Mirror Mode Research Articles

Tangential discontinuities at high heliographic latitudes (∼−80°)

In this study, tangential discontinuities (TDs) near −80° heliographic latitude have been studied. Based on our quantitative definitions, we find that the TDs may generally be divided into two clear types. There is a distinct population of TDs small (<40°) directional changes. About 19% of all high‐latitude TDs are in this category. These types of TDs are found at the edges of mirror mode structures. The latter are presumed to be locally generated by ion anisotropies, based on examination of the mirror mode instability criteria. Another 50% of high latitude TDs are associated with large field directional changes (>60°). These TDs typically are found at the boundary between two streams. The discontinuities have large normals in the plane perpendicular to the background field, as might be expected for features generated by currents flowing along the field. These discontinuities usually have larger current intensities than those of the mirror‐mode related TDs. The remainder of the discontinuities have angular changes which lie in between the mirror‐mode‐associated and the current‐sheet‐associated TDs.

On the stability of rotational discontinuities: One‐ and two‐dimensional hybrid simulations

Studies of rotational discontinuities (RDs) and their role in affecting the magnetic field rotations at the magnetopause have been generally conducted using one‐dimensional simulations and for RDs in isolation from external perturbations. The conditions at the magnetopause are, however, often turbulent with large Alfvénic and mirror mode fluctuations. Here, previous calculations are extended to two‐dimensions using the hybrid code and the effect of external perturbations on the stability of both isotropic and anisotropic RDs is examined for the first time. As in the one‐dimensional simulations and in agreement with observations at the magnetopause, RDs are found to satisfy the minimum shear condition (rotation angles less than or equal to 180°) and have gradient scale half‐widths of the order of 1–4 ion inertial lengths. In addition, RDs are found to be quite stable even when large amplitude mirror and Alfvén waves impinge upon them. No evidence for two‐dimensional (e.g., surface or shear) instabilities were found. Although simulations show the presence of a coherent wavetrain for some of the RDs, the observations of RDs at the magnetopause have not identified any wavetrain. It is shown that under the turbulent conditions prevalent at the magnetopause, the detection of wavetrain in the data would most likely require multispacecraft measurements.

Observations of mirror waves and plasma depletion layer upstream of Saturn's magnetopause

The two inbound traversals of the Saturn's magnetosheath by Voyagers 1 and 2 have been studied using plasma and magnetic field data. In a great portion of the subsolar magnetosheath, large‐amplitude compressional waves are observed at low frequency (∼0.1 fp) in a high‐β plasma regime. The fluctuations of the magnetic field magnitude and ion density are anticorrelated, as are those of the magnetic and thermal pressures. The normals to the structures are almost orthogonal to the background field, and the Doppler ratio is on the average small. Even though the data do not allow the determination of the ion thermal anisotropy, the observations are consistent with values of T⊥/T∥ > 1, producing the onset of the mirror instability. All the above features indicate that the waves should be most probably identified with mirror modes. One of the two magnetopause crossings is of the high‐shear type and the above described waves are seen until the magnetopause. The other crossing is of the low‐shear type and, similarly to what has been observed at Earth, a plasma depletion occurs close to the magnetopause. In this layer, waves with smaller amplitude, presumably of the mirror mode, are present together with higher‐frequency waves showing a transverse component.

