Drift Mirror Research Articles

THEMIS observations of compressional Pc5 pulsations in the dawn- and duskside magnetosphere

We present case and statistical studies of compressional Pc5 pulsations observed by the THEMIS spacecraft in the dawn- and duskside magnetosphere from 2007 to 2011. A case study provides evidence for compressional Pc5 pulsations in the dawnside magnetosphere following the arrival of particles injected by a substorm and the subsequent growth of the drift mirror instability on February 27, 2011. The statistical study shows that the Pc5 pulsations occur in a weak or moderately disturbed magnetosphere but rarely develop during strong magnetic activity (i. e., for Dst index below −25 nT). The most striking characteristic of the compressional Pc5 pulsations is their localization in latitude and longitude over many consecutive days. Dawnside Pc5 pulsations occur under quieter conditions, last longer, and attain greater amplitudes than duskside Pc5 pulsations. We attribute compressional pulsations in both sectors to the drift mirror instability, with a warmer, more energized, and gradient-curvature drifting population of substorm-injected ions on the duskside and a colder ExB drifting population of plasma sheet ions on the dawnside.

Statistical Study of the Energetic Electron Microinjections at the High‐Latitude Magnetosphere

AbstractUnderstanding the formation of the seed population for the energetic electrons trapped within the Earth's Van Allen radiation belts has been under debate for decades. The magnetic reconnection in the Earth's magnetotail during the substorms is the main process of accelerating the electrons to the tens to hundreds of keV. These electrons are further injected toward the radiation belts, where they get further accelerated to relativistic energies. Recently, it has been suggested that another source could come from the dayside diamagnetic cavities where electrons and ions can be locally energized to hundreds of keV energies. It has been shown that the physical mechanism within the cavities can create a strong acceleration perpendicular to magnetic field, which can lead to temperature anisotropy and drift mirror instability. The electron fluxes localized within the troughs of the mirror mode waves exhibit the counter‐streaming “microinjection” signature. To investigate the origin of microinjections and their dependence on solar wind conditions, here we have performed an event search and a statistical study of their properties encompassing a total of ∼165 hr (47 microinjection events) of Magnetospheric Multiscale observations at the pre‐dusk sector high‐latitude boundary layer. The ultralow frequency range magnetic field fluctuations coincided with the counter‐streaming energetic electron fluxes. For most events, the interplanetary magnetic field was duskward and anti‐sunward; over 60% of these microinjections satisfy the criteria of the drift mirror instability, which indicates the temperature anisotropy could play an important role for the microinjection.

Identifying the Structure and Propagation of Dawnside Pc5 ULF Waves Using Space‐Ground Conjunctions

AbstractPc5 ultralow frequency waves are important for transferring energy between the magnetosphere and ionosphere. While many observations have been performed on Pc5 waves properties, it has been difficult to determine the source region, signal propagation path, and the two‐dimensional structure of Pc5 waves beyond coverage by a small number of satellites. Pc5 waves often show a dawn‐dusk asymmetry, but the cause of the asymmetry is under debate. To address these issues, we used conjunction events between the THEMIS satellites and all‐sky imagers and analyzed two Pc5 wave events that were stronger on the dawnside. For both events, the Pc5 waves propagated from dawnside magnetopause toward the nightside magnetosphere. The Pc5 waves were also associated with dawnside magnetopause surface waves, which were probably induced by the Kelvin‐Helmholtz instability. The ionospheric equivalent currents identified multiple vortices on the dawnside associated with quasi‐periodic auroral arcs and much weaker perturbations on the duskside. Global auroral imaging also presented a similar dawn‐dusk asymmetry with multiple arcs on the dawnside, while only one or two major arcs existed on the duskside. Pc5 waves in the magnetosphere had an anti‐phase relation between the total magnetic field and thermal pressure, with a slower propagation velocity compared with magnetohydrodynamic waves. The Poynting flux was anti‐sunward with an oscillating field‐aligned component. These properties suggest that Pc5 waves were slow or drift mirror mode waves coupled with standing Alfven waves. The ground‐based and multi‐satellite observations provide crucial information for determining the Pc5 waves properties, possible source region, and signal propagation path.

