The double-peaked Doppler-velocity spectra described previously have been identified as a special feature of the F-layer during certain ionospheric conditions. The following section will try to summarize several possible mechanisms that can produce a double-peaked Doppler-velocity spectrum.
These featured spectra co-locate approximately with the auroral oval and, for some events near magnetic noon, the cusp. Therefore conditions related to auroral and cusp particle precipitation can contribute to the generation of these spectra. Furthermore, a correlation with low-energy electron precipitation can be observed; this form of electron precipitation produces a region of enhanced ionization of the upper E- or lower F-layer. Thus, the spectra could be linked to an increased ionization rate. A feature that was observed in the region of the low-energy electron precipitation is the great spatial inhomogeneity of the flux. It is also interesting to note here that Grant et al. (1995) observed that, although SuperDARN and CADI ionosonde data in general were in agreement, there was some disagreement in the vicinity of spatial structures of strong F-region ionization. Therefore, if strong ionization is a factor in producing double-peaked Doppler-velocity spectra it could also be that the greatest error using the SuperDARN phase-fit analysis technique occurs because the method, which is very effective for single-peaked spectra, is less effective for multiple peaked spectra. Since most double peaked spectra events occurred during relatively quiet magnetospheric conditions, magnetic substorms are probably not related to the production of the spectral features. Nevertheless, these events are frequently seen near magnetic local noon and could be related to dayside aurora or the cusp/cleft region which is closely associated with reconnection and the resulting plasma turbulence and FACs. The analysis of the averaged plasma flow maps shows that the spectral features occur regardless of the general flow direction and speed. There is, however, evidence that a shear in flow is co-located with double-peaked spectra.
In general, the spectrum of a single F-region scatterer consists of one peak of Gaussian or Lorentzian shape [HVG 93]. If there are several scatterers in the field of view, signal-mixing occurs and several peaks corresponding to the distinct sources could be present in the spectrum. Since the scattering volume produced by the beam-forming and range-gating of the radar has a modest spatial extent (approximately by at a range) and the observation time is of the order of seconds, it is possible that different Doppler velocities are observed in the same volume. Nevertheless, the analysis in this thesis has shown that the double-peaked spectra constitute only a small fraction ( %) of the total scatter. The bulk of the radar echoes exhibit single peaks even when double-peaked regions appear in limited regions. This fact is of course used in the current SuperDARN data-processing scheme using the phase-fit method to determine the mean Doppler velocity in the scattering region.
To generate a double-peak in the spectrum, a mechanism is needed that will increase the Doppler velocity in one area of the scattering volume and decrease it in another. The scale of the mechanism should be small enough to fit into a single scattering volume observed by the radar. It should also preserve the mean Doppler velocity of the bulk medium as the average velocity maps do not show any anomalies when double-peaked spectra are present. We can distinguish two classes of mechanisms that produce double-peaked spectra: either there are two adjacent distinct regions of different flow velocities (a region of velocity shear) or there is a single structure with varying flow.
The first class of distinct regions could be observed when a gradient drift instability is dominant. If a plasma enhancement is created through ionization of the F-layer, the gradient drift instability will produce density waves that travel away from the enhancement at a speed , where is the polarization electric field and the B the magnetic field. The main problem with the gradient drift instability is that the observed speeds, which are of the order of hundreds of m/s, are too large to be produced and maintained easily by the polarization electric fields as they would be required to have the same order of magnitude as the large scale electric fields. Table 6.1 lists the mean velocity separation and corresponding standard deviation from the mean for the events. The mean separation of 254 m/s is well defined and comparable to the usual convection velocity component measured by a single radar in the F-region.
Table 6.1: Statistics of the double-peak spectra: number of spectra, mean velocity separation and standard deviation from the mean
The second class of mechanisms occurs in a number of situations that are similar in their velocity profiles. Doppler velocity spectral measurements of the D-region have produced double-peaked spectral features which have been attributed to gravity waves. The motion of gravity waves through the field of view of the radar beam produces a modulation pattern that generates a spectrum that is broadened to two distinct peaks. Such a behavior has been described by several authors [LT89, SGR 90, JCN91]. Traveling ionospheric disturbances modulate the phase of received F-region HF signals, but produce only a median jitter velocity of 0.4 m/s [JCN91, p. 71,] which is far less than the observed velocity separation of most peaks (and of course the resolution of the instrument). The main effect of gravity waves on SuperDARN data is the quasi-periodic enhancement of ground-scatter [BGS94].
Another possibility that is more appropriate for the SuperDARN geometry is the generation of a vortical flow pattern of the plasma (and the embedded instabilities). A vortical flow pattern generates a Doppler velocity spectrum similar to that from gravity waves. In the ionosphere, one can identify vortices at all scale sizes which means they are a common feature. On a global scale, a consistent two-cell convection pattern is observed that looks like twin-vortices (see for example the recent and well known HM-model [HM87]). Long-lived vortices in the plasma flow of the F-region with a size of about 1000 km have been observed with the SuperDARN radar and ground-based magnetometers and are believed to be caused by the Kelvin-Helmholtz instability at the inner edge of the low-latitude boundary layer [BSJ 95]. Traveling convection vortices (TCVs) are short-lived and fast moving vortical plasma flow structures of 500-1000 km in size that have been observed for several years and are believed have a significant effect on the localized ionosphere [SZS94]. Vortices are frequently associated with auroral observations [Dav92]. The pertubation of the geomagnetic field by the field of a sheet current tends to warp the sheet into a vortex. This process applies to the electron precipitation that causes auroral emissions and creates a visible auroral spiral of 20-1500 km diameter. A similar development caused by excess electric charge creates 2-10 km sized auroral curls in which geomagnetic field lines remain mutually parallel. A recent dynamic theory of auroral spirals included the effects of field-aligned current in a velocity shear driven Kelvin-Helmholtz instability model. The model produces vortices which are wound in a sense consistent with spiral observations and that grow faster than predicted by the simpler models [LS96].
