Andrew N. Wright

In this paper, we consider the process of Alfvén-fast wave mode coupling due to non-uniform field geometry in a dipole magnetic field through numerical simulation. We model the process using the linear magnetohydrodynamic equations on a 3D grid based on a modified dipole coordinate system in the low plasma β limit. The Alfvén wave is launched along the background field from the equatorial region and is then allowed to bounce between reflecting ionospheres. To focus on the effects of field geometry, we adopt a uniform Alfvén speed in the simulations. Initially, there is some Alfvén wave energy loss through coupling to the fast mode, but this is 80%) and maintain its identity. Our results further show that this is due to the evolution of the Alfvén wave pulse, through phase mixing, to spatial scales which allow it to asymptotically decouple from the fast mode despite the non-uniform magnetic field. Our results provide an explanation for the observed ability of Alfvén waves to persist in nonuniform space plasmas. A surprising result is that Alfvén waves in a nonuniform medium can have a compressible flow.

The plasmapause in Earth's magnetosphere represents the boundary between the plasma which co‐rotates with the Earth (plasmasphere), and the more tenuous plasmatrough outside. The density change across the plasmapause can be large, changing by approximately 1–2 orders of magnitude depending on the prevailing conditions. This would suggest it to be a location where magnetohydrodynamic (MHD) surface waves can form, and indeed, this has been proposed in previous works to explain ultra‐low frequency (ULF) wave observations around the plasmapause location. The main question is how such a large scale surface wave on the plasmapause would be excited. In this paper, we propose a model whereby surface waves at the plasmapause are driven by energy input from the magnetopause through solar wind driving. We derive an analytical form for the amplitude of these surface waves with this new driven boundary condition at the magnetopause. The excitation of these waves is then tested in several MHD simulations, where the model geometry, wavenumbers and temporal dependence of the magnetopause driver are varied. We establish that surface waves on the plasmapause can be excited by driving from the magnetopause, and that this still occurs with impulsive and continuous broadband driving. The azimuthal scale of the wave is a critical factor for this excitation, with longer azimuthal scales more favorable for driving larger amplitude surface waves. This mechanism provides new insight for how large scale and large amplitude ULF waves can access the inner magnetosphere, with potential implications for their interaction with radiation belt particles.

We present numerical simulations of the excitation of resonant poloidal Alfvén waves. The resulting Alfvén waves could be loosely described as “high‐” ( is the azimuthal wave number) in as much as the azimuthal scale of the wave is much less than the scale in the direction normal to ‐shells. Such waves are generally excited by wave‐particle interactions. In this article we show how resonant poloidal Alfvén waves can be excited by a fast mode (of large azimuthal scale) in a cold plasma. The key property that enables this is a three‐dimensional equilibrium, which facilitates the process of phasemixing in the azimuthal direction. We show that the classification of resonant Alfvén waves as high‐ and low‐ has limited applicability in 3D inhomogeneous media and suggest an alternative classification be based on the excitation mechanism.

In this paper, we consider the process of Alfvén-fast wave mode coupling, through numerical simulation. We model the process using the ideal, linear magnetohydrodynamic equations on a three-dimensional Cartesian grid; assuming the cold plasma limit, β≪1. We initialize the simulation with a cylindrical Alfvén wave pulse (comprising an azimuthal magnetic field and velocity perturbations) propagating along a uniform magnetic field. The wave starts in a region where the density is uniform. As it propagates, part of the Alfvén wave encounters a change in density, before emerging into a second uniform region. We introduce the natural Helmholtz Hodge decomposition as a method to identify the properties of the Alfvén wave perturbations at the end of the simulation. Our results show that the Alfvén wave propagates efficiently through the non-uniform region, with the wave pulse's final structure sharing strong characteristics of the initial wave pulse structure. More than 69% of the initial energy is carried by the transmitted Alfvén wave. Alfvén-fast wave coupling has potential applications in planetary magnetospheres, such as in the Io-Jupiter Alfvén wave interaction, and the solar corona.