Magnetospheric Multiscale Observations of the Source Region of Energetic Electron Microinjections Along the Duskside, High‐Latitude Magnetopause Boundary Layer

AbstractThe present paper demonstrates the first observations by the Magnetospheric Multiscale (MMS) mission of the counter‐streaming energetic electrons and trapped energetic protons, localized in the magnetic field depressions between the mirror mode peaks, in the Earth's dusk sector high‐latitude magnetosphere. This region is characterized by high plasma beta, strong ion temperature anisotropy, and intermediate plasma density between magnetospheric and magnetosheath plasma. We show that these plasma conditions are unstable for the drift mirror instability. The counter‐streaming electron feature resembles those of the previously reported energetic electron microinjections, but without the energy‐time dispersion signature. This suggests that MMS is passing through one of the potential microinjection source regions. The energetic ion data in the present study is mainly used to estimate the scale size of the mirror mode structures.

Quasiperiodic field‐aligned current dynamics associated with auroral undulations during a substorm recovery

AbstractA substorm recovery event in the early morning sector is explored by means of ground and spacecraft data. The ground data are provided by stations of the MIRACLE network, in northern Scandinavia and Svalbard, while spacecraft data are observed by the Cluster satellites, toward the end of the recovery phase. Additional information is provided by the Fast Auroral SnapshoT (FAST) satellite, conjugate to Cluster 3 (C3). A prominent signature in the Cluster data is the low‐frequency oscillations of the perturbation magnetic field, in the Pc5 range, interpreted in terms of a motion of quasi‐stationary mesoscale field‐aligned currents (FACs). Ground magnetic pulsations in the Ps6 range suggest that the Cluster observations are the high‐altitude counterpart of the drifting auroral undulations, whose features thus can be explored closely. While multiscale minimum variance analysis provides information on the planarity, orientation, and scale of the FAC structures, the conjugate data from FAST and from the ground stations can be used to resolve also the azimuthal motion. A noteworthy feature of this event, revealed by the Cluster observations, is the apparent relaxation of the twisted magnetic flux tubes, from a sequence of 2‐D current filaments to an undulated current sheet, on a timescale of about 10 min. This timescale appears to be consistent with the drift mirror instability in the inner magnetosphere, mapping to the equatorward side of the oval, or the Kelvin‐Helmholtz instability related to bursty bulk flows farther downtail, mapping to the poleward side of the oval. However, more work is needed and a better event statistics, to confirm these tentative mechanisms as sources of Ω‐like auroral undulations during late substorm recovery.

Slow drift mirror kinetic instability at a finite electron temperature in a nonmaxwellian space plasma

A slow drift mirror (SDM) instability has been analyzed in the scope of kinetic approximation, with accounting for the electron pressure for different particle distribution functions. The dependence of the SDM instability increment growth rate on the parameters of the anisotropic κ distribution with the loss cone, which is used to model real space plasma particle distributions, has been studied. An analysis indicated that the appearance of the loss cone in the ion distribution function results in a decrease in the SDM mode frequency, and an enhancement of the suprathermal tail (a decrease in κ) increases the SDM mode frequency as compared to the Maxwellian distribution. In other words, particle redistribution from the region of low velocities into that of high velocities results in an increase in the SDM mode frequency.

