By Daniel Ratliff (Northumbria University)
Whistler-Mode Chorus (WMC) waves remain a key contributor to the processes underpinning space weather modelling and have garnered considerable interest for their unique frequency properties (known as tones, where the frequency will rise or fall coherently). This role and phenomena are in no small part due to the interplay between these waves and the electrons present in the magnetosphere. At present, these wave particle interactions are difficult to model simultaneously effectively, and we normally restrict ourselves to the effect of one on the other – either a known wave is used to develop a particle distribution, or a supplied particle distribution generates WMC waves. Can we develop models that do both? And furthermore, can we develop a model that can reproduce this interesting set of frequency dynamics?
In our paper, we use formal perturbation techniques to derive a reduced, nonlinear model for (parallel propagating) WMC that is driven by wave-particle interactions via ponderomotive effects. Our first attempt, the famous Nonlinear Schrodinger equation, fails to generate tones – and so we dig a little deeper to find a term responsive for nonlinear frequency shifts. Surprisingly, this new term responsible for tones vanishes precisely at the WMC band gap at half the electron gyrofrequency, and provides a theoretical basis for why such a bandgap exists. By exploring this model numerically, we also find that there are cases where this tonal behaviour comes with a significant enhancement of the electron kinetic energy – so maybe the magnetosphere’s dawn chorus is at times a swan song in disguise?
See publication for further information:
Ratliff DJ, Allanson O. The nonlinear evolution of whistler-mode chorus: modulation instability as the source of tones. Journal of Plasma Physics. 2023;89(6):905890607. doi:10.1017/S0022377823001265
By Rosie Hodnett (University of Leicester)
The Ionospheric Alfvén Resonator (IAR) occurs when Alfvén waves partially reflect from boundaries in the ionosphere, towards the bottom of the ionosphere and above the F-region peak. The frequencies of the IAR are strongly controlled by the plasma mass density in the ionosphere, which is not uniform.
We have observed IAR in induction coil magnetometer data at Eskdalemuir, UK (BGS site), and extracted the harmonic frequencies for nine years of data. To model the harmonic frequencies, we used the International Reference Ionosphere and the International Geomagnetic Reference Field to model Alfvén velocity profiles. By solving a one-dimensional wave equation, we modelled the first five harmonics of the IAR for times where we had data. The wave structure of the electric field for a uniform case is shown in panel (a), and the resulting modelled harmonics for a non-uniform case is shown in panel (b). We modelled the frequencies with the lower boundary condition of the electric field of the wave being a node (shown in the figure below) and an antinode. By looking at the percentage difference between the fundamental frequency and the average separation of the harmonics (ζ) for both the node and antinode models and comparing this with the data, we find that the lower boundary is closest to being a node. ζ is presented for the node case, with UT, in panels (c) and (d), which show the data and the model respectively, binned by UT. The trend of increasing ζ towards midnight is due to changing Alfvén velocity profiles (shown in panel (e)), and suggests that the ionosphere is becoming more non-uniform. As such, measurements of IAR could be used to gain insight into the shape of the Alfvén velocity profile of the ionosphere.
BGS induction coil magnetometer data, search for 'induction coil': https://webapps.bgs.ac.uk/services/ngdc/
See publication for further information:
Hodnett, R. M., Yeoman, T. K., Beggan, C. D., & Wright, D. M. (2024). Modeling and observations of the effects of the Alfvén velocity profile on the Ionospheric Alfvén Resonator. Journal of Geophysical Research: Space Physics, 129, e2023JA032308. https://doi.org/10.1029/2023JA032308
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