Density depletions and current singularities observed by Freja K. Stasiewicz and G. Holmgren
Swedish Institute of Space Physics, Uppsala Division, Uppsala
L. Zanetti
Applied Physics Laboratory, Johns Hopkins University, Laurel, Maryland
Abstract. High time resolution data collected by the Freja spacecraft in the
topside ionosphere (h 1500 km) reveal that the \low-frequency turbulence" observed commonly below the ion gyrofrequency consists of a large number of coherent plasma structures which represent intense eld-aligned currents (jk 30 , 300 Am,2 ) accompanied by plasma density depletions (cavities). The electromagnetic uctuations are identi ed with inertial electron Alfven waves (IEAW) at perpendicular wavelengths < 6 km. The coherent structures with singularly strong jk are consistent with being the resonance cones of IEAW generated by localized sources at h 1 RE . The density cavities are observed to be directly related to the magnetic eld gradient, i.e., intensity of eld-aligned current. Using multiresolution wavelet analysis we have investigated also the wave impedance and the polarization of the electromagnetic structures at di erent scales. The polarization records show phase discontinuities at small-scale electromagnetic structures which is consistent with the hypothesis that they represent resonance cones or interference patterns of IEAW.
1. Introduction
Low-frequency electromagnetic turbulence is a persistent feature of satellite observations in the auroral zone, and it is well documented in the literature [Maynard et al., 1982; Gurnett et al., 1984; Temerin et al., 1986; Berthelier et al., 1988]. On the other hand, there are numerous reports on coherent, localized electromagnetic eld perturbations, described as nonlinear Alfven waves [Chmyrev et al., 1986; Dubinin et al., 1990] or as solitary kinetic Alfven waves [Louarn et al., 1994; Wahlund et al., 1994; Volwerk et al., 1996]. The coherent structures have perpendicular widths comparable to the electron inertial length e = c=!pe (c is speed of light, and !pe is the electron plasma frequency), and they are associated with eldaligned currents of 100 Am,2 , parallel electric elds of tens of mV/m, strong electron heating and acceleration [Stasiewicz et al., 1997]. These phenomena are believed to be related to thin auroral arcs which have similar thickness when observed from ground [Maggs and Davis, 1968; Borovsky, 1993]. One of the unsolved questions is what causes a coherent structure to be formed in a particular location, and what are the key controlling
1
2 parameters. Unclear is also the relation, if any, between the broadband electromagnetic turbulence and coherent structures. There has been a few approaches to the establishment of localized Alfven structures. One school of thought suggests that short wavelength kinetic or inertial Alfven waves are generated by eld line resonances [Hasegawa, 1976; Samson et al., 1991; Wei et al., 1994; Streltsov and Lotko, 1995]. In this model, short length waves are supposed to be excited at the Alfven layer, ! = kk VA (y) by long waves propagating obliquely between the magnetosphere and ionosphere. Here VA = B (0 ),1=2 is the Alfven speed dependent also on the transverse coordinate y, and kk is the parallel wave number. The eld line resonance is expected to be located at the macroscopic density gradient where the wave phase speed matches the local Alfven speed. The concept of eld line resonances has been criticized recently by Bellan [1994, 1996a], who has argued that the singularity at the Alfven layer is a result of an erroneous assumption of MHD models that the parallel electric eld is equal to zero, in the derivation of the wave dispersion equation. Another hypothesis is that obliquely propagating waves would re ect from the ionosphere and the interference between the downgoing and the re ected wave would produce a solitary (arc) structure [Goertz and Boswell, 1979; Mallinckrodt and Carlson, 1978; Leontyev and Lyatsky, 1982; Haerendel, 1983; Lysak and Dum, 1983; Mishin and Forster, 1995]. In some models the ionosphere plays a major role in creating the spatial patterns by the resonant coupling between the drift waves and the Alfven waves, ! = k? vE , where vE is the ionospheric convection velocity [Trakhtengerts and Feldstein, 1991]. However, Borovsky [1993] has argued that small ? waves would be heavily damped in the ionosphere and would not be re ected. It has been also suggested that the downward propagating wave would steepen at some location along the eld line and become a \solitary wave" [Seyler et al., 1995], or a \stationary wave" [Knudsen, 1996]. There has been also a few analytical solutions for solitons and other nonlinear Alfvenic structures [Shukla et al., 1982; Shukla and Sten o, 1995; Kalita and Kalita, 1986; Wu et al., 1995; Pokhotelov et al., 1996], and for twodimensional vortices [Chmyrev et al., 1991; Streltsov et al., 1990], which may be relevant for discrete auroral structures. The above mentioned nonlinear solutions were obtained in a local geometry and do not address the macroscopic boundary conditions and propagation characteristics.
3 Recently, Stasiewicz [1997] have suggested that discrete, thin auroral structures could be related to the resonance or propagation cones of Alfven waves. We should recall here that in the Freja environment < me =mi , and the low-frequency (! < !ci ), cold plasma wave mode is the inertial electron Alfven wave. IEAW propagate inside the angle
r !! ;
(1)
vk = (1 + kV2A2 )1=2 ;
(2)
with the parallel velocity of and the cross- eld velocity
gm
? e
jv? j = e ! 1 +k?k2e2 c 2!! :
(3)
pe 1 = 2 1 = 2 where !gm = (!ce !ci ) = (mi =me ) !ci is the geo-
? e
metric mean of the electron and ion gyrofrequencies. In case of a localized source region, the short perpendicular wavelengths of a given frequency ! propagate on the surface of the (resonance) cone [Fisher and Gould, 1969; Kuehl, 1974; Borg et al., 1985; Morales et al., 1994; Bellan, 1996b]. In case of a horizontally elongated source region, the resonance surface would represent a curtain inclined to the magnetic eld. If the source of waves is localized and emits waves in broad frequency range, then each frequency component ! excites a resonance cone at di erent angles. An observer should see a family of resonance cones which would appear as short wavelength magnetic uctuations in satellite data. The purpose of this paper is to investigate further the environment of small-scale current structures in order to determine the key parameters controlling their generation and occurrence.