THEMIS observations of compressional pulsations in the dawn-side magnetosphere: a case study

Abstract. We present THEMIS-A low- and high-energy plasma, magnetic field, and energetic particle observations of long period (11–36 min) irregular compressional pulsations in the dawnside magnetosphere from 08:00 to 12:24 UT on 7 November 2007. We demonstrate that the pulsations maintain thermal and magnetic pressure balance, then employ finite gyroradius techniques to determine wave properties from the gyrophase distributions of 5–10 keV ions. The waves generally move sunward at velocities ~10 km s−1 with the background plasma convection flow. Wavelengths range from 6700 to 23 300 km, corresponding to azimuthal wavenumbers m from 18 to 76. Wave periods decrease with increasing radial distance. Having determined the parameters describing the waves, we consider three previously proposed explanations: generation by substorm injection, generation by bounce or drift-bounce instabilities, and generation by the drift-mirror instability. The interval was quiet geomagnetically, arguing against any relationship to substorm injections. We found that ions with low energies of 69–628 eV or high energies of 28–615 keV would have been required to account for drift-bounce resonance during this interval, but inspection reveals ion fluxes at these energies near background levels during the time period considered. On the other hand, the criteria for the drift mirror instability are marginally satisfied. As predicted for the drift mirror instability, particle distributions peak more sharply near 90° pitch angles during magnetic field strength enhancements than during strength depressions. At this point we therefore interpret the compressional pulsations observed by THEMIS A in terms of the drift mirror instability.

Linear theory of slow drift mirror kinetic instability at finite electron temperature

A slow drift mirror (SDM) instability has been analyzed in the scope the kinetic theory, taking into account electron pressure. Both known branches of the SDM mode have been analyzed, and two regions of the kinetic SDM instability—low and high anisotropies—have been revealed. It has been indicated that different branches are intensified at low and high anisotropies. The dependence of the SDM wave modes on different plasma parameters has been studied.

THEMIS observations of duskside compressional Pc5 waves

The five Time History of Events and Macroscale Interactions during Substorms (THEMIS) spacecraft offer new possibilities to analyze ULF waves in the magnetosphere by means of multipoint measurements. During the coast phase, THEMIS observed many compressional oscillations with periods in the Pc5 range and longer. The observed events occur inside a well‐defined spatial domain in the outer equatorial duskside magnetosphere. We analyze these waves using the unique string‐of‐pearls configuration of the THEMIS constellation to evaluate their phase speed and propagation direction. We find that the waves are propagating sunward (westward) and radially outward, orthogonal to the mean magnetic field, with phase speeds around 30 km/s and higher in the spacecraft frame. In the plasma frame the propagation direction is still sunward, with lower speeds (up to 30 km/s for most events). The oscillations exhibit a strong anticorrelation between the magnetic field and the plasma density. On the basis of this, as well as their low propagation speed, orthogonal to the mean magnetic field propagation direction and almost parallel to the magnetic field maximum variance direction, we conclude that the most likely source of these waves is the drift mirror instability.

Comment on the drift mirror instability

Drift mirror instability is investigated in a slightly inhomogeneous plasma in a low-frequency, long-wavelength limit of the Vlasov–Maxwell equation. It is shown that previously derived threshold conditions for the drift mirror instability in the case of one cold species are incorrect and that it is hard to get analytically a simple threshold condition for the drift mirror instability in this case. It is argued that the same is true for the drift mirror instability in general.

Equator‐S observations of drift mirror mode waves in the dawnside magnetosphere

The mirror mode is a plasma instability that is typically excited in high‐beta plasmas where there is significant pressure anisotropy and is most commonly observed in the magnetosheath. However, it is possible under sufficiently anisotropic conditions to generate the mirror instability inside the magnetosphere, though as yet there are few examples. We present an extended interval of ∼7 hours of mirror mode activity on 19 March 1998 when the Equator‐S spacecraft was traversing the dawnside magnetosphere above the equatorial plane at radial distances of up to L ∼ 11 and encountered quasi‐monochromatic ∼2‐min oscillations in magnetic field and ion number density, temperature, and velocity. The magnetic field strength and number densities were in antiphase, and the plasma and magnetic field pressure perturbations were also in antiphase while the observed total pressure remained constant. This is consistent with excitation via a mirror instability. We are able to discern that the mirror activity must be confined to approximately within ±20° of the equatorial plane through a conjunction with the Geotail spacecraft. We find that the condition for mirror mode waves to grow is strongly met throughout the interval (Hasegawa, 1969). We believe that this is an excellent high temporal resolution example of the mirror instability exciting ULF waves inside the Earth's magnetosphere. Given the coexistence of toroidal oscillations at almost the same frequency, we suggest coupling between the mirror mode and local standing Alfvén waves. Our observations hence add to the understanding of how energy can be transferred from hot plasma into ULF waves in the magnetosphere before being dissipated in the ionosphere.