Low‐frequency fluctuations in the magnetosheath near the magnetopause

There are four low‐frequency modes which may propagate in a high‐beta nearly bi‐Maxwellian plasma. These are the magnetosonic, Alfvén, ion acoustic, and mirror modes. This manuscript defines a procedure based on linear Vlasov theory for the unique identification of these modes by use of transport ratios, dimensionless ratios of the fluctuating field and plasma quantities. A single parameter, the mode deviation, is defined which characterizes the difference between the theoretical transport ratios of a particular mode and the observed ratios. The mode deviation is calculated using the plasma and magnetic field data gathered by the Active Magnetospheric Particle Tracer Explorers/Ion Release Module spacecraft to identify the modes observed in the terrestrial magnetosheath near the magnetopause. As well as determining the mode which best describes the observed fluctuations, it gives us a measure of whether or not the resulting identification is unique. Using 17 time periods temporally close to a magnetopause crossing, and confining our study to the frequency range from 0.01 to 0.04 Hz, we find that the only clearly identified mode in this frequency range is the mirror mode. Most commonly, the quasi‐perpendicular mirror mode (with wave vector k roughly perpendicular to the background magnetic field B0) is observed. In two events the quasi‐parallel mirror mode (k ∥ B0) was identified.

Magnetic holes in the solar wind and their relation to mirror-mode structures

Data obtained by the Ulysses magnetometer and solar wind analyzer have been combined to study the properties of magnetic holes in the solar wind between 1 and 5.4 AU and to 23° south latitude. Although the plasma surrounding the holes was generally stable against the mirror instability, there are indications that the holes may have been remnants of mirror mode structures created upstream of the points of observation. Those indications include: (1) For the few holes for which proton or alpha-particle pressure could be measured inside the hole, the ion thermal pressure was always greater than in the plasma adjacent to the holes. (2) The plasma surrounding many of the holes was marginally stable for the mirror mode, while the plasma environment of all the holes was significantly closer to mirror instability than was the average solar wind. (3) The plasma containing trains of closely spaced holes was closer to mirror instability than was the plasma containing isolated holes. (4) The near-hole plasma had much higher ion β (ratio of thermal to magnetic pressure) than did the average solar wind.

Electron temperature effects in the linear proton mirror instability

It is shown that when the electron temperature Te is of the same order of the proton temperature parallel to the background magnetic field, the growth rate of the proton mirror mode in the long‐wavelength limit is reduced by the presence of a longitudinal electric field. The field is due to the electron pressure gradient which builds up when Te ≠ 0, because the electrons are dragged by nonresonant protons which are mirror accelerated from regions of high into regions of low parallel magnetic field flux. In return, the longitudinal electric field causes the density of nonresonant protons with a perpendicular velocity smaller than a strongly Te‐dependent critical velocity υ⊥,crit to increase (decrease) at maxima (minima) of the parallel magnetic field flux. These nonresonant protons thus behave differently from the “circulating” protons described by Southwood and Kivelson (1993) in the cold electron limit. Although the instability threshold is only weakly affected by changes in Te, quantities like the growth rate, the compressibility, the polarization, and the angle between wave vector and magnetic field for the most unstable mode, as well as the structure of the perturbed proton distribution itself, are strongly modified by variations in the electron temperature. The predictions of the model are shown to agree well with numerical solutions of the full Vlasov dispersion relation, indicating that most long‐wavelength aspects of the proton mirror instability are included in the model.

Waves in the Earth's magnetosheath: Observations and interpretations

We review the nature and the location of waves observed in the magnetosheath at and below the proton gyrofrequency. The directions of propagation imply that some waves originate in the bow shock and in the magnetopause. Waves are also growing in the whole magnetosheath, wherever the ion distribution functions are unstable. This occurs downstream of the quasi-perpendicular bow shock and in the inner sheath, where the proton temperature T p‖ perpendicular to the ambient magnetic field is larger than the parallel temperature T p‖ . An anticorrelation between T p‖ T p‖ and β p‖ is observed in the inner sheath; this can result from a quasilinear interaction between unstable waves and particles. The α particles present in the sheath modify the dispersion relation of the waves. We discuss the best parameters for identification of the wave modes. The phase difference between the parallel magnetic field and the density fluctuations is not a good identifier: it can be about 180° for a mirror mode, for an oblique slow mode, and also for an oblique Alfvén ion cyclotron mode. For a given mode, this phase difference depends on the local shape of the particle distribution functions and, if the mode is known from other identifiers, it can help to detect the presence of a hot proton halo or of a cold electron core in the distribution functions.