2. Data Analysis
The spin-stabilized Freja spacecraft was designed to investigate small-scale auroral phenomena. Launched in October 1992 and operated until 1995, Freja had an inclination of 63, perigee of 600 km, apogee of 1700 km, and rotation period of 6 s (for a detailed description of Freja instrumentation, see Space Science Reviews, 70, 405-602, 1994). Vector quantities discussed in this paper are presented in a coordinate system closely related to the the despun satellite coordinates. The Ox axis is along the main magnetic eld, the Oz axis is perpendicular to the magnetic eld in the plane containing the spin axis. The Oy axis completes the right-hand system.
4
2.1. Plasma Density and Magnetic Fluctuations
Figure 1 shows a short time interval of data from orbit 2396. The satellite was located at an altitude of 1760 Fig. 1 km with footprint location of 65.4 magnetic latitude and 15.6 MLT. This case shows multiple current structures which would correspond presumably to multiple auroral arcs in the afternoon sector of the auroral oval. The plasma density (Figure 1b) exhibits strong structuring which appears to be related to magnetic eld gradients, i.e., eld-aligned currents. Strong structuring is seen also in the electric eld component ey (Figure 1c), which is measured by two wire boom antennas in the spin plane of the satellite [Marklund et al., 1994b]. To identify the nature of the observed uctuations, we shall compare the magnetic and electric eld records. For Alfvenic perturbations the ratio between the electric and magnetic eld amplitudes should be equal or greater than the local Alfven speed; e?=b? > VA . In several previous studies [Louarn et al., 1994; Volwerk et al., 1996] such estimates have been made for a few solitary structures, with conclusions that the observed eld ratios are consistent with structures being (solitary) Alfven waves. A comprehensive way to analyze time series is provided by the wavelet technique which makes it possible to decompose a signal into a sequence of successively smaller scales, preserving orthogonality at the di erent scales, and maintaining full reversibility of the signal and its transforms [Mallat, 1989; Daubechies, 1991; Farge, 1992]. The result of a multiresolution analysis with orthogonal wavelets is that from a data set of, for example, 2J points uniformly spaced over the interval y, one obtains a sequence of j = 1 : J , 1 series which represent the components of the original signal corresponding to increasingly smaller scales yj = y=2j , referred to as dyad j . The sum of all subresolution components gives exactly the original signal. This technique makes also possible frequency separation of a signal, equivalent to low-pass and high-pass ltering. Figure 2 shows multiresolution decomposition of the Fig 2 magnetic eld component bz and the corresponding electric eld component ey . Each dyad level contains both electric and magnetic signals individually normalized and labeled with the apparent frequency and with the wave impedance (4) Z (f ) = 0 ~e~y (f ) ; bz (f ) expressed in ohms. A spatial scale corresponding to vs =f is also given at each dyad level. In contradis-
5 tinction to the standard Fourier analysis, the wavelet technique retains information on the localization of different scales contained in the original signal, as can be seen clearly in higher dyads in Figure 2. The wave impedance at each frequency is computed as the ratio of the root-mean-square values of each signal within the plotted time interval. The Alfven speed VA = B (0 nmi ),1=2 , and the equivalent impedance ZA = 0 VA can be computed with the number density of 6:5 103 cm,3 (Figure 1b) and the measured magnetic eld B = 2:6 104 nT. The e ective ion mass can be deduced from the observed cuto of the lower hybrid waves [Stasiewicz et al., 1994], which is about 4.5 kHz in the analyzed case. The above parameters give the ion composition equivalent to 90% of O+ and 10% of H+ , assuming that these two ion species dominate the plasma composition. The Alfven speed is then about 1900 km/s, and the impedance ZA 2:3 . Figure 2 shows that the wave impedance matches the local Alfven speed at frequencies 2-6 Hz, or spatial scale of < 6 km. Thus electromagnetic uctuations at kilometer scales are consistent with interpretation that these are (inertial) Alfven waves. The wave impedance is not given in dyads 5 and 6 which are a ected by residual spin e ects and the eld ratio there has no physical meaning. For a comparison, Figure 3 shows the wave impedance (4) computed for the interval 40-55 s in Figure 1 with the standard Fourier transform. The frequency range Fig. 3 is extended up to 1 kHz using the search coil magnetometer sensor. The Alfven wave impedance is observed in the frequency range 1-10 Hz (marked with \xx"), consistent with the previous wavelet analysis. In the frequency range 1-40 Hz there is an overlap and good correspondence between the uxgate and the search coil magnetometers. Above 50 Hz the uxgate magnetometer exhibits enhanced noise which is seen in Figure 3 as reduced impedance labeled \Ins." Above the frequency of 10 Hz one can see increasingly electrostatic character of waves. The label \H" marks a naturally reduced wave impedance just above the proton gyrofrequency fcH+ 398 Hz. Figure 4a shows a shorter time interval of the data from Figure 1. Now we can better see the relation be- Fig.4 tween the cavities (Figure 4b) and the magnetic eld gradients. Deep plasma cavities before time labels 42 and 44 are clearly related to strong magnetic gradients in Figure 4a indicating that cavitation process is related to eld aligned currents. Wavelet technique makes it possible to extract additional information from the observed time series. In
6 Figure 4c we show phase information contained in signals by ; bz of Figure 4a. The phase is shown as polarization angle, tan,1 (bz =by ) at di erent frequencies (spatial scales). The vertical scale within each dyad is from -180 to 180 degrees with the maximum just below the text label. In this case the signals are decomposed not in single dyads, as in Figure 2, but in \high-pass cumulative" dyads. This means that signals at each dyad level contain also higher-frequency components (up to 8 Hz, in this case). Such a decomposition is equivalent to high-pass ltering of a signal with increasing cuto frequencies. Labels given at each dyad show amplitude and scale of the signal. For example, the label for the bottom record reads that the signals used to compute the angles contain structures smaller than 26 km or frequencies greater than 0.2 Hz and the maximum eld amplitude is 94 nT. To interpret the polarization patterns, we should note that a linearly polarized Alfven wave or an elongated current sheet would produce a constant polarization angle at the value determined by the ratio of the components. A linearly