 enhancements. The estimated maximum energy gain per particle by reconnection remains below 1 keV, thus clearly below the tens to hundreds of keV energy range observed by the RAPID instrument. These observations support the earlier statistical result of the magnetospheric origin of energetic particles in the exterior cusp. Reconnection near the exterior cusp partly releases the particles in the closed field lines of the adjacent HLPS region into the exterior cusp.

Energetic particle fluxes in the exterior cusp and the high-latitude dayside magnetosphere: statistical results from the Cluster/RAPID instrument

Abstract. In this paper we study the fluxes of energetic protons (30–4000 keV) and electrons (20–400 keV) in the exterior cusp and in the adjacent high-latitude dayside plasma sheet (HLPS) with the Cluster/RAPID instrument. Using two sample orbits we demonstrate that the Cluster observations at high latitudes can be dramatically different because the satellite orbit traverses different plasma regions for different external conditions. We make a statistical study of energetic particles in the exterior cusp and HLPS by analysing all outbound Cluster dayside passes in February and March, 2002 and 2003. The average particle fluxes in HLPS are roughly three (protons) or ten (electrons) times larger than in the exterior cusp. This is also true on those Cluster orbits where both regions are visited within a short time interval. Moreover, the total electron fluxes, as well as proton fluxes above some 100 keV, in these two regions correlate with each other. This is true even for fluxes in every energy channel when considered separately. The spectral indices of electron and proton fluxes are the same in the two regions. We also examine the possible dependence of particle fluxes at different energies on the external (solar wind and IMF) and internal (geomagnetic) conditions. The energetic proton fluxes (but not electron fluxes) in the cusp behave differently at low and high energies. At low energies (<70 keV), the fluxes increase strongly with the magnitude of IMF By. Instead, at higher energies the proton fluxes in the cusp depend on substorm/geomagnetic activity. In HLPS proton fluxes, irrespective of energy, depend strongly on the Kp and AE indices. The electron fluxes in HLPS depend both on the <Kp index and the solar wind speed. In the cusp the electron fluxes mainly depend on the solar wind speed, and are higher for northward than southward IMF. These results give strong evidence in favour of the idea that the high-latitude dayside plasma sheet is the main source of energetic particles in the exterior cusp. Energetic particles can reach HLPS from the near-Earth tail. The closed field lines of HLPS act as storage for these particles. Direct diffusion (for electrons and high-energy protons) and magnetic reconnection in the high-latitude magnetopause near HLPS (for low energy protons) control the number of particles released into the exterior cusp. Note that this explanation, in contrast to other suggested theories, works both for the energetic protons and electrons in the exterior cusp. Keywords. Magnetospheric physics (Magnetopause, cusp and boundary layers; Solar wind-magnetosphere interactions) – Space plasma physics (magnetic reconnection)

On the formation of the high‐altitude stagnant cusp: Cluster observations

On 16 March 2002, Cluster moved from nightside to dayside, across the high‐altitude northern cusp during an extended period of relatively steady positive IMF BY and BZ. Combined Cluster and SuperDARN data imply the existence of two reconnection sites: in the high‐latitude northern hemisphere dusk and southern hemisphere dawn sectors. Within the cusp, Cluster encounters 3 distinct plasma regions. First, injections of magnetosheath‐like plasma associated with dawnward and sunward convection suggest Cluster crosses newly‐reconnected field lines related to the dusk reconnection site. Second, Cluster observes a Stagnant Exterior Cusp (SEC), characterized by nearly isotropic and stagnant plasma. Finally, Cluster crosses a region with significant anti‐field‐aligned flows. We suggest the observed SEC may be located on newly re‐closed field lines, reconnected first poleward of the northern hemisphere cusp and later reconnected again poleward of the southern hemisphere cusp. We discuss how the Cluster observations correspond to expectations of 'double reconnection' model.