Some properties of geomagnetic field pulsations in the 0.1–1.0-Hz frequency range: A quantitative description and comparison with the satellite and ground-based observations

By using an image-dipole magnetic field model for a variety of plasma density profiles we have studied the latitude effect of the 0.1–1.0-Hz hydromagnetic wave propagation in the Earth's magnetosphere. On comparing the results of signal group delay time calculations for dipole and model magnetic fields with ground and satellite observations we obtain some propagation characteristics of Pc1s and localize the regions of their generation. Our results show that most high-latitude Pc1 events are generated in the outer magnetosphere in accordance with ground and satellite observations and theoretical considerations. The non-dipole geometry of the geomagnetic field in the outer magnetosphere (at geomagnetic latitudes φ₀ > 66°, L > 6) has a significant effect on the hydromagnetic wave propagation.     

Low-frequency upstream wave as a probable source of low-latitude Pc 3–4 magnetic pulsations

Daytime Pc 3–4 pulsation activities observed at globally coordinated low-latitude stations [SGC (L = 1.8,λ = 118.0°W), EWA(1.15,158.1°W), ONW(1.3,141.5°E)] are evidently controlled by the cone angle θ_XB of the IMF observed at ISEE 3. Moreover, the Pc 3–4 frequencies ($\text{?}$) at the low latitudes and high latitude (COL; L = 5.6 and λ = 147.9°W) on the ground and that of compressional waves at geosynchronous orbit (GOES 2; L = 6.67 and λ = 106.7°W) are also correlated with the IMFmagnitude(B_IMF).The correlation of $\text{?}$ of the compressional Pc 3–4 waves at GOES 2 against B_IMF is higher than those of the Pc 3–4 pulsations at the globally coordinated ground stations, i.e., γ = 0.70 at GOES 2, and (0.36,0.60,0.66,0.54) at (COL, SGC, EWA, ONW), respectively. The standard deviation ($\text{σ}{}_{\mathrm{n}}\text{= ± Δ?}\text{mHz}$) of the observed frequencies from the form $\text{?}$ (mHz) = 6.0 × B_IMF (nT) is larger at the ground stations than at GOES 2, i.e., $\text{Δ? = ± 6.6}\text{mHz at}$GOES 2, and ±(13.9, 9.1, 10.7, 12.1) mHz at (COL, SGC, EWA, ONW), respectively. The correlations between the IMF magnitude B_IMF and Pc 3–4 frequencies at the low latitudes are higher than that at the high latitude on the ground, which can be interpreted by a “filtering action” of the magnetosphere for daytime Pc 3–4 magnetic pulsations. The scatter plots of pulsation frequency $\text{?}$ against the IMF magnitude B_IMF for the compressional Pc 3–4 waves at GOES 2 are restricted within the forms $\text{? = 4.5 × B}{}_{\mathrm{<mtext>IMF</mtext>}}\text{and}\text{? = 7.5 × B}{}_{\mathrm{<mtext>IMF</mtext>}}$. The frequency distribution is in excellent agreement with the speculation ($\text{<ω}{}_{\mathrm{sc}}\text{Ω}{}_{\mathrm{i}}\text{= 0.3 ～ 0.5}$) of the spacecraft frame frequency of the magnetosonic right-hand waves excited by the anomalous ion cyclotron resonance with reflected ion beams with V₆ = 650 ～ 1150 km s^?1 in the solar wind frame observed by the ISEE satellite in the Earth's foreshock. These observational results suggest that the magnetosonic right-handed waves excited by the reflected ion beams in the Earth's foreshock are convected through the magnetosheath to the magnetopause, transmitted into the magnetosphere without significant changes in spectra, and then couple with various HM waves in the Pc 3–4 frequency range at various locations in the magnetosphere.     