polarized wave can be distinguished from a linear current by regular, repetitive polarization patterns. At the by zero crossing there will be discontinuous switch from a positive to negative polarization angle (180 ). Monotonically increasing (decreasing) angles correspond to the right-hand (left-hand) circular rotation when looking along the direction of the main magnetic eld. Elliptical polarization is manifested by appearance of two steps in the rising or decreasing angle. In the limit of linear polarization these steps expand and the rising/decreasing parts become discontinuous jumps. A more detailed description, with some examples of the polarization patterns can be found in the companion paper [Stasiewicz and Potemra, 1997] which also deals with macroscopic environment of the discussed here structures. The polarization records show that strong magnetic gradients in Figure 4a are associated with phase discontinuities. A possible explanation for this observation is that the analyzed magnetic singularities are produced as a result of interference of waves or vortices. For example, the current structure at time label 44 is clearly located at the interface between left- and righthand vortices of 10-km scale. On the other hand the structure at time 42 is consistent with a single current sheet. The importance of electromagnetic vortex structures in space plasmas is implied both from theoretical modeling [Chmyrev et al., 1991] and from observations [Marklund et al., 1994a]. It must be realized, however, that it is impossible for magnetometer data from a sin-
7 gle spacecraft to resolve the spatial-temporal structure of a measured event. It can be demonstrated that for inertial Alfven waves the perpendicular electric eld is a gradient of a scaler, which implies that the wave is linearly and not circularly polarized. Thus the eld rotations observed in the data indicate spatial vortices or current laments rather than circularly polarized waves in the time domain. Maggs and Morales [1996] reported recently laboratory observations of magnetic uctuations in an arti cially created density depression and suggested that these may be directly applicable to measurements in space. They have found that density and magnetic uctuations arise spontaneously in a narrow eld-aligned density striation in a magnetized discharge plasma. The nature of the uctuations is observed to depend upon the electron plasma beta. For e > me =mi the density and magnetic uctuations are strongly coupled, and the mode is identi ed as the drift Alfven wave. For e me =mi the density and magnetic uctuations separate in frequency and broadband Alfven wave turbulence develops. In both cases the driving source for the
uctuations was the cross- eld pressure gradient in the edge of the striation. The width of the cavity in the laboratory experiment is indeed about the width of the cavities measured by Freja ( 6 e ). However, the magnetic uctuations shown in Figures 1 and 4 are clearly a di erent phenomenon from the laboratory experiment of Maggs and Morales [1996]. The Alfven waves observed by Freja are not in the density cavities, rather it is the density cavities that are in waves. For example, the magnetic
uctuations in Figure 4a are not likely to be generated inside the cavities seen in Figure 4b. It is rather obvious that the cavities are produced by the waves and not vice versa. The mechanism responsible for the creation of cavities is most likely related to the ponderomotive force associated with the parallel electric eld of Alfven waves. A detailed analysis of plasma cavitation caused by inertial Alfven waves will be published elsewhere.
2.2. Resonance Cones
In the analyzed case, ne = 6000 cm,3 , Te 1 eV, B 26000 nT, the electron beta is e 3 10,5. Thus e < me =mO+ me =mH + corresponds to the low-beta case even for the oxygen dominated plasma. The natural low-frequency wave mode in < me =mi environment is the inertial electron Alfven wave with the characteristic resonance cone propagation patterns. Fisher and Gould [1969] presented the rst experimental veri cation of the existence of resonance cones
8 along which the observed elds become very large. For waves exp(,i!t), emitted by a point source, an exact mathematical solution to the homogeneous cold plasma wave equations for ! !ci is [Borg et al., 1985]
Ez
q
2 r2 =!2) exp(ikA z 2 , !gm
q2
2 r2 =!2 z , !gm
;
(5)
where kA = !=VA , and cylindrical coordinates are used with the z axis along the magnetic eld line and r the radial distance from the z axis. The solution for the parallel electric eld has a singular behavior on the conical surface r = !z=!gm and a phase behavior Ez exp(ikA z ) on the z axis. We present here further evidence that the electromagnetic singularities shown in Figures 1 and 4 could be explained as resonance cone patterns produced by a localized source above the Freja orbit in the acceleration region (h 1RE ), or further out in the magnetosphere. Let us focus on two singular density structures seen in Figure 4b. The spatial separation between the singularities in Figure 4 (and many others in Figure 1) could be associated with di erent frequency components in the wave spectrum at the source region. Two waves (!j : j = 1; 2) emitted by a small size (< c=!pe ) magnetospheric source would propagate on the cone surface given by the eiconal drj =dz = !j =!gm (z ) which is a generalization of (1) for inhomogenous magnetic eld. The related electromagnetic singularities (5) would spread in space and be separated by the distance y(z ) = r2 , r1 governed by dy = ! ; (6) dz ! (z ) gm
where ! = !2 , !1 . The electromagnetic singularities in Figure 4, are separated in space by y 15 km (2 s in time) and can be traced backwards to the origin y 0 with equation (6). The integration can be easily performed with a model magnetic eld, and the result is shown in Figure 5 for the case of a dipole eld on L = 8. Because we do not know exactly the separation Fig. 5 frequency of waves, the result is shown for three possible frequencies !=2 = 0:1; 1; 10 Hz in a purely hydrogen plasma (Figure 5a) and a purely oxygen plasma (Figure 5b). The results should be interpreted as follows. The separation distance of 15 km observed on Freja (left upper point on the plots) could be reached in several ways, depending on the wave frequencies and ion composition. For example, if two waves at oscillating frequencies, say, f1 = 1 Hz and f2 = 2 Hz are emitted by a localized source at an altitude of 3.2 (2.0) RE in purely hydrogen (oxygen) plasma, they would form two
9 resonance cone structures separated by 15 km at Freja altitude. As seen in Figures 5a and 5b, heavy ion plasma and larger di erential frequency lead to lower altitude for the source region, with the same nal separation y. The results show that the model is plausible and gives reasonable source locations above ' 1 RE .