The resonant coupling of the fast magnetosonic wave to the Alfvén wave is considered in the ideal magnetohydrodynamic limit in a 3D equilibrium. It has previously been shown that the most efficient coupling occurs on particular paths that satisfy the “tangential alignment condition” (Wright et al., 2022, https://doi.org/10.1029/2022ja030294). In this article we show how this criterion is equivalent to a minimization principle which may lead to a deeper understanding of the physics of the wave coupling process.

The Earth's magnetosphere supports a variety of Magnetohydrodynamic (MHD) normal modes with Ultra Low Frequencies (ULF) including standing Alfvén waves and cavity/waveguide modes. Their amplitudes and frequencies depend in part on the properties of the magnetosphere (size of cavity, wave speed distribution). In this work, we use ∼13 years of Time History of Events and Macroscale Interactions during Substorms satellite magnetic field observations, combined with linearized MHD numerical simulations, to examine the properties of MHD normal modes in the region L > 5 and for frequencies 5 depend on both the magnetopause location and the location of peaks in the radial Alfvén speed profile. Finally, we discuss how these results might be used to better model radiation belt electron dynamics related to ULF waves.

Field Line Resonances (FLRs) are a critical component in Earth's magnetospheric dynamics, associated with the transfer of energy between Ultra Low Frequency waves and local plasma populations. In this study we investigate how the polarisation of FLRs are impacted by cold plasma density distributions during geomagnetic storms. We present an analysis of Van Allen Probe A observations, where the spacecraft traversed a storm time plasmaspheric plume. We show that the polarisation of the FLR is significantly altered at the sharp azimuthal density gradient of the plume boundary, where the polarisation is intermediate with significant poloidal and toroidal components. These signatures are consistent with magnetohydrodynamic modeling results, providing the first observational evidence of a 3D FLR associated with a plume in Earth's magnetosphere. These results demonstrate the importance of cold plasma in controlling wave dynamics in the magnetosphere, and have important implications for wave‐particle interactions at a range of energies.

A 2D Cartesian simulation is presented and used to solve the ideal, low‐beta, linear magnetohydrodynamics equations. A simulation is used to investigate the propagation of Alfvén waves through inhomogeneities in Alfvén speed and density. In particular, the loss of Alfvén wave energy through coupling to the fast wave, and also the form of the Alfvén wave as it emerges from the inhomogeneous region is studied. Potential applications of this include the magnetospheres of both Jupiter and the Earth. The results show that Alfvén waves can be significantly distorted by a nonuniformity and still propagate through the region efficiently, with relatively small amounts of Alfvén wave energy lost through mode conversion and reflection.

Many previous studies have reported that magnetospheric ultralow frequency waves excited by interplanetary shocks exhibit a strong toroidal component, corresponding to azimuthal displacement of magnetic field lines. However, the toroidal oscillations excited by an interplanetary shock on 27 February 2014 and observed on the dayside by multiple spacecraft were accompanied by a strong poloidal component (radial field line displacement). The frequency of the toroidal oscillations changed with the radial distance of the spacecraft as expected for standing Alfvén waves. We run a 3D linear numerical simulation of this wave event using a model magnetosphere with a realistic radial variation of the Alfvén velocity. The simulated wave fields, when sampled at a radial distance comparable to those of the observations in the real magnetosphere, exhibit polarization similar to the observations. In the simulation, the poloidal component comes from radially standing fast mode waves and the toroidal component results from a field line resonance driven by the fast mode waves. As a consequence, the relative amplitude and phase of the toroidal and poloidal components change with radial distance.

The resonant excitation of Alfvén waves using the fast magnetosonic mode is important in space plasmas. In this paper, we consider a simple model of a three-dimensional (3D) coronal arcade. A numerical approach is used to produce a driven normal mode. We find that resonant coupling can occur in 3D, but there are new features that are absent in 2D. In particular, the polarisation of the Alfvén waves can vary with position throughout the Resonant Zone. Moreover, there are an infinite number of possible paths the resonant waves can exist on.