Motivated by recent satellite observations. the authors have carried out a comprehensive theoretical analysis on the generation of hydromagnetic Alfven waves in a realistic magnetospheric plasma environment consisting of a core ({approximately}100 eV) component and an energetic ({approximately}10 keV) component. The theoretical formulation employs the gyrokinetic equations and, thus, retains anisotropy, finite Larmor radii, magnetic trapping, and wave-particle interactions in addition to nonuniform plasma equilibria. A set of coupled equations for transverse and compressional magnetic perturbations is derived and analyzed for its stabilities assuming equilibrium distribution functions which are interchange stable. The findings are as follows: (1) compressional and transverse shear Alfven oscillations are generally coupled in realistic plasmas; (2) in the decoupled limit, for the compressional wave branch, one recovers the drift mirror instability due to the Landau resonances and {tau}{triple bond} 1 + 4{pi}({partial derivative}P{sub {perpendicular}}/B{partial derivative}B) 0; (4) for both branches, the most unstable modes have antisymmetric structures and propagatemore » in the diamagnetic drift direction of the energetic ions; and (5) finite coupling can be shown to further enhance the drift Alfven ballooning instabilities. Thus they conclude that for {tau}{ge}0, the coupled drift Alfven ballooning mirror instability constitutes an important internal generating mechanism of geomagnetic pulsations. The various predicted features of this instability are consistent with satellite observations.« less

Kinetic theory of geomagnetic pulsations 1. Internal excitations by energetic particles

A hybrid kinetic-magnetohydrodynamic (MHD) model is presented for describing low-frequency phenomena in high-beta (β ∼ O(1)) anisotropic plasmas that consist of two components: a low-energy core component and an energetic component with low density. The kinetic-MHD model treats the low-energy core component by magnetohydrodynamic description, the energetic component by a kinetic approach such as the gyrokinetic equation, and the coupling between the dynamics of these two components through plasma pressure in the momentum equation. The kinetic-MHD model optimizes both the physics contents and the theoretical efforts in studying low-frequency MHD waves and transport phenomena in general magnetic field geometries and can be easily modified to include the core plasma kinetic effects if necessary. It is applicable to any magnetized collisionless plasma system where the parallel electric field effects are negligibly small. In the linearized limit, two coupled eigenmode equations for describing the coupling between the transverse Alfven type and the compressional Alfven type waves are derived. The eigenmode equations are identical to those derived from the full gyrokinetic equation in the low-frequency limit and were previously analyzed both analytically and numerically to obtain the eigenmode structure of the drift mirror instability (Cheng and Lin, 1987) which explains successfully the multisatellite observation of the antisymmetric field-aligned structure of the compressional magnetic field of Pc 5 waves (Takahashi et al., 1987) in the magnetospheric ring current plasma. Finally, a quadratic form is derived to demonstrate the stability of the low-frequency transverse and compressional Alfven type instabilities in terms of the pressure anisotropy parameter τ the magnetic field curvature-pressure gradient parameter αp as defined in equations (31) and (69), respectively. A procedure for determining the stability of a marginally stable MHD wave due to wave-particle resonances is also presented.

