Hybrid Kelvin‐Helmholtz/Rayleigh‐Taylor instability in the plasma sheet

Abstract

[1] This paper is to generalize the previous linear analysis of the hybrid KelvinHelmholtz/Rayleigh-Taylor (KH/RT) instability in a system of the magnetosphereionosphere (M-I) coupling, which is valid in the long-wavelength limit of Lk y ( 2, where k y is the azimuthal wave number and L stands for the scale length of a latitudinal profile in azimuthal velocity or energy density. For the first time, the linear growth rate profile of a hybrid wave can be revealed in an essentially overall range of k y . When the gradient of the energy density is directed inward (toward inner magnetic shells), the hybrid growth rate is positive (meaning growth) in a certain range of k y : 0 < Lk y < e k y m . As the inertial relaxation rate v approaches zero, the growth rate curve is close to the KH ''spectrum'' with e k y m = 2, where v S P /C m , the ratio between the inertial capacitance of the magnetospheric plasma and the height-integrated Pedersen conductivity in the ionosphere. Without a velocity shear in the background flow, the spectrum much broadens, namely, the RT spectrum appears. The hybrid growth rate is shown to have a spectrum intermediate between the two ones of the corresponding KH and RT ''root'' instabilities. It is also found that the electrostatic KH instability is completely suppressed when the KH growth rate, estimated excluding the M-I coupling, is less than v, which is a straightforward extension of that previous work. On the basis of the evaluation of C m in the Tsyganenko model, electrostatic waves (with wavelengths greater than a few tens of kilometers at the ionospheric height) are unlikely to grow by the KH instability alone in the nighttime plasma sheet. Instead, hybrid waves can grow at the places where the particle energy density has an inward gradient. This fact may account for the frequent appearance of periodic auroral luminosity in a high-latitude part of the nighttime oval as well as the formation of omega bands typically in the recovery phase of a substorm.

Numerical simulation for a vortex street near the poleward boundary of the nighttime auroral oval

“…Such a region 1 FAC is necessarily localized in the adiabatic/nonadiabatic transition zone, and it is ideally expected to unveil itself when the magnetosphere is embedded, for a long time, in a steady solar wind so that the property of injected particles may not significantly change in time and (latitudinal) fluctuations of * may be insignificant. This type of region 1 FAC is termed the “region 1 fundamental structure” (see Appendix A of Y09) because it depends on the robust existence of gradient of (<1). (While the interplanetary magnetic field is strongly northward, no region 1 fundamental structure will form.)…”

“…(For examples of the fundamental structure, see Figure 1 of YI04.) All the selected current structures are shown to have distortion angles of “right” sign so as to produce the region 1 currents, where the distortion angle is the acute angle between the average magnetic drift direction and the orientation of a current sheet approximating the region 1 FAC structure, both of which are projected to the ionospheric plane (see Figure A1 of Y09).…”

“…In passing, note that the linear analysis of a hybrid KH/RT instability is yet to be conducted for a plasma in the adiabatic/nonadiabatic transition zone where ∇ cannot be neglected, and that the linear theory is not applicable to a situation that the wave growth time is comparable to the relaxation time of an unstable plasma. (The linear analysis of hybrid waves by Y09 is just for adiabatic plasmas. So it may not directly be applicable to the periodic distortions observed near the poleward boundary of the PS.…”

“…Such a scatterplot could not simply be understood in view of the λ − A relationship that is predicted from a linear theory of the electrostatic KH instability, but it looks like a feature of vortex streets to be seen in the present simulation where a hybrid Kelvin‐Helmholtz/Rayleigh‐Taylor (KH/RT) instability develops. The hybrid KH/RT instability is defined to be a type of RT instability having a relationship between wavelength and growth rate which is modified by the effect of a velocity shear [e.g., Yamamoto , 2008, 2009, hereinafter Y09]. The situation is in contrast with the case of curls, where the observed relationship between λ and A may be better fitted to a linear function characteristic of the KH instability [see Trondsen and Cogger , 1998, Figure 10a].…”

“…Theoretically, the electrostatic KH instability in the magnetosphere can be suppressed by the effect of ionospheric (Pedersen) current closure [e.g., Keskinen et al , 1988]: the growth rate, γ with a positive value for growth, is given by γ = ϒ KH − ν (Y09), where ϒ KH is the (classic) KH growth rate estimated without the Pedersen coupling, and ν is the inertial relaxation rate defined as ν ≡ Σ p / C m , the ratio between the height‐integrated Pedersen conductivity in the ionosphere and the inertial capacitance of the magnetospheric plasma. Although the above formula is derived using the drift approximation requiring that the wavelength and growth time are much greater than the proton cyclotron radius and period, respectively, it is tentatively assumed to be valid, as a first approximation, for arbitrary wavelength and growth time.…”