Polar rain aurora

Global FUV auroral imagers (IMAGE/SI‐13 and DMSP/SSUSI) observed, for the first time, two similar auroral events in the southern polar cap due to intense (keV) polar rain electrons from the solar wind as observed by DMSP and Geotail. Such an aurora is called polar rain aurora. The polar rain aurora could fill the dayside polar cap initially and developed a dawn‐dusk alignment while they moved anti‐sunward. The associated IMF Bz was mostly southward. The IMF Bx changed from negative to positive for the first event and stayed positive for the second event. The strong IMF By was associated with the two events. The dawn‐dusk alignment of polar rain aurora might be due to the dawn‐dusk aligned magnetic flux tubes in the magnetosheath caused by the dominant IMF By and modulation of the keV electrons by the nonoscillatory drift mirror waves and pitch angle diffusion via the electron cyclotron instability.

Spatial structure and dispersion of drift mirror waves coupled with Alfvén waves in a 1-D inhomogeneous plasma

Abstract. The paper employs the frame of a 1-D inhomogeneous model of space plasma,to examine the spatial structure and growth rate of drift mirror modes, often suggested for interpreting some oscillation types in space plasma. Owing to its coupling with the Alfvén mode, the drift mirror mode attains dispersion across magnetic shells (dependence of the frequency on the wave-vector's radial component, kr). The spatial structure of a mode confined across magnetic shells is studied. The scale of spatial localization of the wave is shown to be determined by the plasma inhomogeneity scale and by the azimuthal component of the wave vector. The wave propagates across magnetic shells, its amplitude modulated along the radial coordinate by the Gauss function. Coupling with the Alfvén mode strongly influences the growth rate of the drift mirror instability. The mirror mode can only exist in a narrow range of parameters. In the general case, the mode represents an Alfvén wave modified by plasma inhomogeneity.

Slow drift mirror modes in finite electron‐temperature plasma: Hydrodynamic and kinetic drift mirror instabilities

We develop a fully kinetic linear theory of the drift mirror (DM) instability accounting for arbitrary particle velocity distribution functions including nonzero electron temperature effects and plasma pressure anisotropy. In the quasi‐hydrodynamic limiting case the theory reproduces the results obtained for the ion mirror instability. However, for the very low frequency electron DM modes which can develop in a nonuniform plasma of nonzero electron temperature, Te ≠ 0, such an equivalence does not exist. We refer to these modes as slow drift mirror (SDM) modes in order to distinguish them from the conventional ion‐DM mode. Two new instabilities, one hydrodynamic and one kinetic, that lead to the growth of SDM modes are found in the fully kinetic regime. The first instability develops for values of the ion anisotropy lower than required for the classical ion‐DM instability. The second instability occurs when the conditions for the ion‐DM instability are satisfied as well. The frequency of the SDM mode is less than the frequency of the ion‐DM mode, ω ≪ ωDM ∼ ωn, where ωn is the density gradient‐drift frequency of the ions. However, when the electron temperature is of the order of the parallel ion temperature, the SDM instability growth rate may become comparable or even higher than that of the ion‐DM instability. The free energy necessary for these new instabilities is taken from two sources. The main source is the energy stored in the ion pressure anisotropy. The second source is the electron pressure gradient which builds up in a plasma of nonzero electron temperature.