Ultra low frequency waves at the Earth's bow shock

The Earth's bow shock is a bountiful generator of waves. Some of these waves have group velocities that exceed the solar wind velocity directed into the shock and can propagate upstream against the flow. Upstream whistlers observed close to one Hertz in the spacecraft frame have been seen many Earth radii upstream. A second whistler mode wave, called the precursor, propagates upstream along the shock normal but is phase standing in the solar wind flow. The damping of both whistler mode waves is consistent with Laudau damping. At low Mach numbers the precursor is connected to the non-coplanarity component in the shock ramp. At higher Mach numbers the upstream waves cannot propagate upstream and ion reflection becomes more important in providing free energy for wave particle interactions. The non-coplanarity component is still present but it now initiates a downstream wave train. Generally the waves just downstream from the bow shock are left hand circularly polarized ion cyclotron waves propagating along the magnetic field at the Alfven velocity. When the upstream Mach number is high and the helium content of the plasma is high, mirror mode waves are observed.

Whistler mode waves in the Jovian magnetosheath

During the Ulysses flyby of Jupiter in February 1992, the spacecraft traversed the Jovian magnetosheath for a few hours during the inbound pass and for a few days during the outbound pass. Burstlike electromagnetic waves at frequencies of ∼0.1‐0.4 of the local electron cyclotron frequency have been observed by the Unified Radio and Plasma Wave (URAP) experiment. The waves were more often observed in the regions which were probably the outer or middle magnetosheath, especially near the bow shock, and rarely seen in the magnetosphere/magnetosheath boundary layer. The propagation angles of the waves are estimated by comparing the measurements of the wave electric and magnetic fields in the spacecraft spin plane with the corresponding values calculated using the cold plasma dispersion relation under local field and plasma conditions. It is found that the waves propagate obliquely with wave angles between ∼30° and 50°. These waves are likely to be the whistler mode waves which are excited by suprathermal electrons with a few hundred eV and a slight anisotropy (T⊥/T∥ ∼1.1‐1.5). They are probably similar in nature to the lion roars observed in the Earth's magnetosheath. Signature of coupling between the mirror mode and the whistler mode have also been observed. The plasma conditions which favor the excitation of the whistler mode instability during the wave events exist as observed by the plasma experiment of Ulysses.

Ulysses field and plasma observations of magnetic holes in the solar wind and their relation to mirror‐mode structures

The term “magnetic hole” has been used to denote isolated intervals when the magnitude of the interplanetary magnetic field drops to a few tenths, or less, of its ambient value for a time that corresponds to a linear dimension of tens to a few hundreds of proton gyro‐radii. Data obtained by the Ulysses magnetometer and solar wind analyzer have been combined to study the properties of such magnetic holes in the solar wind between 1 AU and 5.4 AU and to 23° south latitude. In order to avoid confusion with decreases in field strength at interplanetary discontinuities, the study has focused on linear holes across which the field direction changed by less than 5°. The holes occurred preferentially, but not without exception, in the interaction regions on the leading edges of high‐speed solar wind streams. Although the plasma surrounding the holes was generally stable against the mirror instability, there are indications that the holes may have been remnants of mirror‐mode structures created upstream of the points of observation. Those indications include the following: (1) For the few holes for which proton or alpha‐particle pressure could be measured inside the hole, the ion thermal pressure was always greater than in the plasma adjacent to the holes. (2) The plasma surrounding many of the holes was marginally stable for the mirror mode, while the plasma environment of all the holes was significantly closer to mirror instability than was the average solar wind. (3) The plasma containing trains of closely spaced holes was closer to mirror instability than was the plasma containing isolated holes. (4) The near‐hole plasma had much higher ion β (ratio of thermal to magnetic pressure) than did the average solar wind. (5) Near the holes, T⊥/T∥ tended to be either >1 or larger than in the average wind. (6) The proton and alpha‐particle distribution functions measured inside the holes occasionally exhibited the flattened phase‐space‐density contours in ν⊥‐ν∥ space found in some numerical simulations of the mirror instability.

