Tsutomu Tamao

Does the ballooning instability trigger substorms in the near‐Earth magnetotail?

The stability of the near-Earth magnetotail against ballooning (or configurational) instability is examined in the framework of the MHD approximation. It is emphasized that a change in plasma pressure induced by a meridional electric field drift δun is an important factor that determines the stability. We have to consider two ways in which plasma pressure changes, that is, a convective change −δun · ▽P0, where P0 is background plasma pressure, and plasma expansion/compression -P0▽ · δun. Since δun is perpendicular to the magnetic field and its magnitude is inversely proportional to the magnetic field strength, δun diverges/converges in usual tail magnetic field configurations. For the instability, the convective change must overwhelm the effects of the plasma expansion/compression. However, near the equator in the near-Earth tail, the latter may overcompensate for the former. We describe the ballooning instability in terms of a coupling between the Alfven and slow magnetosonic waves in an inhomogeneous plasma and derive instability conditions. The result shows that the excessive curvature stabilizes, rather than destabilizes, perturbations. It is also found that the field-aligned flow stabilizes perturbations, as well as the field-aligned current. We infer that under quiet conditions, the plasma pressure gradient in the near-Earth tail is not sharp enough to trigger the instability. The plasma sheet is expected to become more stable during the substorm growth phase because of an increase in the field line curvature associated with the plasma sheet thinning. In the region closer to the Earth, including the ring current, the plasma pressure gradient may be localized in a limited range of the radial distance during the growth phase. However, recently reported plasma and magnetic field parameters before substorm onsets do not provide very convincing evidence that the ballooning instability is the triggering mechanism of substorms.

Coupling between Alfvén and slow magnetosonic waves in an inhomogeneous finite-β plasma. I: Coupled equations and physical mechanism

Abstract Hybrid properties of transverse and compressional waves are important in understanding mechanisms of Pc4–5 ULF pulsations exhibiting a diamagnetic plasma pressure perturbation in the ring current region. The shear Alfven wave and slow magnetosonic wave are candidates for localized hydromagnetic waves, since both waves are guided along magnetic field-lines. A system of ordinary differential equations describing the coupling between the Alfven and slow modes is derived for standing oscillations along a magnetic field-line in the two-fluid approximation. The finite Larmor radius effect is taken account of for ions, so the drift mode is also consistently included in the formulation. Of the most interest in the coupling mechanisms is a combined effect between the pressure gradient and the field-line curvature, which can be the free energy source of ballooning-interchange instability for exciting the coupled mode oscillations. The coupling mechanisms are applied to explain the observed characteristics of storm-time Pc5 pulsations. Previous observational results are discussed from a point of the field-line curvature and it is concluded that the curvature effect is important in determining the structure of standing oscillations. Phase relationship between the radial and compressional magnetic disturbances can be explained by assuming a fundamental harmonic mode of standing oscillations along a field-line. This favours the suggestion that the storm-time Pc5 is excited by the ballooning-interchange instability, since a fundamental standing mode is expected to be the most unstable to this instability.

Coupling between alfvén and slow magnetosonic waves in an inhomogeneous finite-β plasma—II. Eigenmode analysis of localized ballooning-interchange instability

Abstract Ballooning-interchange instability of guided hydromagnetic waves is examined by performing a numerical eigenmode analysis along a model field-line. This instability is driven by a combined effect of the plasma pressure gradient and the field-line curvature and can be considered as a candidate of the excitation mechanism of storm-time Pc5 pulsations in the outer magnetosphere. The system of eigenmode equations derived in an accompanying paper describes the coupling between Alfven and slow magnetosonic modes due to inhomogeneity. Such a coupling results in oscillations with hybrid properties between the two, for example, the transverse magnetic perturbation in the radial direction and the out-of-phase relation in perturbed plasma and magnetic pressures ; they are important characteristics of the storm-time Pc5 pulsation. Eigenvalues of the fundamental mode oscillation have a positive imaginary part, that is, the fundamental eigenmode is unstable. The oscillation frequency of this unstable mode is proportional to the azimutha wave number, and is comparable with the ion drift frequency at the equator. These results suggest that the ion drift mode plays an important role in the unstable mode. Although the broad distribution of eigenfunctions along the field-line and a somewhat small value of the oscillation frequency are not consistent with observations, such inconsistencies are due to the oversimplification adopted in the model of plasma and magnetic fields. In practice, high energy particles can be expected to play a decisive role in determining the properties of the pulsations in the magnetosphere. Hence, it is concluded that the ballooning-interchange instability is a strong candidate for the excitation mechanism of the storm-time Pc5 pulsation.

Coupling modes of hydromagnetic oscillations in non-uniform, finite pressure plasmas: Two-fluids model

Abstract Within a framework of the two-fluids approximation, basic modes constituting hydromagnetic coupling oscillations in non-uniform, finite-β plasmas are examined. It is shown that the oscillations consist of a coupling between a localized mode and a propagating one, and a strong peak appears at a resonance point. In the case of isothermal plasma ( T e = T i ), there are two localized modes, the Alfven (or drift Alfven) and the ion drift modes, and a propagating mode being known as the fast magnetosonic wave. Coupling oscillations associated with the Alfven mode exhibit a nearly incompressible character, whereas those with the ion drift mode are compressional and diamagnetic. Furthermore, the slow magnetosonic wave also couples with the localized mode in the case of T e > T i . Based on characteristics of these oscillations, the origin of geomagnetic pulsations is discussed in connection with the distribution of plasma parameters in the outer magnetosphere.