2.3. Electromagnetic Singularities
To provide further evidence that the electromagnetic singularities seen in Figures 1 and 4 are consistent with resonance cone singularity (5), we focus in Figure 6 on the details from Figure 4. Field-aligned current com- Fig. 6 puted as jk (0 vs ),1 db? =dt is about 300 Am,2 in the upward direction. Here b? is the perpendicular perturbation eld transverse to the satellite velocity. The current computed in this way contains both stationary component as well as oscillatory wave currents. These two components cannot be separated with the available set of measurements. However, inspection of the electron distributions measured during this period (Figure 7) gives a supportive evidence that we observe indeed a thin upward current carried by a low-energy elec- Fig.7 tron beam, < 100 eV. The electron distributions are measured with an electrostatic spectrometer [Boehm et al., 1994] in the energy range 20 eV to 25 keV. Each data box represents grey-scale coded electron ux as function of energy and pitch angle, taken at 31.25 ms time resolution. Time runs from left to right and down. Usually, the currents carried by hot electrons represent only a fraction of the magnetometer current [Stasiewicz et al., 1997], which indicates the importance of thermal electrons (< 20 eV) as current carriers for thin auroral structures. The polarization plot (Figure 6d) shows that the magnetic ramp in Figure 6a is consistent with a single current sheet. The full width of the current structure in Figure 6c is about 400 m which corresponds to 6e with the measured value of e 65 m. The other plasma parameters that may be of interest are the following: Debye length D (1 eV) 0:1 m, cold oxygen gyroradius rO+ (1 eV) = 22 m, hot proton gyroradius rH + (1 keV) = 170 m. Another case of a small-scale (large intensity) current structure is taken from orbit 6889. The satellite was located at an altitude of 1730 km, 71 magnetic latitude, and 9.1 MLT. Figure 8 shows magnetic eld components, plasma density, electron energy ux in the downward direction, and eld-aligned current computed from the magnetometer data. One can see excellent Fig.8 correlation between the magnetometer current, density cavity, and the electron uxes. The orientation of the spacecraft spin plane with re-
10 spect to the magnetic eld does not make it possible to estimate the parallel electric eld in the case of singularities in Figure 6 and 8. However, similar structures reported previously [Stasiewicz et al., 1997] had the parallel electric eld about 2 orders of magnitude larger than expected for unbounded inertial Alfven waves. We suggest here that the measured anomalously large jk (and anomalously large Ek ) are directly related to the resonance cone singularity described by (5). The observations of strong eld-aligned currents, electron heating and formation of plasma cavities inside the current channels indicate dissipative, electrostatic-type processes driven by Ek , which support the resonance cone hypothesis. We should mention here that similar structures have been previously studied by other authors [Louarn et al., 1994; Wahlund et al., 1994; Seyler et al., 1995; Wu et al., 1995] who have suggested that these are manifestation of solitary kinetic Alfven waves (SKAW), postulated rst by Hasegawa and Mima [1976]. The analytical solutions for solitary (kinetic) waves obtained by Hasegawa and Mima [1976] are applicable for me =mi , which is not encountered in Freja environment.
2.4. Plasma Cavities and Langmuir Waves
For the veri cation of the true depth of the cavities associated with electromagnetic singularities, it is of primary importance to determine the range of instrumental e ects in the density measurements. The cavities discussed in this paper are clearly related to electromagnetic phenomena with the fundamental scale being the electron inertial length and should be distinguished from others, purely electrostatic structures, as for example \lower hybrid cavitons" [Eriksson et al., 1994], or double layers. Freja spacecraft carried also a high frequency snapshot receiver and could capture waveforms of Langmuir waves [Kintner et al., 1995]. The waveforms contain frequently strong, almost monochromatic signals which represent Langmuir and whistler waves excited by electron beams [Stasiewicz et al., 1996]. If the waves are in Langmuir mode, then they are excited near the electron plasma frequency !pe = (ne2 =me )1=2 which is determined by the plasma density. Figure 9 shows the density derived from the probe current in case of orbit 7199. The measurements were Fig. 9 taken at an altitude of 1650 km, magnetic latitude of 63 , and magnetic local time 2.4 hours. At 36 locations during this time interval we have data from the HF snapshot receiver. Assuming that the dominant mode is a Langmuir wave at frequency just below fpe , we com-
11 pute the density as ne (fpe =9)2 , where the frequency is in kHz and the density in cm,3 . Apart from a few data points, one can see rather good correspondence between the density derived from the probe current and from the Langmuir wave frequency. On smaller scales we see sometimes good consistency between the density derived from probe current and from the high frequency waves (Figure 10). The diverging points in Figure 9 Fig. 10 could be explained in a number of ways. First, the probe current ispdependent also on the electron temperature; jp / ne Te (1 + eVp =Te ), where Vp is the probe potential with respect to the plasma. In the density mode, the probe potential is p8 V (Vp =Te 1) and the collected current is jp / ne = Te . A localized increase in the electron temperature would produce similar e ect as decreasing density. Information on the electron temperature we can derive only once per 2 min from a diagnostic probe sweep. On shorter timescales we assume a constant electron temperature when deriving plasma density from the current. Thus variations of the electron temperature, of the satellite potential, or strong ambient electric eld can cause discrepancies seen in Figure 9, and even produce false plasma cavities. In addition, some of the narrowband HF waves could be excited in other modes and misinterpreted as Langmuir waves. The HF receiver logic selects the highest amplitude snapshot during the 1-4 s duty cycle so that the time of HF snapshot is not clock-determined but instead corresponds to the location of the strongest waves and so indirectly to the most unstable electron distribution. Examination of data from many orbits shows that the Langmuir snapshots are almost always displaced from the strong current channels and from the density cavities. This spatial displacement means that the electron beam exciting the Langmuir waves does not propagate along a eld-aligned density cavity but is instead related to an electromagnetic structure oblique to the magnetic eld, consistent with the resonance cone model. The absence of HF snapshots inside the cavities means also that the Langmuir wave frequency cannot be used to measure cavity depth or the density pro le inside the cavity, and that the cavities are not lled with strong Langmuir waves, and so are unlikely the result of the Langmuir waves pressure.