Nature and origin of wave modes in the dayside earth magnetosheath

The day side magnetosheath displays turbulence at frequencies lower than the local proton frequency. The nature of the waves modes is studied from ISEE-1-2 electron density and magnetic field data. We compare the polarization and the compressibility of the observed fluctuations to the polarization and the compressibility of the linear wave modes in a Maxwellian kinetic plasma model with an anisotropic proton temperature. Downstream of the undershoot of a supercritical quasi-perpendicular shock we successively observe Alfvén Ion Cyclotron (AIC) modes, mirror modes and then AIC modes. From the crossing of an oblique shock to the inner sheath we observe AIC modes propagating toward the magnetopause. Along the Sun-Earth line, from the inner sheath to the magnetopause, AIC modes are observed during one crossing while mirror modes are seen during another crossing. In the sheath depletion layer we observe right-hand polarized AIC modes. At 0600 LT and at equal distance from the magnetopause and from the shock both types of modes are observed, the mirror mode appearing when the magnetic field is draping the magnetopause. From these analysis we infer the source of the propagating AIC modes to be the magnetosheath frontier regions, while the mirror modes grow in situ in the inner magnetosheath when specific conditions are reached.

Sources of magnetosheath waves and turbulence

In this paper the possible sources of waves and turbulence in the magnetosheath are discussed. In particular, three separate sources resulting in different types of waves are identified. One is the quasi-parallel portion of the bow shock which contains large amplitude magnetosonic waves generated at or upstream of the shock. Due to their small group velocity these waves are convected back into downstream. It is suggested that the convected wave energy results in the generation of Alfvén waves through a linear mode conversion process. Another source is the quasi-perpendicular portion of the shock which results in an anisotropic plasma downstream of the shock. This temperature anisotropy is unstable to the excitation of both Alfvén and mirror waves with the former having a larger growth rate. The competition between these two wave modes is discussed and it is shown that the mirror mode can be excited despite its lower growth rate. Finally, it is shown that the magnetopause itself can generate slow magnetosonic waves in the magnetosheath. It is suggested that these waves can be thought of as part of the overall magnetopause structure, as are dispersive whistlers associated with low Mach number shocks.

Mirror instability in the magnetosheath

We describe mirror mode structures observed by ISEE 1 and ISEE 2. We cite an example where there is a good correlation between signals measured at the two spacecraft while they are 2250 km apart, and another example where the correlation is much poorer, although the spacecraft are only 340 km apart. We attempt to explain the three dimensional form of the plasma and magnetic field structures which the spacecraft encountered in each case.

Theory of ballooning‐mirror instabilities for anisotropic pressure plasmas in the magnetosphere

A kinetic‐MHD eigenmode analysis of ballooning‐mirror instabilities is performed for anisotropic pressure plasmas in the magnetosphere. The energetic particle kinetic effects and the coupling between the ballooning and mirror modes are taken into account. Without energetic trapped particle kinetic effects the ballooning‐mirror modes with symmetric field‐aligned structure of parallel perturbed magnetic field δB∥ and electrostatic potential Φ have lower β instability threshold than the antisymmetric modes. Pressure anisotropy with (P⊥/P∥ > 1) reduces the β threshold for ballooning‐mirror instabilities. In the limit that the wave frequency is smaller than the energetic trapped particle magnetic drift frequency, the symmetric ballooning‐mirror mode is completely stabilized by the energetic trapped particle kinetic effects. However, the antisymmetric ballooning‐mirror mode is only weakly influenced by the energetic trapped particle kinetic effects and has the lowest β threshold. For symmetric modes the energetic trapped particles experience a bounce‐averaged wave structure due to their rapid bounce motion, and their nonadiabatic kinetic pressure response cancels with their fluid pressure response so that they do not contribute to the mode stability. Physically, the energetic trapped particles precess very rapidly across the field, and their motion becomes very rigid with respect to low‐frequency symmetric MHD perturbations. For antisymmetric modes the energetic trapped particle kinetic pressure response from the northern hemisphere cancels with that from the southern hemisphere in a bounce period, and thus the instability β thresholds is mainly determined by the energetic particle fluid free energy. The field‐aligned perturbed magnetic field structure of the antisymmetric mode changes from a ballooning mode with dominant transverse magnetic field components at P⊥/P∥ = 1 to a mixed ballooning‐mirror mode with comparable transverse and compressional components near the equator as P⊥/P∥ increase. With large equatorial plasma β (β∥ ≥ O(1)) and pressure anisotropy (P⊥/P∥ > 1) the field‐aligned wave structure of antisymmetric ballooning‐mirror mode resembles the multisatellite observation of a long lasting compressional Pc 5 wave event during November 14‐15, 1979 [Takahashi et al., 1987].

