Title:

Coupling of the solar wind, magnetosphere and ionosphere by MHD waves

The solar wind, magnetosphere and ionosphere are coupled by magnetohydrodynamic waves, and this gives rise to new and often unexpected behaviours that cannot be produced by a single, isolated part of the system. This thesis examines two broad instances of coupling: fieldline resonance (FLR) which couples fast and Alfvén waves, and magnetosphereionosphere (MI) coupling via Alfvén waves. The first part of this thesis investigates fieldline resonance for equilibria that vary in two dimensions perpendicular to the background magnetic field. This research confirms that our intuitive understanding of FLR from 1D is a good guide to events in 2D, and places 2D FLR onto a firm mathematical basis by systematic solution of the governing equations. It also reveals the new concept of ‘imprinting’ of spatial forms: spatial variations of the resonant Alfvén wave correlate strongly with the spatial form of the fast wave that drives the resonance. MIcoupling gives rise to ionospheremagnetosphere (IM) waves, and we have made a detailed analysis of these waves for a 1D sheet Eregion. IMwaves are characterised by two quantities: a speed v_{IM} and an angular frequency ω_{IM} , for which we have obtained analytic expressions. For an ideal magnetosphere, IMwaves are advective and move in the direction of the electric field with speed v_{IM}. The advection speed is a nonlinear expression that decreases with heightintegrated Eregion plasmadensity, hence, wavepackets steepen on their trailing edge, rapidly accessing small lengthscales through wavebreaking. Inclusion of electron inertial effects in the magnetosphere introduces dispersion to IMwaves. In the strongly inertial limit (wavelength λ << λ_{e} , where λ_{e} is the electron inertial length at the base of the magnetosphere), the group velocity of linear waves goes to zero, and the waves oscillate at ω_{IM} which is an upper limit on the angular frequency of IMwaves for any wavelength. Estimates of v_{IM} show that this speed can be a significant fraction (perhaps half) of the E_{⊥} × B_{0} drift in the Eregion, producing speeds of up to several hundred metres per second. The upper limit on angular frequency, ωIM , is estimated to give periods from a few hundredths of a second to several minutes. IMwaves are damped by recombination and background ionisation, giving an efolding decay time that can vary from tens of seconds to tens of minutes. We have also investigated the dynamics and steadystates that occur when the magnetosphereionosphere system is driven by largescale Alfvénic fieldaligned currents. Steadystates are dominated by two approximate solutions: an ‘upper’ solution that is valid in places where the Eregion is a near perfect conductor, and a ‘lower’ solution that is valid where Eregion depletion makes recombination negligible. These analytic solutions are extremely useful tools and the global steadystate can be constructed by matching these solutions across suitable boundarylayers. Furthermore, the upper solution reveals that Eregion density cavities form and widen (with associated broadening of the magnetospheric downward current channel) if the downward current density exceeds the maximum current density that can be supplied by background Eregion ionisation. We also supply expressions for the minimum Eregion plasmadensity and shortest lengthscale in the steadystate. IMwaves and steadystates are extremely powerful tools for interpreting MIdynamics. When an Eregion density cavity widens through coupling to an ideal, singlefluid MHD magnetosphere, it does so by forming a discontinuity that steps between the upper and lower steadystates. This discontinuity acts as part of an ideal IMwave and moves in the direction of the electric field at a speed U = \sqrt{v_{IM} {+} v_{IM} {}}, which is the geometric mean of v_{IM} evaluated immediately to the left and right of the discontinuity. This widening speed is typically several hundreds of metres per second. If electron inertial effects are included in the magnetosphere, then the discontinuity is smoothed, and a series of undershoots and overshoots develops behind it. These undershoots and overshoots evolve as inertial IMwaves. Initially they are weakly inertial, with a wavelength of about λ_{e}, however, strong gradients of ω_{IM} cause IMwaves to phasemix, making their wavelength inversely proportional to time. Therefore, the waves rapidly become strongly inertial and oscillate at ω_{IM}. The inertial IMwaves drive upgoing Alfvén waves in the magnetosphere, which populate a region over the downward current channel, close to its edge. In this manner, the Eregion depletion mechanism, that we have detailed, creates smallscale Alfvén waves in largescale current systems, with properties determined by MIcoupling.