3. Conclusions
We have analyzed high time resolution data measured on Freja around small-scale current structures occurring in the auroral region and discussed several new aspects of the measurements with the following conclusions.
12
3.1. Origin of B, n Fluctuations
The magnetic perturbations have the relative amplitude B? =B 10,2 , spatial scale > c=!pe , are perpendicular to the main magnetic eld in the plasma environment me =mi . This is consistent with uctuations being electron inertial Alfven waves. Intermittently, singular magnetic eld gradients are observed on the electron skin-depth scale, accompanied by density cavities of similar width. These cavities appear to be produced by waves, and we nd no indication that the cavities could generate the observed waves by the pressure gradient at the edges of the cavities.
3.2. Wave Impedance
The spectral analysis of wave impedance (4) shows that waves in the frequency range 1-10 Hz (or spatial scales 0.6-6 km) have impedance consistent with the local Alfven impedance ZA = 0 VA . Waves at higher frequencies, (10-30 Hz) which may also include Dopplershifted short ? Alfvenic modes, exhibit increasingly electrostatic character.
3.3. Electromagnetic Singularities/Alfven Resonance Cones
They manifest in the data as strong magnetic eld gradients associated with increased perpendicular and parallel electric eld and with density depletions. These occur typically in an ensemble of similar structures with quasiperiodic separation. It is suggested that these singularities are directly related to the resonance cone solutions (5) for waves emitted by localized sources above the Freja orbit. Backward tracing of the resonance cones observed on Freja indicates that the source of waves could be located at altitudes h 1 RE .
3.4. Multiresolution Wavelet Analysis
A novel wavelet technique is applied to timeseries with electromagnetic singularities observed on Freja. The technique is used to study the wave impedance of the scale decomposed E and B signals and also for studying the polarization pattern of the magnetic components, b? = (by ; bz ) of shear Alfven waves. The analysis shows phase discontinuities of the magnetic signals at the positions of the electromagnetic singularities. Such phase discontinuities are consistent with structures being produced by interference of IEAW waves or vortices.
3.5. Langmuir Waves and the Plasma Density
Plasma density derived from the thermal electron current to the Langmuir probe is compared with the
13 density estimated from the frequency of Langmuir waves. We obtain fairly good agreement between these two methods. However, the Langmuir wave snapshots almost never occur inside the cavities associated with electromagnetic singularities, which indicates that the electron beams driving these waves are displaced from the electromagnetic structure. We interpret this spatial mismatch as a signature of electromagnetic structure being inclined to the magnetic eld, consistent with the resonance cone model. In summary, we have provided several new arguments in favor of the hypothesis that the small-scale, largeamplitude, electromagnetic structures observed by Freja are related to Alfven resonance cones (ARCs).
Acknowledgments. The authors would like to thank P.-A. Lindqvist for providing the electric eld (F1) data and J. Clemmons for making available to us the electron (F7) data used in this publication. The Editor thanks G. J. Morales and another referee for their assistance in evaluating this paper.
References
Bellan, P. M., Alfven resonance reconsidered: Exact equations for wave propagation across a cold inhomogenous plasma, Phys. Plasmas, 1, 3523{3541, 1994. Bellan, P. M., Mode conversion into non-MHD waves at the Alfven layer: The case against the eld line resonance concept, J. Geophys. Res., 101, 24,887{24,898, 1996a. Bellan, P. M., New model for ULF pc5 pulsations: Alfven cones, Geophys. Res. Lett., 23, 1717{1720, 1996b. Berthelier, J.-J., C. Machard, J.-C. Cerisier, A. Berthelier, and J. M. Bosqued, ULF electromagnetic turbulence in the high-altitude topside ionosphere, J. Geophys. Res., 93, 5701, 1988. Boehm, M., G. Paschmann, J. Clemmons, H. Hofner, R. Frenzel, M. Ertl, G. Haerendel, P. Hill, H. Lauche, L. Elliasson, and R. Lundin, The TESP electron spectrometer and correlator F7 on Freja, Space Sci. Rev., 70, 509{540, 1994. Borg, G. G., M. H. Brennan, R. C. Cross, L. Giannone, and I. J. Donnelly, Guided propagation of Alfven waves in a toroidal plasma, Plasma Phys. Controlled Fusion, 27, 1125, 1985. Borovsky, J. E., Auroral arc thicknesses as predicted by various theories, J. Geophys. Res., 98, 6101{6138, 1993. Chmyrev, V. M., S. V. Bilichenko, Y. B. Kazanskaya, V. M. Kostin, V. I. Lazarev, and M. V. Teltsov, Auroral particles associated with nonlinear Alfven waves, Geomagn. Aeron., 26, 224{229, 1986. Chmyrev, V. M., V. Marchenko, O. A. Pokhotelov, L. Sten o, A. V. Streltsov, and A. Steen, Vortex structures in the ionosphere and the magnetospere of the Earth, Planet. Space Sci., 39, 1025{1030, 1991. Daubechies, I., Ten Lectures on Wavelets, Lecture Notes Series, Soc. for Ind. and Appl. Math., Philadelphia, Pa, 1991. Dubinin, E. M., P. L. Israelevich, and N. S. Nikolayeva,