Identification of low‐frequency fluctuations in the terrestrial magnetosheath

On the basis of MHD theory we develop a scheme for distinguishing among the four low‐frequency modes which may propagate in a high‐β anisotropic plasma such as the magnetosheath: the fast and slow magnetosonic, the Alfvén, and mirror modes. We use four parameters: the ratio of transverse to compressional powers in the magnetic field, the ratio of the wave powers in the thermal pressure and in the magnetic field, the ratio of the perturbations in the thermal and magnetic pressures, and the ratio of the wave powers in the velocity and in the magnetic field. In the test case of an Active Magnetospheric Particle Tracer Explorers/Ion Release Module (AMPTE/IRM) magnetosheath pass near the Sun‐Earth line downstream of a quasi‐perpendicular shock, the four modes can be clearly distinguished both spatially and spectrally. Near the bow shock, the waves are Alfvénic in a large frequency range, 1 to 100 mHz. In the middle and inner magnetosheath, the waves below 10 mHz are Alfvénic. The fast mode waves occur in the higher‐frequency end of the enhanced spectrum, 80 mHz for the middle magnetosheath and 55 mHz for the inner sheath. The wave enhancement in the intermediate frequencies is slow modes in the inner sheath and mirror modes in the middle sheath. This confirms the earlier report of the existence of the slow mode waves near the magnetopause. These slow waves provide evidence that the magnetopause is an active source of the waves in the sheath. We also show that the measured frequency of a wave is close to an invariant if the magnetosheath flow is in a steady state. Therefore changes in the frequencies of enhanced waves indicate emergence, or damping, or mode conversion of the waves.

Mode properties of low‐frequency waves: Kinetic theory versus Hall‐MHD

In fluid theory, the ordering of low‐frequency modes in a homogeneous plasma is based on the phase velocity, since modes do not intersect each other in dispersion diagrams as a function of wavenumber or other parameters. In linear kinetic theory, modes cross each other. Thus a consistent and useful classification should be based on the physical properties of the modes instead. This paper attempts such a classification by documenting the dispersion and general mode properties of the low‐frequency waves (ω « (ΩciΩce)1/2, where Ωci, Ωce are the cyclotron frequencies of the ions and electrons, respectively) in kinetic theory, and by comparing them to the results of two‐fluid theory. Kinetic theory gives a separate Alfvén/ion‐cyclotron (A/IC) wave with phase speed ω/k ≈ υAcosθ for ω « Ωci, where υA is the Alfvén velocity and θ the angle of propagation between wave vector k and background magnetic field Bo. For a given wavenumber, the magnetosonic mode is a double‐valued solution with a singular point in θ, β parameter space, where β is the ratio of thermal pressure to magnetic pressure. It is shown that a branch cut starting at the singular point θ ∼ 30°, β ∼ 3 and leading to larger β gives a practical and consistent separation of this double‐valued magnetosonic solution. Selection of this branch cut results in a moderately damped fast/magnetosonic and a heavily damped slow/sound wave. A comprehensive review of the polarization, compressibility and other mode properties is given and shown to be consistent with the selected branch cut. At small wavenumbers, the kinetic mode properties typically start to deviate significantly from their fluid counterparts at β ∼ 0.5. At larger β, there is no longer a consistent correspondence between the fluid and kinetic modes. Kinetic theory also dictates the use of different mode properties to distinguish between them in observational data. For example, the phase between the density and magnetic field perturbations may become useless at high β, whereas the direction of the magnetic field perturbation with respect to k and Bo remains a useful characteristic. Two quantities based on this characteristic are suggested and are shown to be useful also to distinguish between the mirror mode and A/IC waves in a plasma with temperature anisotropy.