Multipoint observations of low latitude ULF Pc3 waves in south-east Australia

Geomagnetic pulsations recorded on the ground are the signatures of the integrated signals from the magnetosphere. Pc3 geomagnetic pulsations are quasi-sinusoidal variations in the earth’s magnetic field in the period range 10–45 seconds. The magnitude of these pulsations ranges from fraction of a nT (nano Tesla) to several nT. These pulsations can be observed in a number of ways. However, the application of ground-based magnetometer arrays has proven to be one of the most successful methods of studying the spatial structure of hydromagnetic waves in the earth’s magnetosphere. The solar wind provides the energy for the earth’s magnetospheric processes. Pc3–5 geomagnetic pulsations can be generated either externally or internally with respect to the magnetosphere. The Pc3 studies undertaken in the past have been confined to middle and high latitudes. The spatial and temporal variations observed in Pc3 occurrence are of vital importance because they provide evidence which can be directly related to wave generation mechanisms both inside and external to the magnetosphere. At low latitudes (L < 3) wave energy predominates in the Pc3 band and the spatial characteristics of these pulsations have received little attention in the past. An array of four low latitude induction coil magnetometers were established in south-east Australia over a longitudinal range of 17 degrees at L = 1.8 to 2.7 for carrying out the study of the effect of the solar wind velocity on these pulsations. Digital dynamic spectra showing Pc3 pulsation activity over a period of about six months have been used to evaluate Pc3 pulsation occurrence. Pc3 occurrence probability at low latitudes has been found to be dominant for the solar wind velocity in the range 400–700 km/s. The results suggest that solar wind controls Pc3 occurrence through a mechanism in which Pc3 wave energy is convected through the magnetosheath and coupled to the standing oscillations of magnetospheric field lines.     

A generation mechanism for Pc 5 micropulsations in the morning sector

In the companion paper (Lam and Rostoker, 1978) we have shown that Pc 5 micropulsations are intimately related to the behaviour and character of the westward auroral electrojet in the morning sector. In this paper we show that Pc 5 micropulsations can be regarded as LC-oscillations of a three-dimensional current loop involving downward field-aligned current flow near noon, which diverges in part to form the ionospheric westward electrojet and returns back along magnetic field lines into the magnetosphere in the vicinity of the ionosphere conductivity discontinuity at the dawn meridian. The current system is driven through the extraction of energy from the magnetospheric plasma drifting sunwards past the flanks of the magnetosphere in a manner discussed by Rostoker and Boström (1976). The polarization characteristics of the pulsations on the ground can be understood in terms of the effects of displacement currents of significant intensity which flow near the F-region peak in the ionosphere and induced currents which flow in the earth. These currents significantly influence the magnetic perturbation pattern at the Earth's surface. Model current system calculations show that the relative phase of the pulsations along a constant meridian can be explained by the composite effect of oscillations of the borders of the electrojet and variations in the intensity of current flow in the electrojet.     

Pc3-4 geomagnetic pulsations at very low latitude in Brazil

In order to investigate Pc3-4 geomagnetic pulsations at very low and equatorial latitudes, L=1.0 to 1.2, we analyzed simultaneous geomagnetic data from Brazilian stations for 26 days during October-November 1994. The multitaper spectral method based on Fourier transform and singular value decomposition was used to obtain pulsation power spectra, polarization parameters and phase. Eighty-one (81) simultaneous highly polarized Pc3-4 events occurring mainly during daytime were selected for the study. The diurnal events showed enhancement in the polarized power density of about 3.2 times for pulsations observed at stations close to the magnetic equator in comparison to the more distant ones. The phase of pulsation observed at stations near the magnetic equator showed a delay of 48-62° in relation to the most distant one. The peculiarities shown by these Pc3-4 pulsations close to the dip equator are attributed to the increase of the ionospheric conductivity and the intensification of the equatorial electrojet during daytime that regulates the propagation of compressional waves generated in the foreshock region and transmitted to the magnetosphere and ionosphere at low latitudes. The source mechanism of these compressional Pc3-4 modes may be the compressional global mode or the trapped fast mode in the plasmasphere driving forced field line oscillations at very low and equatorial latitudes.     