Drift mirror instability in space plasmas, 2, Nonzero electron temperature effects

A linear theory of drift mirror instability accounting for the nonzero electron temperature effects is developed. Generalizing our previous approach to the analysis of this instability by accounting for a nonvanishing parallel electric field, we have derived the expressions for the mode frequency and instability growth rate. The origin of the electric field is due to the electron pressure gradient which builds up in a plasma with nonzero electron temperature, because the electrons are dragged by mirror‐accelerated protons as they pass from regions of high magnetic flux into those of lower magnetic flux. The electrostatic force drag associated with the parallel electric field provides a substantial reduction of the wave phase velocity and increases the drift mirror instability threshold. It is shown that in a plasma with nonzero electron temperature the drift mirror mode is accompanied by the field‐aligned current which varies in phase with the compressional changes in the magnetic field. The transition to the cold electron temperature limit is discussed.

A kinetic‐magnetohydrodynamic model for low‐frequency phenomena

A hybrid kinetic‐magnetohydrodynamic (MHD) model is presented for describing low‐frequency phenomena in high‐beta (β ∼ O(1)) anisotropic plasmas that consist of two components: a low‐energy core component and an energetic component with low density. The kinetic‐MHD model treats the low‐energy core component by magnetohydrodynamic description, the energetic component by a kinetic approach such as the gyrokinetic equation, and the coupling between the dynamics of these two components through plasma pressure in the momentum equation. The kinetic‐MHD model optimizes both the physics contents and the theoretical efforts in studying low‐frequency MHD waves and transport phenomena in general magnetic field geometries and can be easily modified to include the core plasma kinetic effects if necessary. It is applicable to any magnetized collisionless plasma system where the parallel electric field effects are negligibly small. In the linearized limit, two coupled eigenmode equations for describing the coupling between the transverse Alfvén type and the compressional Alfvén type waves are derived. The eigenmode equations are identical to those derived from the full gyrokinetic equation in the low‐frequency limit and were previously analyzed both analytically and numerically to obtain the eigenmode structure of the drift mirror instability (Cheng and Lin, 1987) which explains successfully the multisatellite observation of the antisymmetric field‐aligned structure of the compressional magnetic field of Pc 5 waves (Takahashi et al., 1987) in the magnetospheric ring current plasma. Finally, a quadratic form is derived to demonstrate the stability of the low‐frequency transverse and compressional Alfvén type instabilities in terms of the pressure anisotropy parameter τ the magnetic field curvature‐pressure gradient parameter αp as defined in equations (31) and (69), respectively. A procedure for determining the stability of a marginally stable MHD wave due to wave‐particle resonances is also presented.

A comprehensive investigation of compressional ULF waves observed in the ring current

Eighteen months of data provided by the magnetometer and energetic particle spectrometer on board the geosynchronous satellite GEOS 2 were used to investigate compressional ULF waves with frequencies of a few megahertz associated with large anticorrelated modulations of the ion pressure. The events are classified into two groups according to the behavior of the background magnetic field/plasma configuration at the onset of the oscillations. For one group the oscillation onset is preceded by a sharp increase of the plasma energy density due to the arrival of drifting ion bunches at the satellite and a corresponding diamagnetic decrease of the magnetic field strength. The other group is observed in a steady configuration in the presence of an enhanced ring current. Besides striking differences between the two groups as regards the average event duration and wave frequency, as well as the phase relation between electron and ion flux modulations, we present evidence that both groups of events are of antisymmetric structure with respect to the geomagnetic equator (where symmetry is defined according to the field line displacement) and have a small field‐aligned wavelength. Furthermore, for both groups the frequency variation with local time and the azimuthal propagation are closely connected with the ion magnetic gradient curvature drifts, and the waves are associated with a plasma distributed anisotropically in velocity space. Therefore the waves most likely represent the excitation of a single wave mode generated via wave‐particle interactions. Using plasma parameters measured in situ we calculated the growth rate of different hydromagnetic wave modes. It was found that the plasma is able to support a wave mode similar to the drift mirror mode with a large parallel wave number, if the effects of a strongly curved magnetic field are taken into account.