Magnetic spectral signatures in the Earth's magnetosheath and plasma depletion layer

Correlations between plasma properties and magnetic fluctuations in the subsolar magnetosheath downstream of a quasi‐perpendicular shock have been found and indicate that mirror and ion cyclotronlike fluctuations correlate with the magnetosheath proper and plasma depletion layer, respectively (Anderson and Fuselier, 1993). We explore the entire range of magnetic spectral signatures observed from the AMPTE/CCE spacecraft in the magnetosheath downstream of a quasi‐perpendicular shock. The magnetic spectral signatures typically progress from predominantly compressional fluctuations, δB∥/δB⊥ ≈ 3, with F/Fp <0.2 ( F and Fp are the wave frequency and proton gyrofrequency, respectively) to predominantly transverse fluctuations, δB∥/δB⊥ ≈ 0.3, extending up to Fp. The compressional fluctuations are characterized by anticorrelation between the field magnitude and electron density, ne, and by a small compressibility, Ce ≡ (δne/ne)2(B/δB∥)2 ≈ 0.13, indicative of mirror waves. The spectral characteristics of the transverse fluctuations are in agreement with predictions of linear Vlasov theory for the H+ and He2+ cyclotron modes. The power spectra and local plasma parameters are found to vary in concert: mirror waves occur for β∥p (β∥p ≡ 2µ0npkT∥p/B2) ≈ 2, Ap ≡ T⊥p/T⊥ ‐ 1 ≈ 0.4, whereas cyclotron waves occur for β∥p ≈ 0.2 and Ap ≈ 2. The transition from mirror to cyclotron modes is predicted by linear theory. The spectral characteristics overlap for intermediate plasma parameters. The plasma observations are described by Ap = 0.85β∥p−0.48 with a log regression coefficient of −0.74. This inverse Ap ‐ β∥p correlation corresponds closely to the isocontours of maximum ion anisotropy instability growth, γm/Ω = 0.01, for the mirror and cyclotron modes. The agreement of observed properties and predictions of local theory suggests that the spectral signatures reflect the local plasma environment and that the anisotropy instabilities regulate Ap. We suggest that the spectral characteristics may provide a useful basis for ordering observations in the magnetosheath and that the Ap ‐ β ∥p inverse correlation may be used as a beta‐dependent upper limit on the proton anisotropy to represent kinetic effects.

Low‐frequency magnetic fluctuation spectra in the magnetosheath and plasma depletion layer

Recent observations have delineated several different kinds of enhanced magnetic fluctuation spectra below the proton cyclotron frequency in the terrestrial magnetosheath. A model is presented that represents the variation of plasma parameters across the plasma depletion layer and into the magnetosheath proper. Using this model, we find that many of the properties of the observed spectra follow directly from the predictions of linear Vlasov instability theory. The observed progression of spectral features is a natural progression from mirror mode to merged (in frequency range) proton and He2+ cyclotron modes to bifurcated (in frequency range) cyclotron modes as plasma convects earthward in the magnetosheath. The necessary change in dispersion surface topology from separated proton and He2+ cyclotron surfaces at low beta to merged surfaces at high beta is described.