Long-period magnetic pulsations generated in the magnetospheric boundary layers

Long-period hydromagnetic waves can be excited by the velocity shear instability in the magnetospheric boundary layers, where the penetrated bulk flow of the solar wind comprises a fairly strong velocity shear. Model spaces of the boundary layers are considered to estimate amplification rates on the HM waves in the low-latitude flank-side and in the dayside high-latitude and mantle-side boundary layers, where the ambient magnetic field is assumed to be perpendicular and parallel to the bulk flow of the solar wind, respectively. Wave characteristics of the HM waves are also investigated for the k-vector almost normal to the magnetopause.The localized HM waves in the Pc 3–4, Pc 4–5 and Pc 6 frequency ranges, of which group velocities are mostly parallel to the plane in the ambient magnetic field and the bulk flow directions, i.e., parallel to the magnetopause, are sufficiently amplified in the dayside low- and high-latitude, in the low-latitude flank-side, and in the mantle-side boundary layers, respectively. A left-handed toroidal (transverse) and a right-handed poloidal (compressional) mode of long-period $\text{(T ? 120}\text{s}\text{)Ω}{}_{\mathrm{A}}$-wave are generated in the dawn- and the duskflank boundary layers, respectively, where the k-vector of Alfvénic signals was assumed to be almost in the Archemedean spiral direction. The localized compressional HM waves in the Pc 3–4 range indicate both lefthanded and right-handed polarizations in the dayside boundary layer, which are functions of the k-vector of the waves and the sense of the velocity shear. The variance directions of perturbation fields of the HM waves in the magnetospheric boundary layers tend to be nearly parallel to the magnetopause. These localized HM waves can propagate into the high-latitude ionosphere. We conclude that the localized HM waves driven by the velocity shear instability in the magnetospheric boundary layers are the most probable source of the daytime Pc 3–5 magnetic pulsations in the outer magnetosphere.     

Global Pc5 wave activity observed using SuperDARN radars and ground magnetometers during an extended period of northward IMF

Observations are presented of long-lived global Pc5 ULF wave activity observed at a wide range of local times. The event was monitored in the high latitude ionosphere (∼60–80° magnetic latitude) by several SuperDARN HF radars and 5 magnetometer chains in Scandinavia, Greenland, Canada, Alaska and Russia. The event coincided with a protracted period (∼36 h) of northward interplanetary magnetic field (IMF). The study focuses on 4 h during which distinct dawn/dusk asymmetries in the wave characteristics were observed with multiple field line resonance (FLR) structures observed in the dawn flank at 1.7, 2.6, 3.3, 4.2 and 5.4 mHz and compressional oscillations in the dusk flank at 1.7 and 2.3 mHz. The data indicated an anti-sunward propagation in both the dawn and dusk flanks and a low azimuthal m number (∣m∣∼6) suggesting a generation mechanism external to the Earth's magnetosphere. A sudden increase in the solar wind dynamic pressure followed by a period of strongly northward, B_z dominated IMF, coincides with the observations and also a large increase in Pc5 wave power observed in the dawn flank. The observed enhancements in the wave activity and FLR structures are thought to be due to a Kelvin–Helmholtz driven waveguide mode. Additionally, there is no evidence that the frequencies of the FLRs are intrinsic to the solar wind. It thus seems that the frequencies were determined by the dimensions of the magnetospheric cavity.     

Magnetic pulsation behaviour in the magnetosphere inferred from whistler mode signals

During a long series of recordings of the Doppler shift of signals from NLK, Seattle, which have propagated in ducts in the whistler mode, a number of occasions have been noted where the duct has been acted on by the electric field of micropulsation events in the Pc4–5 range. Large oscillations are produced in the Doppler shift of the received VLF signal.It is shown that the field line has an antinode of motion in the equatorial plane, and that the Doppler shift is responding almost entirely to the radial component of the duct motion. The latter enables a comparison to be made between the magnetic disturbance in the magnetosphere and that seen on the ground. Some support is given to the prediction of Hughes (1974) and Inoue (1973) that the magnetospheric disturbance vector when seen on the ground is rotated 90° by the currents induced in the ionosphere. Models of the oscillating field line enable an estimate to be made of the azimuthal component of the electric field in the equatorial plane. This is typically $\text{1}\text{mV}\text{m}$. The model also predicts the north-south magnetic field strength of the transverse standing wave at the base of the magnetosphere, and this value may be compared with that seen on the ground. Values of the order 1–2 times the ground H-component or 5–10 times the ground D-component were found.     

Do we need a surface wave approach to the magnetospheric resonances?

