Inhomogeneous energy density driven instability as the most appropriate theory for the interpretation of broadband turbulence in the high-latitude region

Using a general, second-order, nonlocal formalism of Inhomogeneous energy density driven (IEDD) instability, it is possible to explain satellite and rocket data. Broadband fluctuations of both electric and magnetic fields in ULF-ELF band have been repeatedly observed by means of satellites and rockets in the high-latitude ionosphere and they are known as broadband low-frequency turbulence. Its electrostatic component, broadband electrostatic noise observed in the almost total absence of magnetic component of fluctuations within the range of 0.01–1 kHz is of great interest. Broadband electrostatic perturbations are detected in the presence of gradients of electric and magnetic fields, that is, in essentially inhomogeneous plasma configurations. The basics of theory of waves, generated by IEDD instability, were initially developed by Ganguli at al 1985. This instability mechanism does not explicitly depend on any specific shear in the E × B equilibrium velocity. Instead, it requires neighboring regions in space with different signs of wave energy density which may be generated by a localized flow profile. If a coupling between these two regions is possible such that the energy can flow from the region with negative wave energy density to the adjacent region with positive wave energy, the instability can grow while the total energy remains constant as required by the energy conservation principle. This theoretical prediction was validated in a number of laboratory experiments using plasma laboratory devices with a uniform magnetic field such as Q machines, space-simulation chambers, etc. It was also corroborated experimentally that broadband waves in the ion-cyclotron frequency range can be driven solely by a transverse, localized electric field, without the dissipation of a field-aligned current as well as simultaneous, colocated shears in both parallel flow and perpendicular flow were studied.

In our works, it is suggested that this plasma instability leads to formation of the broadband electrostatic turbulence. Detailed study of the IEDD instability is performed for electrostatic ion cyclotron modes using Freja and Fast satellite data. The results of these studies verify the suggestion that the broadband electrostatic turbulence can be identified with the nonlocal electrostatic ion cyclotron mode. The broadband wave spectra were observed that are believed to be the consequence of the nonresonant nature of the IEDD instability. An enhancement of the IEDD instability growth with increase of the field-aligned current was predicted for the ion cyclotron mode. It is also demonstrated that the oblique ion-acoustic modes can be excited because of a shear of the parallel drift velocity of the ions. Moreover, for ion-acoustic waves, this mechanism provides a broadband spectrum in the frequency range of ~0.1 of the ion gyrofrequency, and for ion-cyclotron-type waves, the instability is excited in a wide range of frequencies near the gyrofrequency of the ions without a clearly pronounced maximum. Consequently, the spectrum of IEDD waves has a set of natural frequencies and wavelengths that give rise to a broadband spectrum, in good agreement with the known experimental data and electrostatic broadband turbulence can be identified as a kind of electrostatic ion-cyclotron or oblique ion-acoustic waves excited by an inhomogeneous distribution of wave energy density. Due to the IEDD mechanism, we are also able to explain the results obtained in ICI-3 rocket experiment.

Sometime satellite observations show that the electrostatic instability, which is expected to occur in most cases due to an inhomogeneous energy density caused by a strongly inhomogeneous transverse electric field (shear of plasma convection velocity), occasionally does not develop inside nonlinear plasma structures in the auroral ionosphere, even though the velocity shear is sufficient for its excitation. We show that the IEDD instability damping can be caused by out-of-phase variations of the electric field and field-aligned current acting in these structures. Therefore, the mismatch of sources of free energy required for the wave generation nearly nullifies their common effect. So, the observational fact that different branches may dominate the electrostatic turbulence in different conditions can be explained by the interplay of various destabilizing factors inside a particular structure. Thus, a large magnetic-field-aligned current, especially in combination with a background density depletion, suggests that the ion-acoustic branch is dominating rather than electrostatic ion-cyclotron modes. The work was supported by RFBR, project №18-29-21037.