Shear flow‐ballooning instability as a possible mechanism for hydromagnetic fluctuations

Abstract

It is suggested that an MHD instability termed the “shear flow‐ballooning instability,” which unifies both the Kelvin‐Helmholtz and the interchange (“ballooning”) instabilities, can excite hydromagnetic waves in the inner magnetosphere. The stability analysis resembles studies of hydrodynamic flows, where the stabilizing factor is the gravitational buoyancy represented by the Brunt‐Väisälä (or Rayleigh‐Taylor) frequency Ω g ( r ). Here the “magnetic buoyancy” due to the curvature of the field lines replaces the gravitational buoyancy and allows the derivation of the MHD analogue to Ω g ( r ). Stability is then found to depend on a dimensionless quantity termed the magnetic Richardson number (similar to hydrodynamic) Ri = [Ω g ²( r ) + k ∥ ² C a ²](1 + k ∥ ²/ k ⊥ ²)/( dV ϕ / dr )² representing the relative importance of gravitational, thermal, rotational, magnetic, and shear flow effects. Unstable MHD modes are found to be represented by Alfvén drift waves which are the hydromagnetic, and shear flow effects. Unstable MHD modes are found to be represented by Alfvén drift waves which are the hydromagnetic analogue to hydrodynamic gravity waves and like them are trapped in the shear zone. The study is applied to the plasmapause boundary, and the results indicate that low‐frequency hydromagnetic pulsations (Pc 4‐Pc 5) with typical wave periods between 123 and 428 s and wavelengths in the range of 5×10³ to 17.2×10³ km can be excited in such a region. The analysis can be extended to other shear flow boundaries such as the magnetopause.