In this paper we study a possible existence of surface wave (SW) global modes of the outer magnetosphere. The SW modes are supported by two plasma discontinuities: the plasmapause and the boundary between the open and closed field lines of the magnetosphere. Conditions under which the SW global modes can propagate azimuthally and along the magnetic field lines are examined. The ionosphere at the ends of the field lines is considered as reflecting boundaries of these SW modes. As a result SW standing wave structures along the magnetic field fluxes can be formed. Two branches of SW modes are derived. The low frequency branch, f_s,1 falls in the Pc5 range, while the high frequency branch, f_s,2—in the Pc4 range, where f_s,1(2) is the fundamental SW global mode frequency. Their frequencies possess quantized properties in the following way: f≡(1,2,3, …)f_s,1(2). The high frequency SW branch, f_s,2 exists only for relatively great azimuthal wavenumbers k_⊥. It is pointed out that most of the SW global mode characteristics are similar to those of the FLR. These results are applied to 1.8 mHz global mode observations on 11 January 1997. Spectral, phase and polarization properties of this Pc5 pulsation event under northward IMF conditions are examined as we see them from ground-based (L’Aquila and TNB observatories) and satellite (POLAR and INTERBALL) observations.     

Generation mechanism of Pc3 magnetic pulsations at very low latitudes

Polarization properties of Pc3 magnetic pulsations at very low latitudes cannot be explained by existing theories which are based on the field line resonance model, because magnetic field lines at ¦Φ¦ < 22° are almost entirely in the ionosphere. In order to interpret Pc3 polarization characteristics observed at very low latitudes (¦Φ¦ < 20°), I would like to propose a possible, new qualitative model in which two superimposed ionospheric eddy currents, oscillating with slight differences in frequency in the Pc3 range and in azimuthal wave number, move azimuthally at very low latitudes. The equatorial ionospheric Pedersen eddy currents are believed to be predominantly caused by inductive electric fields of compressional Pc3 source waves which may possibly arrive in the equatorial ionosphere from the outer magnetosphere.     

Quasi-periodic VLF emissions and concurrent magnetic pulsations seen at L = 4

The first observations are presented from Halley, Antarctica, of quasi-periodic (QP)_VLF intensity variations modulated at the frequency of concurrent Pc3 magnetic pulsations. Seen on broadband frequency-time plots, the QP emissions are of both the dispersive and non-dispersive types. From the frequency and phase variation with time of the QP emissions and magnetic pulsations, estimates are obtained of the travel times of the ULF waves from the interaction region to the ground. The observations appear consistent with the idea of modulation of a pre-existing VLF hiss source in the magnetosphere by the compressional components of ULF waves. A significant change in the travel time during one event is consistent with a crossing of the plasmapause by the Halley fieldline.     

Interaction of energetic particles with HM-waves in the magnetosphere

Energetic particle response in electromagnetic fields of ULF HM-waves in the magnetosphere is reviewed. Pc4–5 geomagnetic pulsations observed at the synchronous altitude are classified into three types, in respect to their major magnetic field polarization in different directions, local time dependence, and different characteristics of accompanied flux modulations of energetic particles, i.e., two nearly transverse waves with the azimuthal and the radial polarization, and the compressional stormtime pulsations. Firstly, we formulate the drift kinetic theory of particle flux modulations under the constraint of the magnetic moment conservation. A generalized energy integral of the particle motion interacting with a ULF-wave with the three-dimensional structure propagating to the azimuthal direction is obtained in the L-shell coordinate of a mirror magnetic field. Its linearized form is reduced to the same form as the previously derived energy change, including the bounce-drift resonant interaction. It is shown that the perturbed guiding center distribution function of energetic particles consists of four contributions, the adiabatic mirror effect corresponding to pitch-angle change, the kinetic effects due to energy change and the accompanying L-shell displacement, and the bounceaveraged drift phase bunching. Secondly, the basic HM-wave modes constitutingcoupling ULF oscillations in non-uniform plasmas are discussed in different models of approach for different plasma states. The diamagnetic drift Alfvén wave and the compressional drift wave with a larger azimuthal mode number in a high-beta plasma are candidates for the stormtimes pulsations. The former is intrinsically a guided localized mode, while the latter is a non-localized mode. By making use of the above preparation, we apply the developed drift kinetic theory to interpret the phase relationships between the ion flux modulation and the geomagnetic pulsation in some selected examples of observations, demonstrating a fair agreement in theoretical results with the observations.     