14 Auroral electromagnetic disturbances at an altitude of 900 km, Planet. Space Sci., 38, 97{108, 1990. Eriksson, A., B. Holback, P. O. Dovner, R. Bostrom, G. Holmgren, M. Andre, L. Eliasson, and P. M. Kintner, Freja observations of correlated small-scale density depletions and enhanced lower hybrid waves, Geophys. Res. Lett., 21, 1843-1846, 1994. Farge, M., Wavelet transforms and their application to turbulence, Ann. Rev. Fluid Mech., 24, 395{457, 1992. Fisher, R. K., and R. W. Gould, Resonance cones in the eld pattern of a short antenna in an anisotropic plasma, Phys. Rev. Lett., 22, 1093, 1969. Goertz, C. K., and R. W. Boswell, Magnetosphereionosphere coupling, J. Geophys. Res., 84, 7239{7246, 1979. Gurnett, D., R. L. Hu , J. D. Menietti, J. L. Burch, J. D. Winningham, and S. D. Shawhan, Correlated lowfrequency electric and magnetic noise along the auroral eld lines, J. Geophys. Res., 89, 8971-8985, 1984. Haerendel, G., An Alfven wave model of auroral arcs, in High-Latitude Space Plasma Physics, edited by B. Hultqvist and T. Hagfors, pp. 515{535, Plenum, New York, 1983. Hasegawa, A., Particle acceleration by MHD surface wave and formation of aurora, J. Geophys. Res., 81, 5083{5090, 1976. Hasegawa, A., and K. Mima, Exact solitary Alfven wave, Phys. Rev. Lett., 37, 690, 1976. Kalita, M. K., and B. C. Kalita, Finite-amplitude solitary Alfven waves in a low-beta plasma, J. Plasma Phys., 35, 267, 1986. Kintner, P. M., J. Bonnel, S. Powell, and J.-E. Wahlund, First results from the Freja HF snapshot receiver, Geophys. Res. Lett., 22, 287{290, 1995. Knudsen, D. J., Spatial modulation of electron energy and density by nonlinear stationary inertial Alfven waves, J. Geophys. Res., 101, 10761-10772, 1996. Kuehl, H. H., Resonance cones for frequencies below the ion cyclotron frequency, Phys. Fluids, 17, 1636, 1974. Leontyev, S. V., and W. B. Lyatsky, Solitary auroral arc generation, Planet. Space Sci., 30, 1{4, 1982. Louarn, P., J.-E. Wahlund, T. Chust, H. de Feraudy, A. Roux, B. Holback, P.-O. Dovner, and G. Holmgren, Observations of kinetic Alfven waves by the Freja spacecraft, Geophys. Res. Lett., 21, 1847{1850, 1994. Lysak, R. L., and C. T. Dum, Dynamics of magnetosphereionosphere coupling including turbulent transport, J. Geophys. Res., 88, 365{380, 1983. Maggs, J. E., and T. N. Davis, Measurements of the thickness of auroral structures, Planet. Space Sci., 16, 205, 1968. Maggs, J. E., and G. J. Morales, Magnetic uctuations associated with eld-aligned striations, Geophys. Res. Lett., 23, 633-636, 1996. Mallat, S., A theory for multiresolution signal decomposition, IEEE, Trans. Pattern Anal. Machine Intell., 2, 7, 1989. Mallinckrodt, A. J., and C. W. Carlson, Relations between transverse electric elds and eld-aligned currents, J. Geophys. Res., 83, 1426-1432, 1978. Marklund, G., L. Blomberg, C.-G. Falthammar, and P.-A. Lindqvist, On intense diverging electric elds associated
15 with black aurora, Geophys. Res. Lett., 21, 1859{1862, 1994a. Marklund, G. T. et al., The double probe electric eld experiment on Freja: Experiment description and rst results, Space Sci. Rev., 70, 483{508, 1994b. Maynard, N. C., J. P. Heppner, and A. Egeland, Intense, variable electric elds at ionospheric altitudes in the high latitude regions as observed by DE-2, Geophys. Res. Lett., 9, 981-984, 1982. Mishin, E. V., and M. Forster, Alfvenic shocks and lowaltitude auroral acceleration, Geophys. Res. Lett., 22, 1745{1748, 1995. Morales, G. J., R. S. Loritsch, and J. E. Maggs, Structure of Alfven waves at the skin-depth scale, Phys. Plasmas, 1, 3765{3774, 1994. Pokhotelov, O. A., D. O. Pokhotelov, M. B. Gokhberg, F. Z. Feygin, L. Sten o, and P. K. Shukla, Alfven solitons in the Earth's ionosphere and magnetosphere, J. Geophys. Res., 101, 7913{7915, 1996. Samson, J. C., T. J. Hughes, F. Creutzberg, D. D. Wallis, R. A. Greenwald, and J. M. Ruohoniemi, Observations of a detached discrete arc in association with eld line resonances, J. Geophys. Res., 96, 15,683{15,695, 1991. Seyler, C. E., J.-E. Wahlund, and B. Holback, Theory and simulation of low-frequency plasma waves and comparison to Freja satellite observations, J. Geophys. Res., 100, 21,453{21,472, 1995. Shukla, P. K., and L. Sten o, Nonlinear Alfven waves, Phys. Scr., T60, 32{35, 1995. Shukla, P. K., H. D. Rahman, and R. P. Sharma, Alfven soliton in a low-beta plasma, J. Plasma Phys., 28, 125, 1982. Stasiewicz, K., and T. A. Potemra, Multiscale current structures observed by Freja, J. Geophys. Res., this issue. Stasiewicz, K., G. Gustafsson, G. Holmgren, B. Holback, L. Eliasson, P. Kintner, and L. Zanetti, Wave environment inside an inverted-v electron event observed by Freja, Geophys. Res. Lett., 21, 1839{1842, 1994. Stasiewicz, K., B. Holback, V. Krasnoselskikh, M. Boehm, and P. Kintner, Parametric instabilities of Langmuir waves observed by Freja, J. Geophys. Res., 101, 21,515{ 21,525, 1996. Stasiewicz, K., G. Gustafsson, G. Marklund, P.-A. Lindqvist, J. H. Clemmons, and L. Zanetti, Cavity resonators and Alfven resonance cones observed on Freja, J. Geophys. Res., 102, 2565{2575, 1997. Streltsov, A., and W. Lotko, Dispersive eld line resonances on auroral eld lines, J. Geophys. Res., 100, 19,457{ 19,472, 1995. Streltsov, A. V., V. M. Chmyrev, O. A. Pokhotelov, V. A. Marchenko, and L. Sten o, The formation and nonlinear evolution of convective cells in the auroral plasma, Phys. Scr., 41, 686{692, 1990. Temerin, M., J. McFadden, M. Boehm, C. W. Carlson, and W. Lotko, Production of ickering aurora and eldaligned electron ux by electromagnetic ion cyclotron waves, J. Geophys. Res., 91, 5769-5792, 1986. Trakhtengerts, V. Y., and A. Y. Feldstein, Turbulent Alfven layer in the polar ionosphere: excitation condition and energetics, J. Geophys. Res., 96, 19,363{19,374, 1991. Volwerk, M., P. Louarn, T. Chust, A. Roux, H. de Feraudy, and B. Holback, Solitary kinetic Alfven waves: A study of
