Summary and discussion

We presented two complementary data sets from two different altitudes. Freja observations show that the main part of the turbulence seen in the range 1-500 Hz is due to a Doppler-shifted Alfvénic turbulence of spatial character (large $\Delta k$). Dispersive electron bursts are observed simultaneously with this turbulence and have a quasiperiodical character. Multipoint measurements of AT2 provide a complementary view of the same phenomenon without the strong Doppler-shift effect. Spatially separated slowly moving payloads directly identify spatially localized Alfvénic oscillations and simultaneous dispersive electron precipitations on scales similar to those seen on Freja. The time of existence of these structures is much larger than the wave period of 2 sec.

Both satellite and rocket observations show temporal variations of electron fluxes and spatial localization of Alfvénic structures. It means that purely temporal or spatial models should be disregarded and therefore a spatio-temporal model should be suggested. Alfvén waves form almost field aligned structures which are localized in the perpendicular direction and carry oscillating paralell electric fields. Homogeneous in the paralell direction, Alfvén waves may accelerate electrons through Landau resonance. But this will accelerate particles with a velocity close to the phase velocity of the wave and therefore cannot account for the observed acceleration of cold background electrons. The acceleration of these electrons might be explained if one considers the inhomogeneity of the ionospheric density distribution. From the polarisation relation for inertial Alfvén waves

$$\left \vert E_\parallel \right \vert = \mu_0\omega\lambda_e^2 \left \vert J_\parallel \right \vert$$ (3)

one can see that if $\lambda_e$ decreases (when the density increases) with constant $J_\parallel$ then ${E_\parallel}$will also decrease. As the density of the ionospheric plasma dramatically increases below 4,000-2,000 km of altitude, Alfvénic structures at low altitudes will have significantly smaller ${E_\parallel}$ than at high altitudes. Thus the sharp density gradient will introduce a boundary for the acceleration region of these electrons. Depending on the distance to this boundary one might observe two different electron distibution signatures. One like the burst appearing at 9-10 sec on Figure 1 when all the energies from 1 keV down to 50 eV are present simultaneously. This represents a measurement very close to or inside the acceleration region. The second type of signatures appears at 5-8 sec on Figure 1 or on Figure 1 of Ref. [14]. It exhibits a ''time of flight'' energy dispersion, indicating a measurement which is done below the alcceleration region. This interpretation is supported by the fact that ''time of flight'' dispersive signatures are almost always seen by rockets (below 1000 km), only occasionnaly by Freja (between 1300 and 1800 km) and almost never at higher altitudes by FAST.

In conclusion the observed ULF waves are interpreted as an oscillating Alfvénic turbulence which is confined into a quasistationary spatial region localized in the direction normal to the magnetic field. Region of parallel elecric field of Alfvénic structures responsible for elecron acceleration is limited by the ionospheric density gradient. Multiple point observations of dispersive electron bursts show their clear relation to this Alfvénic turbulence. The quasiperiodical nature of these dispersive electron precipitations is related to the temporal oscillation of the parallel electric field of the dispersive Alfvén wave. The existence of the field itself is closely connected to the spatial localization of the Alfvénic structures and to the presence of a sharp density gradient in the ionospheric plasma.