This paper describes magnetospheric waves of very long wavelength in thin magnetic filaments. We consider an average magnetospheric configuration with zero ionospheric conductance and calculate waves using two different formulations: classic interchange theory and ideal MHD. Classic interchange theory, which is developed in detail in this paper, is basically analytic and is relatively straightforward to determine computationally, but it can’t offer very high accuracy.The two formalisms agree well for the plasma sheet and also for the inner magnetosphere. The eigenfrequencies range over about a factor of seven, but the formulations generally agree with a root-mean-square difference of the $log_{10}$ of the ratio of the interchange to MHD frequencies to be $\sim 0.054$. The pressure perturbations in the classic interchange theory are assumed constant along each field line, but the MHD computed pressure perturbations along the field line vary in a range $\sim 30 \%$ in the plasma sheet but are larger in the inner magnetosphere. The parallel and perpendicular displacements, which are very different in the plasma sheet and inner magnetosphere, show good qualitative agreement between the two approaches. In the plasma sheet, the perpendicular displacements are strongly concentrated in the equatorial plane, whereas the parallel displacements are spread through most of the plasma sheet away from the equatorial plane; and can be regarded as buoyancy waves. In the inner magnetosphere, the displacements are more sinusoidal and are more like conventional slow modes. The different forms of the waves are best characterized by the flux tube entropy $PV^\gamma$.

Fast solar wind streams are known to be dominated by Alfvenic turbulence, i.e. large amplitude magnetic field and quasi-incompressible velocity fluctuations with a correlation corresponding to waves propagating away from the Sun. At the same time the Ulysses spacecraft showed That microstreams, persistent long period (1/2-2 days) fluctuations in the radial velocity field, are ubiquitous in the fast wind. This contribution explores the possible causal relation between microstreams and Alfvenic turbulence. We carry out a parametric study of the stability of the microstream jets to Kelvin-Helmholtz (KH) instabilities: starting from the profiles of density, radial speed and magnetic field observed in the solar wind, we investigate both at what distance from the Sun KH instabilities may be triggered and the ensuing nonlinear dynamics.

The shear flow-interchange instability is proposed as the initiating mechanism behind substorm onset. ULF waves occurring within minutes of substorm onset are observed in the magnetotail at frequencies similar to those of the auroral beads, which are a result of a near-earth magnetospheric instability initiating current disruption in the plasma sheet. Growth rates were statistically determined as a function of wavenumber by Kalmoni et al. (2015) using ASI data from a set of substorm events. The RCM-E provides growth phase-evolved runs of background fields for stability analysis of a magnetospheric wave equation for shear flow-interchange modes derived in Derr et al. (2019), from which growth rates and dispersion relations can be calculated for comparison with the statistically-determined growth rates and frequencies of the beads. In the plasma sheet, interchange and shear flow represent a competition between Kelvin-Helmholtz instability and overall interchange stability. On average, flux-entropy increases with radial distance. As the growth phase proceeds, the middle plasma sheet becomes nearly interchange stable, but flux-entropy decreases sharply at the inner edge. Destabilizing shear is weak in the middle of the sheet but quite strong in the SAPS region, earthward of the inner edge. We examine the conditions under which shear can overwhelm interchange stability to trigger instability. Instability phenomenology will be discussed in detail, including discussion of Doppler-resonance structure and a dimensionless parameter W* for characterizing stability domains. Mapping spatial properties to the ionosphere along field lines allows for comparison of instability wavelengths with those of the auroral beads. All substorms terminate in relaxation, either because higher order nonlinearities ultimately suppress growth or due to external conditions which alter the background fields to suppress nonlinear growth. If higher order amplitude expansion terms contribute negatively at some order, then nonlinear relaxation occurs, and a method for determining field saturation values is established.