Shear flow instabilities in the earth’s plasma sheet region

Shear flow instability arising from the velocity shear between the inner and the outer central plasma sheet regions is studied by treating the plasma as compressible. Based on the linearized MHD equations, dispersion relations for the surface wave modes occurring at the boundary of the inner central plasma sheet (ICPS) and the outer central plasma sheet (OCPS) are derived. The growth rates and the eigenmode frequencies are obtained numerically. Three data sets consisting of parameters relevant to the earth’s magnetotail are considered. The plasma sheet region is found to be stable for constant plasma flows unless M_A>9.6, where M_A is the Alfvén Mach number in the ICPS. However, for a continuously varying flow velocity profile in the ICPS, the instability is excited for M_A\geq1.4. The excited modes have oscillation periods of 2–10 min and 1.5–6 s, and typical transverse wavelengths of 30–100 R_E and 0.5–6 R_E for data sets 1 and 2 (i.e., case of no neutral sheet) respectively. For the data set 3, which corresponds to a neutral sheet at the center of the plasma sheet, the excited oscillations have periods of 2 s-1 min with transverse wavelengths of 0.02–1 R_E.     

Electromagnetic lower hybrid instability in the solar wind

Low frequency electromagnetic lower hybrid waves (so-called hybrid whistlers) propagating nearly transverse to the magnetic field can be driven unstable by a resonant interaction with halo electron distributions carrying solar wind heat flux. The electromagnetic lower hybrid instability is excited when the halo electron drift exceeds the parallel phase velocity of the wave. The growth rate attains a maxima at a certain value of the wavenumber. The maximum growth rate decrease by an increase in _e (the ratio of electron pressure to magnetic field pressure) and halo electron temperature anisotropy. At 0.3 AU the growth time of the electromagnetic lower hybrid instability is of the order of 25 ms or shorter, whereas the most unstable wavelengths associated with the instability fall typically in a range of 27 to 90 km. The instability would give rise to a local heating of solar wind ions and electrons in the perpendicular and parallel directions relative to the magnetic field, B₀. The observations of low frequency whistlers having high values ofB/E ratios (B andE being the magnitude of the wave magnetic and electric field, respectively) and propagating at large oblique angles to B₀ behind interplanetary shocks, can be satisfactorily explained in terms of electromagnetic lower hybrid instability. The instability is also relevant to the generation mechanism of correlated whistler and electron plasma oscillation bursts detected on ISEE-3.     

Electromagnetic velocity gradient instabilities in the magnetosphere

The velocity gradients of the contrastreaming electron beams observed in the Earth's magnetosphere can excite three types of ordinary mode instabilities, namely (i) B-resonance electron instability, (ii) ion cyclotron instability, and (iii) unmagnetized ion instability. The B-resonance electron instability occurs at small values of the shear parameter 10^–4<S<10^–3, whereS = [(1/e){dU _o(x)}/(dx)] (U ₀(x) and _e being the streaming velocity of the electron beams and the electron cyclotron frequency, respectively). Near the equatorial plane of the bouncing electron beams region, this instability can generate electromagnetic waves having frequenciesf(0.045–0.2) Hz and wavelentghs (0.5–10)km, and the wave magnetic field is polarised in a radial direction. This instability can also occur in the plasma sheet region during the earthwards and tailwards plasma flows events and can generate waves, with wave magnetic field polarised along north-south direction, in the frequency rangef(0.007–0.02) Hz with (10–100)km nearR=–35R _E . For 10^–3<S<10^–2, the ion cyclotron instability is excited and it can generate waves up to 5th harmonic or so of ion cyclotron frequency. ForS>10^–2, the unmagnetized ion instability is excited which can generate electromagnetic waves having frequences from 5 to 50 Hz and typical wavelengths (0.5–6)km. The growth rates of all the three velocity shear driven instabilities are reduced in the presence of cold background plasma. The turbulence generated by these instabilities may give rise to enhanced effective electron-electron and electron-ion collisions and broaden the bouncing electron beams.     

Broadband Plasma Waves In The MagnetopauseAnd Polar Cap Boundary Layers

Boundary layers occurring in the magnetosphere can support a wide spectrumof plasma waves spanning a frequency range of a few mHz to tens of kHz andbeyond. This review describes the main characteristics of the broadband plasma waves observed in the Earth's low-latitude magnetopause boundary layer (LLBL), in the polar cap boundary layer (PCBL), and the possible generation mechanisms. The broadband waves at the low-latitude boundary layer are sufficiently intense to cause the diffusion of the magnetosheath plasma across the closed magnetospheric field lines at a rate rapid enough to populate and maintain the boundary layer itself. The rapid pitch angle scattering of energetic particles via cyclotron resonant interactionswith the waves can provide sufficient precipitation energy flux to the ionosphere to create the dayside aurora. In general, the broadband plasma waves may play an important part in the processes of local heating/acceleration of the boundary layer plasma.     

Shear flow instability near the cusp resonance in magnetopause boundary layer

Shear flow instability is studied in the planar magnetopause boundary layer region by treating the plasma as compressible. A necessary criterion for instability near the cusp resonance is obtained analytically. The criterion depends on plasma, Alfvén Mach numberM _A and the ratio of the scale lengths of the gradients in the flow and Alfvén velocities. The instability at the cusp resonance layer can be excited rather easily for the low plasma and for shear flow scale length smaller than the typical scale length over which Alfvén velocity varies. The growth rate for instability is obtained for any from a cubic equation. The unstable modes may contribute to the ULF wave activity at the magnetopause.     

Gradients and thermal effects on ring current loss-cone instability

The proton ring current is found to become unstable to a flute-type loss cone mode in the presence of inhomogeneities in the background plasma. Larger growth rates poleward of the equator are expected when the finite temperature of the electrons is taken into account.     

Collisionless tearing modes in the presence of shear flow

Tearing modes in a plane collisionless current sheet with shear bulk flow are studied. An analytic expression for the growth rate is obtained for the case \(M^2 = (1 - \varepsilon {\text{ sech}}^m \bar z)\) , whereM is the Mach number,m the shear flow index, ε a positive constant less than unity, and \(\bar z\) the (normalized) co-ordinate normal to the current sheet. The growth rates are large and the unstable wave number domain is increased as compared to the case without flow. The relevance of these results to time-dependent reconnection processes in the Earth's magnetosphere is discussed.