16 the Poynting ux, J. Geophys. Res., 101, 13,335{13,343, 1996. Wahlund, J.-E., P. Louarn, T. Chust, H. de Feraudy, A. Roux, B. Holback, P.-O. Dovner, and G. Holmgren, On ion-acoustic turbulence and the nonlinear evolution of kinetic Alfven waves in aurora, Geophys. Res. Lett., 21, 1831{1834, 1994. Wei, C. Q., J. C. Samson, R. Rankin, and P. Frycz, Electron inertial e ects on geometric eld line resonances, J. Geophys. Res., 99, 11,265{11,276, 1994. Wu, D.-J., D.-Y. Wang, and C.-G. Falthammar, An analytical solution of nite amplitude solitary kinetic Alfven waves, Phys. Plasmas, 2, 4476{4481, 1995. G. Holmgren and K. Stasiewicz, Swedish Institute of Space Physics, Uppsala Division, S-755 91 Uppsala. (e-mail:
[email protected],
[email protected]) L. Zanetti, Applied Physics Laboratory, Johns Hopkins University, Laurel, MD 20723-6099, (e-mail:
[email protected]) (Received December 11, 1996; revised June 3, 1997; accepted July 3, 1997.) Copyright 1997 by the American Geophysical Union. Paper number 97JA02007. 0148-0227/97/97JA-02007$09.00
17 97JA02007 High time resolution data collected by the Freja spacecraft in the topside ionosphere (h 1500 km) reveal that the \low-frequency turbulence" observed commonly below the ion gyrofrequency consists of a large number of coherent plasma structures which represent intense eld-aligned currents (jk 30 , 300 Am,2 ) accompanied by plasma density depletions (cavities). The electromagnetic uctuations are identi ed with inertial electron Alfven waves (IEAW) at perpendicular wavelengths < 6 km. The coherent structures with singularly strong jk are consistent with being the resonance cones of IEAW generated by localized sources at h 1 RE . The density cavities are observed to be directly related to the magnetic eld gradient, i.e., intensity of eld-aligned current. Using multiresolution wavelet analysis we have investigated also the wave impedance and the polarization of the electromagnetic structures at di erent scales. The polarization records show phase discontinuities at small-scale electromagnetic structures which is consistent with the hypothesis that they represent resonance cones or interference patterns of IEAW.
Figure 1. An interval of 30 s from orbit 2396: (a)
perpendicular perturbation magnetic eld components (by ; bz ), (b) plasma density derived from Langmuir probe current, and (c) perpendicular component of the electric eld ey . Figure 1. An interval of 30 s from orbit 2396: (a) perpendicular perturbation magnetic eld components (by ; bz ), (b) plasma density derived from Langmuir probe current, and (c) perpendicular component of the electric eld ey . Figure 2. Wavelet decomposition of the electric ey and magnetic bz eld components labeled with the wave impedance Z (f ) = 0 e~y (f )=~bz (f ) at given frequency.
Figure 2. Wavelet decomposition of the electric ey and magnetic bz eld components labeled
with the wave impedance Z (f ) = 0 e~y (f )=~bz (f ) at given frequency. Figure 3. Wave impedance Z (f ) = 0e~y (f )=~bz (f ) computed with Fourier transform for the data from Figure 1. The low-frequency range (up to 64 Hz) is covered by uxgate magnetometer and the higher frequencies are covered by search coil magnetometer. Alfven wave impedance is observed in the frequency range 1-10 Hz (see text). Figure 3. Wave impedance Z (f ) = 0 e~y (f )=~bz (f ) computed with Fourier transform for the data from Figure 1. The low-frequency range (up to 64 Hz) is covered by uxgate magnetometer and the higher frequencies are covered by search coil magnetometer. Alfven wave impedance is observed in the frequency range 1-10 Hz (see text). Figure 4. (a-b) Details of,1the data from Figure 1 and (c) polarization angle tan (bz =by ) for wavelet decomposed signals in Figure 4a; see text. Figure 4. (a-b) Details of the data from Figure 1 and (c) polarization angle tan,1(bz =by ) for wavelet decomposed signals in Figure 4a; see text. Figure 5. Backward tracing of resonance cones observed in Figure 4 with (6). The source of waves could be located at altitudes 1-6 RR , depending on the wave frequency and ion composition (see text for discussion). Figure 5. Backward tracing of resonance cones observed in Figure 4 with (6). The source of waves could be located at altitudes 1-6 RR , depending on the wave frequency and ion composition (see text for discussion). Figure 6. Zoom at a coherent current structure from Figure 4: (a) magnetic eld components, (b) plasma density, (c) eld-aligned current derived from Figure 6a, (d) polarization angle of decomposed signals. Figure 6. Zoom at a coherent current structure from Figure 4: (a) magnetic eld components, (b) plasma density, (c) eld-aligned current derived from Figure 6a, (d) polarization angle of decomposed signals. Figure 7. Electron ux distribution measured around the cavity in Figure 5. Each data box represents greyscale coded electron ux as function of energy and pitch angle, taken at 31.25-ms time resolution.