High-latitude Pc1–2 geomagnetic pulsations and their connection with location of the dayside polar cusp

The result of investigating high-latitude Pc1–2 pulsations are presented in this paper. They show that these unstructured oscillations are typical in intervals of low magnetic activity for regions of projections of the dayside cusp on the Earth's surface. The morphological properties of these pulsations, namely the character of their diurnal variations and dependence of their amplitude and frequency of occurrence on magnetic activity on different latitudes, suggest methods of utilization for tracing the location of the equatorial boundary of the dayside cusp. It is suggested that Pc1–2 pulsations are generated mainly in the dayside magnetosheath on field lines, crossing the magnetopause and entering in the dayside cusp. The possible mechanism of generation is the ion-cyclotron instability of plasma of finite pressure (β_⊥ ? 1) and with anisotropic temperature (T_⊥ > T_∥).     

Flapping motions of the tail plasma sheet induced by the interplanetary magnetic field variations

Flapping motions of the magnetotail with an amplitude of several earth radii are studied by analysing the observations made in the near (x = ?25 ~ ?30 R_E and the distant (x? ?60 R_E) tail regions. It is found that the flapping motions result from fluctuations in the interplanetary magnetic field, especially Alfvénic fluctuations, when the magnitude of the interplanetary magnetic field is larger than ~10 γ and they propagate behind the Earth with the solar wind flow. Flappings tend to be observed in early phases of the magnetospheric substorm, and they have two fundamental modes with periods of ~200 and ~500 sec. In some limited cases a good correspondence with the long period micropulsations (Pc5) in the polar cap region is observed. These observational results are explained by the model in which the Alfvénic fluctuations in the solar wind penetrate into the magnetosphere along the connected interplanetary-magnetospheric field lines. The characteristics of the flapping reveal that the geomagnetic tail is a good resonator for the hydromagnetic disturbances in the solar wind.     

The behaviour of outer radiation belt electrons (> 1·5 MeV) during a geomagnetically disturbed time on 8 March 1970 and its relationship to magnetospheric processes

Omnidirectional intensities of electrons with energies E_e > 1·5 MeV detected by a low orbiting polar satellite (GRS-A/AZUR) in the outer radiation belt are examined during disturbed times including the main phase of a very strong geomagnetic storm on 8 March 1970. The particle intensity features are discussed in relationship with proposed magnetospheric processes. It is found that a superposition of the two following effects can explain the particle behavior in the trapping region:(A) Radial diffusion. After the southward turning of the interplanetary field an inward motion of both the energetic electron belt and the plasmapause took place. This effect was observed at L > 3 R_E and we attribute it to enhanced magnetospheric electric field fluctuations. Later, a strong interplanetary shock impinged upon the magnetosphere which was related to the triggering of intense magnetospheric substorms; a further inward diffusion occurred at L ? 3 R_E, accompanied by an inward movement of the electron slot. A rough estimation of the diffusion coefficient leads to a power spectrum of the electric field fluctuations which seems to be consistent with experimentally determined power spectra (Mozer, 1971).(B) Adiabatic response to ring current changes. Large energetic electron intensity decreases within the outer radiation belt are shown to be adiabatic changes due to ring current variations. The influence of the inflation of the magnetosphere due to the developing ring current is simultaneously observed by the decrease of the solar proton outoff (1·7-2·5 MeV).     

Asymmetry effects associated with the x-component of the IMF in a magnetically open magnetosphere

The origin of magnetospheric asymmetry effects associated with the equatorial plane component of the interplanetary magnetic field (IMF) is discussed in terms of the forces exerted on open flux tubes mapping into the solar wind. It is argued that the downstream relaxation of the magnetosphere under the action of these stresses towards a state of reduced stress is such as to allow, in effect, partial penetration of this field component (both B_x and B_y in magnetospheric coordinates) into the magnetosphere. Many of the associated phenomena are therefore qualitatively described by the ‘dipole plus uniform IMF’ model, since this represents the idealization of exactly zero electromagnetic stress and hence gives a lowest order picture of the effects which result from magnetospheric relaxation toward that state. This is true of IMF B_y-associated effects which are well documented experimentally and which form a rich and consistent set of phenomena which have received considerable attention over the past decade. It is argued here that exactly corresponding phenomena are expected to be associated with the IMF B_x field as well, but because of the differing field direction these will take differing and usually less obvious forms than the similar effects associated with B_y. The suggested partial penetration of the IMF B_x field should be directly testable in the dipolar field region of the magnetosphere, but in the tail North-South displacements of the current sheet (and possibly magnetopause) are expected to occur instead. Some evidence of the latter displacements are presented. The other major IMF B_x effect should be noon-midnight displacements of the polar cap, such as have been recently reported. Little IMF B_x effect on auroral zone flows is anticipated, by contrast with the dawn-dusk asymmetries in this flow associated with IMF B_y.     