Vortical flows can be produced by the Kelvin-Helmholtz instability which in turn requires regions of velocity shear perpendicular to the flow direction. Thus, if the Kelvin-Helmholtz instability is the cause of vortical flow, there should be some correlation with velocity shear. In several events a strong velocity shear can be observed in the north-south direction where double-peaked spectra occur (16 Jan/95, 26 Jan/95, 20 Feb/95 and 21 Feb/95). This shear is expected from the current reversal in the boundary layer as shown in Figure 6.1.
Figure 6.1: Three dimensional view of plasma convection in the equatorial plane and in the ionosphere (from W. J. Heikkila)
The likely region of development of small-scale vortices by the Kelvin-Helmholtz instability is the inner edge of the low latitude boundary layer [Lee84] which would correspond to a ``Region 1'' (R1) field aligned current. Figure 6.2 shows a macroscopic convection vortex on the morning side that is associated with a R1 FAC. Double-peaked spectra were observed within one degree in latitude from N over a longitudinal range from E to E which corresponds to the region with a current of .
Figure 6.2: SuperDARN curl map for 20 Feb/95 showing strong R1-FAC and a large scale vortex at about 10:00 magnetic local time
Another way of generating a vortical flow is the generation of a column of charge. When comparing the flux of the low-energy regions with the high-energy regions, one observes a striking difference in the homogeneity of the flux. In the low-energy precipitation regions the flux is very variable, changing up to two orders of magnitude over distances of less than . This suggests a ray-like auroral structure elongated along field lines. Figure 6.3 shows a possible configuration for such a charged column. A negative charge density enhancement, assuming a cylindrical structure, produces an electric field that is directed radially inward and drives a circular flow.
Figure 6.3: Geometry in a cylindrical density enhancement (left) that produces a vortical flow (right)
The velocity of the vortical flow speed in such a case is related to the electron density enhancement as follows. We apply Gauss' law to a segment of the tube of enhanced electron density with radius R and length l (see Figure 6.3 - left).
If the electron density is assumed to be uniform within the tube, equation 6.1 reduces to
If the tube is field aligned, the velocity of the vortical flow v (see Figure 6.3 - right) is given by v = E/B and perpendicular to the electric field. The density enhancement is then
and can be calculated from the measured peak separation which is assumed to be equal to twice the velocity of the radial flow.
Similarly, one can derive Equation 6.4 from Gauss' Law
and the induced field
Combining these two equations gives
If we expand the dot product and make use of the fact that the curl of is related to the FAC we can write
Applying the charge column geometry to the cross product in the first term and removing the second term which is close to zero due to the dot product, we will again arrive at the same result of Equation 6.4.
For the average peak separation velocity of (see table 6.1) and a tube radius of at F-layer heights, the resulting electron density enhancement is of the order of or a number density of for the excess electrons.
Another structure that can produce a double peaked spectrum is an arc or band of plasma with enhanced electron density. The arc would produce an electric field that points towards the center of the arc, causing an drift in opposite directions on either side of the arc as indicated in Figure 6.4. The detectability of such a structure with the radar will depend on the angle the radar beam makes with the arc. It is best detected when the beam is along the arc. If however the beam is directed approximately perpendicular to the arc, there will only be a small component of the pertubation velocity that can be measured and the spectrum of the arc structure should remain invisible to the radar. This property of the arc structure can therefore explain some of the observations for which double peaked spectra are visible with one radar but not the other.
Figure 6.4: Geometry in a arc-shaped density enhancement (left) that produces a flow in opposite directions on either side of the arc (right)
Kintner and Seyler note that the Kelvin-Helmholtz instability is a common feature of magnetized electron beam sheets in laboratory plasmas [KS85, p. 107,]. This fluid instability is produced by a small excess of electrons within the beam which in turn generates an electric field. The resulting drift results in a velocity shear across the electron beam which is unstable and produces vortex-like structures which are about in size. The beams are associated with electrostatic shocks that are characterized by perpendicular electric fields which are of the order of between the ionosphere and the magnetosphere (2000-8000 km).
Burke et al. [BSH83] have observed auroral vortices with the S3-2 satellite . If the electric and magnetic fields are measured simultaneously along the approximately height flight path of the S3-2 satellite, auroral vortices can be detected from their distinct electric field signature. They concluded that the vortices observed had a scale size of and resulted from unstable auroral charge sheets with electric fields that exceeded .
Johnson et al. [JC95] have observed large, radially divergent, vortex-like electric fields with the FREJA satellite . They found agreement between the observations and a model which treated large amplitude vortex solutions travelling in the E-W direction along a density depletion. The spatial scale of these structures was of the order of and the associated electric fields were large (up to ).
McDiarmid [MYGA94] has observed traveling vortex structures with the GOES 7 satellite and a related field line resonance.
Doppler velocity spectra of model vortices have been calculated numerically by Zrnic and Doviak [ZD75] for the case of tornadoes, scanned with a pulsed Doppler radar. The model showed that bimodal spectra should be produced, both for very narrow and very broad antenna beamwidths and that the spectra should exhibit a rapid power decrease for spectral components near the maximum velocity. These predictions agreed very well with actual radar observations.