The theoretical foundation of 3‐D Alfvén resonances: Time‐dependent solutions

2020

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A novel simulation grid is devised that is optimized for studying magnetohydrodynamic (MHD) wave coupling and phase mixing in a dipole‐like magnetic field. The model also includes flaring on the dawn and dusk flanks. The location of the magnetopause is quite general. In particular, it does not have to coincide with a coordinate surface. Simulations indicate the central role of global fast waveguide modes. These switch from being azimuthally standing in nature at noon, to propagating antisunward on the flanks. The field line resonances (FLRs) seen in the simulation results are three dimensional and not strictly azimuthally polarized. When a plume is present, the FLRs cross a range of 2 in L shell, and have a polarization that is midway between toroidal and poloidal.

“…The above equations are the components of the momentum and induction equations written in our curvilinear coordinates

false(α, β, γ false)

and simulation variables. They are the same as in Elsden and Wright (), except that we now include a nonzero

η

in Ohm's Law.…”

Section: Simulation Detailsmentioning

confidence: 99%

“…In our notation this gives

α_{\max} false(β false) = r_{0} {()(, \frac{2}{1 + \cos false(β false)})}^{\overset{α}{true}}

where

r_{0}

is the distance to the subsolar magnetopause, and the index

\overset{α}{true}

(simply

α

α_{\max} =

const., and the only quantity needing to be defined there was

B_{γ}

(a proxy for the magnetic pressure). This corresponds to the situation in Figure a, where the red line shows the magnetopause in a surface of constant

γ

along with the grid points in

α

and

β

.…”

Section: Simulation Detailsmentioning

confidence: 99%

Simulations of MHD Wave Propagation and Coupling in a 3‐D Magnetosphere

2020

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“…The stability and accuracy of the method under these conditions is evidenced by the conservation of energy, typically to one part in 10 4 at the end of a simulation. All quantities presented in this paper are dimensionless, given that the equations being solved (see Elsden & Wright, , equations (9)–(13)) have been normalized by characteristic values: lengths by R 0 ; magnetic field by the background field B 0 = B ( α max = R 0 , β = 0, γ = 0); densities by ρ 0 = ρ ( α max = R 0 , β = 0, γ = 0); velocities by

V_{0} = B_{0} \sqrt{μ_{0} ρ_{0}}

; times by t 0 = R 0 V 0 .…”

Section: Modelmentioning

confidence: 99%

“…Further, the inclusion of azimuthal magnetic and density asymmetries has also been used to consider the effect of a plasmaspheric plume on ULF wave propagation (Degeling et al, ). A key aspect of the current work is considering the excitation of FLRs in 3‐D (Elsden & Wright, , ; Wright & Elsden, ), where resonances can exist at any given polarization angle between toroidal and poloidal. Elsden and Wright () showed that the important quantity for efficient resonant excitation is the magnetic pressure gradient along the direction of polarization of the Alfvén wave.…”

Section: Introductionmentioning

confidence: 99%

“…A key aspect of the current work is considering the excitation of FLRs in 3‐D (Elsden & Wright, , ; Wright & Elsden, ), where resonances can exist at any given polarization angle between toroidal and poloidal. Elsden and Wright () showed that the important quantity for efficient resonant excitation is the magnetic pressure gradient along the direction of polarization of the Alfvén wave. Hence, it is critical to understand the spatial and temporal structure of the fast waveguide mode in order to predict the behavior of the resulting FLRs.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The Effect of Fast Normal Mode Structure and Magnetopause Forcing on FLRs in a 3‐D Waveguide

2019

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This paper investigates the excitation of waveguide modes in a nonuniform dipole equilibrium and, further, their coupling to field line resonances (FLRs). Waveguide modes are fast compressional ultralow frequency (ULF) waves, whose structure depends upon the magnetospheric equilibrium and the solar wind driving conditions. Using magnetohydrodynamic simulations, we consider how the structure of the excited waveguide mode is affected by various forms of magnetopause driving. We find that the waveguide supports a set of normal modes that are determined by the equilibrium. However, the particular normal modes that are excited are determined by the structure of the magnetopause driver. A full understanding of the spatial structure of the normal modes is required in order to predict where coupling to FLRs will occur. We show that symmetric pressure driving about the noon meridian can excite normal modes which remain around to drive resonances for longer than antisymmetric driving. Further, the critical quantity in terms of efficient coupling is the magnetic pressure gradient aligned with the resonance.

The Broadband Excitation of 3‐D Alfvén Resonances in a MHD Waveguide

2018

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This paper considers the resonant coupling of fast and Alfvén magnetohydrodynamic (MHD) waves. We perform numerical simulations of the time‐dependent excitation of Alfvén resonances in a dipole magnetic field, with nonuniform density providing a 3‐D equilibrium. Wright and Elsden (2016) showed that in such a system where the poloidal and toroidal Alfvén eigenfrequencies are different, the resonance can have an intermediate polarization, between poloidal and toroidal. We extend this work by driving the system with a broadband rather than monochromatic source. Further, we investigate the effect of azimuthal inhomogeneity on the resonance path. It is found that when exposed to a broadband driver, the dominant frequencies are the fast waveguide eigenfrequencies, which act as the drivers of Alfvén resonances. We demonstrate how resonances can still form efficiently with significant amplitudes, even when forced by the medium to have a far from toroidal polarization. Indeed, larger‐amplitude resonances can be generated with an intermediate polarization, rather than purely toroidal, as a result of larger gradients in the magnetic pressure formed by the azimuthal inhomogeneity. Importantly, the resonance structure is shown to be independent of the different forms of driving, meaning their locations and orientations may be used to infer properties of the equilibrium. However, the amplitude of the FLRs are sensitive to the spatial structure and frequency spectrum of the magnetopause driving. These results have implications for the structure of field line resonances (FLRs) in Earth's magnetosphere, although the focus of this paper is on the underlying physics involved.