Generation of magnetic-field aligned currents,parallel electric fields,and inverted-V structures by plasma pressure inhomogeneities in the magnetosphere

Magnetic-field aligned currents driven by plasma pressure inhomogeneities (plasma clouds) in the distant magnetosphere are analyzed quantitatively. A parallel potential drop is found to be established in the upward current region whenever a spatial scale D₀ for the pressure gradient in the equatorial magnetosphere is smaller than $\text{≈ 3g}{}_0\text{B}{}_{\mathrm{i}}\text{B}{}_0$, where g₀ is a hot electron gyroradius in the equatorial magnetic field B₀ (B_i denotes the magnetic induction in the ionosphere). A theoretical derivation is given for the experimentally observed linear relation T = AE_p + T₀ between the characteristic energy T of precipitating magnetospheric electrons and the peak energy E_p in inverted-V electron spectra. Three-dimensional potential structures accelerating electrons earthward are shown to be established beneath some model clouds which could correspond to a large scale inverted-V structure and to a thin (~ 1 km) auroral arc.     

A high resolution study of continuous pulsations in the European sector

Complex demodulation has been described in detail and applied to Pi2 pulsations in a previous paper by Beamish et al. (1979). The technique is now extended to demonstrate spatiotemporal variations in the fundamental characteristics of Pc3 and Pc4 pulsations along a meridional profile extending from the U.K. to Iceland. With the exception of a high latitude Pc4 coupled resonance the results are consistent with a ?90° Hughes rotation (introduced by the ionosphere) of magnetospheric toroidal line resonances. Furthermore, the ionosphere appears capable of smoothing away the polarisation reversal which would be expected across such amplitude maxima within the plasmasphere. However, a toroidal line resonance in the Pc3 period range about which a sense of polarisation reversal is clearly observed on the ground is suggested as occurring at the plasmapause. This is accounted for in terms of the width of the resonance structure.     

Hydromagnetic waves driven by velocity shear instability in the magnetospheric boundary layer

The bulk flow of the solar wind plasma in the flank-side of the magnetospheric boundary layer, where the magnetic field lines are closed, has a component transverse to the ambient field. There is quite a strong velocity shear. The theoretical model ignores inhomogeneities in the ambient field and the mass density which occur at the magnetopause on about the same length scale as that of the velocity shear.Consideration is restricted to hydromagnetic waves which have a k-vector nearly normal to the B_o-V_o plane, i.e., approximately the magnetopause surface (k_x >k_z ～ k_y′k_xL_B > 1 and L_B = 0.1 ～ 1.0 R_E where L_B is a characteristic length of the boundary layer). It is found that a long-period (T ? 40 sec) hydromagnetic wave [the Alfvén-like wave ($\text{Ω}{}_{\mathrm{<mtext>A</mtext>}}$)] driven by velocity shear instability can be excited in the shear plasma. It is also found that the group velocity of the HM-wave is directed almost along the magnetic field line and that the magnetic variance in the shear plasma tends to be parallel to the B_o-V_o plane. The velocity shear instability in the magnetospheric boundary layer is judged to be a likely source of long-period magnetic pulsations.     

Drift anisotropy instability of a finite-β magnetospheric plasma

A unified theory of low frequency instabilities in a two component (cold and hot) finite-β magnetospheric plasma is suggested. It is shown that the low frequency oscillations comprise two wave modes : compressional Alfvén and drift mirror mode. No significant coupling between them is found in the long-wave approximation. Instabilities due to spontaneous excitation of these oscillations are considered. It is found that the temperature anisotropy significantly influences the instability growth rate at low frequency. A new instability due to the temperature anisotropy and density gradient appears when the frequency of compressional Alfvén waves is close to the drift mirror mode frequency. The theoretical predictions are compared in detail with the Pc5 event of 27 October 1978 observed simultaneously by the GEOS 2 satellite and the STARE radar facility. It is shown that the experimental results can be interpreted in terms of a compressional Alfvén wave driven by the drift anisotropy instability.