A kinetic‐magnetohydrodynamic model for low‐frequency phenomena

We have carried out a theoretical analysis of the stability and parallel structure of coupled shear Alfven and slow magnetosonic waves in Earth's inner magnetopause (i.e., at equatorial distances between about five and ten Earth radii) including effects of finite anisotropic Grad-Shafranov equation yields an approximate self-consistent magnetohydrodynamic (MHD) equilibrium. This MHD equilibrium is used in the numerical solution of a set of eigenmode equations which describe the field line eigenfrequency, linear stability, and parallel eigenmode structure. We call these modes anisotropic Alfven-ballooning modes. The main results are: (1) The field line eigenfrequency can be significantly lowered by finite pressure effects. (2) The parallel mode structure of the transverse wave components is fairly insensitive to changes in the plasma pressure, but the compressional magnetic component can become highly peaked near the magnetic equator as a result of increased pressure, especially when P(sub perpendicular to) is greater than P(sub parallel) (here P(sub perpendicular to) and P(sub parallel) are the perpendicular and parallel plasma pressure). (3) For the isotropic (P(sub parallel) = P(sub perpendicular to) = P) case ballooning instability can occur when the ratio of the plasma presure to the magnetic pressure, beta = P/(B squared/8 pi), exceeds a critical value beta(sup B)(sub 0) is approximately equal to 3.5 at the equator. (4) Compared to the isotropic case the critical beta value is lowered by anisotropy, either due to decreased field line bending stabilization when P(sub parallel) is greater than P(sub perpendicular to) or due to increased ballooning-mirror destabilization when P(sub perpendicular to) is greater than P(sub parallel). (5) We use a beta-delta stability diagram to display the regions of instability with respect to the equatorial values of the parameters bar beta and delta, where bar beta = (1/3)(beta(sub parallel) + 2 beta(sub perpendicular to)) is an average beta value and delta = 1 - P(sub parallel)/P(sub perpendicular to) is a measure of the plasma anisotropy. The diagram is divided into regions corresponding to the firehose, mirror and ballooning instabilities. It appears that observed values of the plasma pressure are below the critical value for the isotropic ballooning instability but it may be possible to approach a ballooning-mirror instability when P(sub perpendicular to)/P(sub parallel) is greater than or approximately 2.

/pdf/anisotropic-alfven-ballooning-modes-in-earth-s-magnetosphere-3yh7p3a6v0.pdf

Anisotropic Alfvén-ballooning modes in Earth's magnetosphere

A kinetic-MHD eigenmode analysis of ballooning-mirror instabilities is performed for anisotropic pressure plasmas in the magnetosphere. The energetic particle kinetic effects and the coupling between the ballooning and mirror modes are taken into account. Without energetic trapped particle kinetic effects the ballooning-mirror modes with symmetric field-aligned structure of parallel perturbed magnetic field δB∥ and electrostatic potential Φ have lower β instability threshold than the antisymmetric modes. Pressure anisotropy with (P⊥/P∥ > 1) reduces the β threshold for ballooning-mirror instabilities. In the limit that the wave frequency is smaller than the energetic trapped particle magnetic drift frequency, the symmetric ballooning-mirror mode is completely stabilized by the energetic trapped particle kinetic effects. However, the antisymmetric ballooning-mirror mode is only weakly influenced by the energetic trapped particle kinetic effects and has the lowest β threshold. For symmetric modes the energetic trapped particles experience a bounce-averaged wave structure due to their rapid bounce motion, and their nonadiabatic kinetic pressure response cancels with their fluid pressure response so that they do not contribute to the mode stability. Physically, the energetic trapped particles precess very rapidly across the field, and their motion becomes very rigid with respect to low-frequency symmetric MHD perturbations. For antisymmetric modes the energetic trapped particle kinetic pressure response from the northern hemisphere cancels with that from the southern hemisphere in a bounce period, and thus the instability β thresholds is mainly determined by the energetic particle fluid free energy. The field-aligned perturbed magnetic field structure of the antisymmetric mode changes from a ballooning mode with dominant transverse magnetic field components at P⊥/P∥ = 1 to a mixed ballooning-mirror mode with comparable transverse and compressional components near the equator as P⊥/P∥ increase. With large equatorial plasma β (β∥ ≥ O(1)) and pressure anisotropy (P⊥/P∥ > 1) the field-aligned wave structure of antisymmetric ballooning-mirror mode resembles the multisatellite observation of a long lasting compressional Pc 5 wave event during November 14-15, 1979 [Takahashi et al., 1987].

/pdf/theory-of-ballooning-mirror-instabilities-for-anisotropic-18eqcfxh3e.pdf

Kazue Takahashi

Papers

Multisatellite studies of ULF waves