Ballooning-Mirror Instability and Internally Driven Pc 4-5 Wave Events.

A kinetic-MHD field-aligned eigenmode stability analysis of low frequency ballooning-mirror instabilities has been performed for anisotropic pressure plasmas in the magnetosphere. The ballooning mode is mainly a transverse wave driven unstable by pressure gradient in the bad curvature region. The mirror mode with a dominant compressional magnetic field perturbation is excited when the product of plasma beta and pressure anisotropy (P⊥/P|| > 1) is large. In the limit that the wave frequency is smaller than the energetic trapped particle magnetic drift frequency, which is usually much smaller than the energetic trapped particle bounce frequency, the energetic trapped particles experience the bounce-averaged wave structure due to their rapid bounce motion. For modes with north-south symmetric field-aligned structure of parallel perturbed magnetic field the energetic trapped particle kinetic pressure response is finite and cancels with their fluid pressure response so that the symmetric mode is stable. Physically the energetic trapped particles precess very rapidly across the B field, and their motion becomes very rigid with respect to low frequency symmetric MHD perturbations. For antisymmetric modes the energetic trapped particle kinetic pressure response from the northern hemisphere cancels with that from the southern hemisphere in a bounce period, and the instability β threshold of the antisymmetric mode is determined by the energetic particle fluid free energy. Pressure anisotropy with P⊥/P|| > 1 reduces the β|| threshold. The antisymmetric mode changes from a ballooning mode with dominant transverse magnetic field components at P⊥/P|| = 1 to a hybrid ballooning-mirror type mode with comparable transverse and compressional magnetic field components near the equator as P⊥/P|| increases. With large equatorial plasma beta (β|| ≥ Ο(1)) and pressure anisotropy (P⊥/P|| > 1) the field-aligned wave structure of antisymmetric ballooning-mirror mode resembles the multisatellite observations of a long lasting compressional Pc 5 wave event during November 14-15, 1979 (Takahashi et al., 1987). From the AMPTE/ CCE particle and magnetic field data observed during Pc 4-5 wave events we compute the ballooning-mirror instability parameters and perform a correlation study with the theoretical instability threshold. We find that compressional Pc 5 waves approximately satisfy the ballooning-mirror instability condition, and transverse Pc 4-5 waves are probably related to resonant ballooning instabilities with small pressure anisotropy.

Compressional ULF waves in the outer magnetosphere:, 2. A case study of Pc 5 type wave activity

In previously published work (Zhu and Kivelson, 1991) the spatial distribution of compressional magnetic pulsations of period 2 ‐ 20 min in the outer magnetosphere was described. In this companion paper, we study some specific compressional events within our data set, seeking to determine the structure of the waves and identifying the wave generation mechanism. We use both the magnetic field and three‐dimensional plasma data observed by the ISEE 1 and/or 2 spacecraft to characterize eight compressional ULF wave events with frequencies below 8 mHz in the outer magnetosphere. High time resolution plasma data for the event of July 24, 1978, made possible a detailed analysis of the waves. Wave properties specific to the event of July 24, 1978, can be summarized as follows: (1) Partial plasma pressures in the different energy ranges responded to the magnetic field pressure differently. In the low‐energy range they oscillated in phase with the magnetic pressure, while oscillations in higher‐energy ranges were out‐of‐phase; (2) Perpendicular wavelengths for the event were determined to be 60,000 and 30,000 km in the radial and azimuthal directions, respectively. Wave properties common to all events can be summarized as follows: (1) Compressional Pc 5 wave activity is correlated with β, the ratio of the plasma pressure to the magnetic pressure; the absolute magnitude of the plasma pressure plays aminor role for the wave activity; (2) The magnetic equator is a node of the compressional perturbation of the magnetic field; (3) The criterion for the mirror mode instability is often satisfied near the equator in the outer magnetosphere when the compressional waves are present. We believe these waves are generated by internal MHD instabilities.