Magnetic field and density fluctuations at perpendicular supercritical collisionless shocks

Perpendicular collisionless shocks are studied by means of two‐dimensional hybrid (particle ion, fluid electron) simulations, with emphasis on the relaxation of the highly anisotropic ion distribution that arises primarily from reflection of some of the incident ions but also adiabatic compression of the other, directly transmitted ions and the related growth of low frequency electromagnetic waves. It is commonly assumed that the waves are due to the Alfven ion cyclotron instability that propagate parallel to the ambient magnetic field (k⊥ = 0) and that the isotropization of the ions due to pitch angle scattering by the waves and the corresponding modification of the wave spectrum is quasi‐linear. It is shown that this is indeed a reasonably good description downstream of the shock front, behind the magnetic overshoot. However, at the shock ramp there is a large discrepancy between the wavelengths measured in the simulations and those predicted by linear theory, and large density and magnetic field oscillations parallel to the ambient magnetic field are also seen. By comparing results for both high and low ion beta cases, it is shown that these effects can be understood in terms of obliquely propagating (k⊥ ≠ 0) modes, more likely due to the Alfven ion cyclotron instability instead of the (drift) mirror instability, although a more complete explanation awaits the derivation and analysis of an appropriate dispersion relation describing the growth and coupling of low‐frequency modes in the inhomogeneous high beta environment of the shock. The observational consequences of these results and their application to improving nonlocal leakage models for the ion foreshock are also discussed.

Study of a conjugate Pc 5‐6 magnetic and absorption pulsation event at subauroral latitudes in the morning sector

An interval of long‐period hydromagnetic wave activity occurring in the decays phase of a magnetic storm has been studied using ground‐based magnetic field and cosmic noise absorption data recorded at L ≲ 4.2. During an ∼90‐min interval of decreasing ring current following the storm maximum, a hydromagnetic pulsation train in the Pc 5‐6 range emerged (frequencies decreasing monotonically from ∼3 mHz to ∼1 mHz), accompanied by similar oscillations of the cosmic radio noise signal. There is some evidence in the data for the wave frequencies to be ∼0.2 mHz lower at L ∼ 3.0‐3.2 than at L ∼ 3.8‐4.2. The low wave frequencies are inconsistent with resonant oscillations of the field lines within the L shell range and probable magnetosphere plasma density conditions of observation. The waves were observed to propagate westward over at least 3 hours of local time, near dawn. An azimuthal wave number m ≈ 9 and a westward phase velocity varying from ∼2.5 to ∼7.5 km s−1 at 55° magnetic latitude characterized the event. The low azimuthal phase velocities make it unlikely that the waves were generated by the Kelvin‐Helmholtz instability on the magnetopause. These Pc 5‐6 waves appear to be odd mode, locally driven nonresonant oscillations. The ULF wave generation and propagation were most likely located on geomagnetic field lines in the range 3.5 ≲ L ≲ 6 in the region of hot storm time plasma outside the plasmapause where a gradient in particle precipitation flux was also observed. Neither the drift mirror instability nor the compressional drift wave instability appears to be a likely source for these waves. Modulation by the ULF waves of the pitch angle diffusion of energetic electrons injected into the outer radiation zone during the magnetospheric storm is suggested to account for the cosmic noise absorption pulsations observed outside the plasmapause. Irregular plasma density gradients in this region, inferred from the propagation characteristics of whistler mode VLF signals, may have caused the observed H‐D plane wave polarization variations.

Curvature-driven drift mirror instability in the magnetosphere

The resonant interaction between low frequency waves and magnetospheric plasma particles is examined for the case where the field-aligned phase velocity is much less than the Alfven velocity. The coupling of compressional Alfven and drift mirror modes is obtained by including the field curvature effect. The field curvature is also responsible for a new instability of the coupled mode similar to the drift mirror (DM) instability. However, this instability starts for a lower value of the anisotropy than in the case of the DM instability. The theoretical predictions are compared in detail with the storm-time Pc5 event of 14–15 November 1979.