Hydromagnetic coupling oscillations and drift instabilities in nonuniform, collisionless plasmas

The thermal effects of resonant coupling hydromagnetic oscillations in inhomogeneous, finite‐β plasmas, are studied. There are two thermal effects for such oscillations, the thermal phase mixing due to wave‐particle resonance interactions and the drift effect arising from plasma inhomogeneities. Applying the drift kinetic approximation, the basic equations for the coupling modes between the Alfven and magnetosonic waves in a nonuniform, collisionless plasma are obtained. For the plasma with β ≃ me/mi, ratio of electron to ion mass, it is shown that the electron thermal dissipation of hydromagnetic oscillations with ω/k‖ ≃ VA is most effective within the resonance coupling regions which appear in the cold plasma limit. This dissipation is very large as compared with the same dissipation process in the homogeneous plasma. On the other hand, if the hot plasma with β ∼ 1 is considered, attenuation of hydromagnetic waves due to ion‐wave interaction becomes important. It will be an important process for ion hea...

Interaction of energetic particles with HM-waves in the magnetosphere

Abstract Energetic particle response in electromagnetic fields of ULF HM-waves in the magnetosphere is reviewed. Pc4–5 geomagnetic pulsations observed at the synchronous altitude are classified into three types, in respect to their major magnetic field polarization in different directions, local time dependence, and different characteristics of accompanied flux modulations of energetic particles, i.e., two nearly transverse waves with the azimuthal and the radial polarization, and the compressional stormtime pulsations. Firstly, we formulate the drift kinetic theory of particle flux modulations under the constraint of the magnetic moment conservation. A generalized energy integral of the particle motion interacting with a ULF-wave with the three-dimensional structure propagating to the azimuthal direction is obtained in the L -shell coordinate of a mirror magnetic field. Its linearized form is reduced to the same form as the previously derived energy change, including the bounce-drift resonant interaction. It is shown that the perturbed guiding center distribution function of energetic particles consists of four contributions, the adiabatic mirror effect corresponding to pitch-angle change, the kinetic effects due to energy change and the accompanying L -shell displacement, and the bounceaveraged drift phase bunching. Secondly, the basic HM-wave modes constitutingcoupling ULF oscillations in non-uniform plasmas are discussed in different models of approach for different plasma states. The diamagnetic drift Alfven wave and the compressional drift wave with a larger azimuthal mode number in a high-beta plasma are candidates for the stormtimes pulsations. The former is intrinsically a guided localized mode, while the latter is a non-localized mode. By making use of the above preparation, we apply the developed drift kinetic theory to interpret the phase relationships between the ion flux modulation and the geomagnetic pulsation in some selected examples of observations, demonstrating a fair agreement in theoretical results with the observations.

Modulation of energetic particle fluxes due to long-period geomagnetic oscillations

Abstract Mechanism of flux modulations of energetic protons and electrons, associated with the long-period geomagnetic pulsations in the outer magnetosphere, is examined theoretically. In the first part, a linear perturbation theory of the guiding centre distribution function averaged over the bounce phase of an interacting particle is developed for the case of the three-dimensional magnetic oscillations with a sufficiently long period compared with the bounce time of the particle. Secondly we extend the formulation to include some effects of the perturbed drift orbit on the particle distribution such as the particle trapping in the wave field and the phase bunching process. The latter is important for the interaction with the coupling Alfven mode of magnetic oscillations. Applying these results together with the basic characteristics of the coupling hydromagnetic oscillations in a non-uniform plasma, we discuss the possibilities for the observed particle flux modulations in two different cases, separately, i.e. flux oscillations due to the compressional magnetic perturbation and those from the nearly transverse magnetic variations.

Adiabatic plasma convection in the tail plasma sheet

We investigate the transport process of electrons in the tail plasma sheet by convection electric fields, under the assumption of conservation of the first two adiabatic invariants. The variation of the electron distribution function, and hence the bulk parameters with distance from the Earth are calculated. The results show that the electron distribution has a pressure anisotropy with p⊥/p∥< 1 in the plasma sheet. Finally, the effects of the pressure anisotropy are qualitatively considered in terms of the modification of the geomagnetic field structure in the tail plasma sheet and instabilities due to wave-particle interactions.

On the propagation of auroral electron currents by mhd alfvén waves

Abstract The dilemma of propagating field-aligned currents by the MHD Alfven waves while the current carriers are super-Alfvenic auroral electrons can be reconciled by neutralizing the current running ahead of the Alfven wavefront. The neutralizing currents are generated by the interaction between the electron beam head and the magnetized background plasma. Thus, the auroral electron current is allowed to propagate at the Alfven speed while the electron beam itself propagates at the super-Alfvenic beam speed. Moreover, it is shown that upward field-aligned currents carried by auroral electrons are generated above the auroral acceleration region, while those carried by thermal electrons with energy less than 5 eV are most likely generated below the auroral acceleration region.

Diffusion of trapped particles due to the bounce-drift resonance interaction in the magnetosphere

Within the framework of the quasi-linear approximation, the hybrid diffusion process due to the bounce-drift resonance interaction between trapped particles and low-frequency field fluctuations is examined. The diffusion coefficients obtained, which are valid for particles with large pitch angles, cover the previous results in a few limiting cases. In general, the diffusion coefficients depend strongly on the spatial structure of the power spectrum along field lines, as well as the frequency dependence. The relative importance of the radial diffusion and field-aligned acceleration for ringcurrent particles is discussed. It is shown that the field-aligned acceleration exceeds the inward penetration of the particles near the plasmapause.