18
Figure 7. Electron ux distribution measured around the cavity in Figure 5. Each data box
represents grey-scale coded electron ux as function of energy and pitch angle, taken at 31.25-ms time resolution. Figure 8. A nonlinear current structure from orbit 6889: (a) magnetic eld, (b) plasma density, (c) electron energy ux, (d) eld-aligned current derived from Figure 8a. Figure 8. A nonlinear current structure from orbit 6889: (a) magnetic eld, (b) plasma density, (c) electron energy ux, (d) eld-aligned current derived from Figure 8a. Figure 9. Plasma density derived from the current to a Langmuir probe (solid line), and from the frequency of Langmuir waves (asterisk) for orbit 7199, April 4, 1994. Figure 9. Plasma density derived from the current to a Langmuir probe (solid line), and from the frequency of Langmuir waves (asterisk) for orbit 7199, April 4, 1994. Figure 10. Details from Figure 9. Figure 10. Details from Figure 9. STASIEWICZ ET AL.: DENSITY DEPLETIONS AND CURRENT SINGULARITIES STASIEWICZ ET AL.: DENSITY DEPLETIONS AND CURRENT SINGULARITIES STASIEWICZ ET AL.: DENSITY DEPLETIONS AND CURRENT SINGULARITIES STASIEWICZ ET AL.: DENSITY DEPLETIONS AND CURRENT SINGULARITIES STASIEWICZ ET AL.: DENSITY DEPLETIONS AND CURRENT SINGULARITIES STASIEWICZ ET AL.: DENSITY DEPLETIONS AND CURRENT SINGULARITIES STASIEWICZ ET AL.: DENSITY DEPLETIONS AND CURRENT SINGULARITIES STASIEWICZ ET AL.: DENSITY DEPLETIONS AND CURRENT SINGULARITIES STASIEWICZ ET AL.: DENSITY DEPLETIONS AND CURRENT SINGULARITIES STASIEWICZ ET AL.: DENSITY DEPLETIONS AND CURRENT SINGULARITIES STASIEWICZ ET AL.: DENSITY DEPLETIONS AND CURRENT SINGULARITIES STASIEWICZ ET AL.: DENSITY DEPLETIONS AND CURRENT SINGULARITIES STASIEWICZ ET AL.: DENSITY DEPLETIONS AND CURRENT SINGULARITIES STASIEWICZ ET AL.: DENSITY DEPLETIONS AND CURRENT SINGULARITIES STASIEWICZ ET AL.: DENSITY DEPLETIONS AND CURRENT SINGULARITIES STASIEWICZ ET AL.: DENSITY DEPLETIONS AND CURRENT SINGULARITIES
19
20 STASIEWICZ ET AL.: DENSITY DEPLETIONS AND CURRENT SINGULARITIES STASIEWICZ ET AL.: DENSITY DEPLETIONS AND CURRENT SINGULARITIES STASIEWICZ ET AL.: DENSITY DEPLETIONS AND CURRENT SINGULARITIES STASIEWICZ ET AL.: DENSITY DEPLETIONS AND CURRENT SINGULARITIES STASIEWICZ ET AL.: DENSITY DEPLETIONS AND CURRENT SINGULARITIES STASIEWICZ ET AL.: DENSITY DEPLETIONS AND CURRENT SINGULARITIES STASIEWICZ ET AL.: DENSITY DEPLETIONS AND CURRENT SINGULARITIES STASIEWICZ ET AL.: DENSITY DEPLETIONS AND CURRENT SINGULARITIES STASIEWICZ ET AL.: DENSITY DEPLETIONS AND CURRENT SINGULARITIES STASIEWICZ ET AL.: DENSITY DEPLETIONS AND CURRENT SINGULARITIES STASIEWICZ ET AL.: DENSITY DEPLETIONS AND CURRENT SINGULARITIES STASIEWICZ ET AL.: DENSITY DEPLETIONS AND CURRENT SINGULARITIES STASIEWICZ ET AL.: DENSITY DEPLETIONS AND CURRENT SINGULARITIES STASIEWICZ ET AL.: DENSITY DEPLETIONS AND CURRENT SINGULARITIES STASIEWICZ ET AL.: DENSITY DEPLETIONS AND CURRENT SINGULARITIES STASIEWICZ ET AL.: DENSITY DEPLETIONS AND CURRENT SINGULARITIES STASIEWICZ ET AL.: DENSITY DEPLETIONS AND CURRENT SINGULARITIES STASIEWICZ ET AL.: DENSITY DEPLETIONS AND CURRENT SINGULARITIES STASIEWICZ ET AL.: DENSITY DEPLETIONS AND CURRENT SINGULARITIES STASIEWICZ ET AL.: DENSITY DEPLETIONS AND CURRENT SINGULARITIES STASIEWICZ ET AL.: DENSITY DEPLETIONS AND CURRENT SINGULARITIES STASIEWICZ ET AL.: DENSITY DEPLETIONS AND CURRENT SINGULARITIES
