Nuggets of MIST science, summarising recent papers from the UK MIST community in a bitesize format.
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by Homayon Aryan (University of Sheffield)
Numerical codes modelling the evolution of the radiation belts often account for wave-particle interaction with magnetosonic waves. The diffusion coefficients incorporated in these codes are generally estimated based on the results of statistical surveys of the occurrence and amplitude of these waves. These statistical models assume that the spectrum of the magnetosonic waves can be considered as continuous in frequency space, however, this assumption can only be valid if the discrete nature of the waves satisfy the Chirikov resonance overlap criterion.
The Chirikov resonance overlap criteria describes how a particle trajectory can move between two resonances in a chaotic and unpredictable manner when the resonances overlap, such that it is not associated with one particular resonance [Chirikov, 1960]. It can be shown that the Chirikov resonance overlap criterion is fulfilled if the following equation is satisfied:
δθ = (vl / tanθm) / (1 - (ω2/vΩce2))
where θm is the mean angle between the propagation direction and the external magnetic field, δθ is the standard deviation of the wave propagation angles , l is the harmonic number, v=me/mp is the electron to proton mass ratio, and Ωce is the electron gyro-frequency [Artemyev et al., 2015].
Here we use Cluster observations of magnetosonic wave events to determine whether the discrete nature of the waves always satisfy the Chirikov resonance overlap criterion, extending a case study by Walker et al. [2015]. An example of a magnetosonic wave event is shown in panels a-c of the Figure. Panel d shows that the Chirikov overlap criterion is satisfied for this case. However, a statistical analysis shows that most, but not all, discrete magnetosonic emissions satisfy the Chirikov overlap criterion. Therefore, the use of the continuous spectrum, assumed in wave models, may not always be justified. We also find that not all magnetosonic wave events are confined very close to the magnetic equator as it is widely assumed. Approximately 75% of wave events were observed outside 3° and some at much higher latitudes ~21° away from the magnetic equator. This observation is consistent with some past studies that suggested the existence of low-amplitude magnetosonic waves at high latitudes. The results highlight that the assumption of a continuous frequency spectrum could produce erroneous results in numerical modelling of the radiation belts.
For more information please see the paper below:
2019). Equatorial magnetosonic waves observed by Cluster satellites: The Chirikov resonance overlap criterion. Journal of Geophysical Research: Space Physics, 124. https://doi.org/10.1029/2019JA026680
, , , & (Figure: Observation of a magnetosonic wave event measured by Cluster 2 on 16 November 2006 at around 02:08 to 02:33~UT. The top three panels (a, b, and c) show the dynamic wave spectrogram (Bx, By, and Bz respectively) measured by STAFF search coil magnetometer. Panel d shows the analysis of the Chirikov resonance overlap criterion outlined in equation shown on top-left of the panel. The blue and red dots represent 10~s averaged values of dqand the ratio on the right hand side of equation respectively.
by Mai Mai Lam (University of Southampton)
The substorm cycle comprises the loading and explosive release of magnetic energy into the Earth system, causing complex and brilliant auroral light displays as large as a continent. Within one substorm, over 50% of the total solar wind energy input to the Earth system is estimated to be converted to Joule heating of the atmosphere.Such Joule heating is highly variable, and difficult to measure for individual substorms. One quantity that we need to measure in order to calculate the Joule heating is the distribution of Pedersen conductance. Ideally this should be done across the very large range of latitudes and local times that substorms expand into. Pedersen conductance can be examined with high accuracy by exploiting ground-based incoherent scatter radar data, but only on the scale of a few kilometres.
The THEMIS all-sky imagers form a network of nonfiltered cameras that spans North America. Previous results have shown that the optical intensity of a single ground camera with a green filter can be used to find a reasonable estimate of Pedersen conductance. Therefore we asked whether THEMIS white-light cameras could measure the conductance as precisely as radars can, but at multiple locations across a continent. We found that the conductance estimated by one THEMIS camera has an uncertainty of 40% compared to the radar estimates on a spatial scale of 10 – 100 km and a timescale of 10 minutes. In addition, our results indicate that the THEMIS camera network could identify regions of high and low Pedersen conductance on even finer spatio-temporal scales. This means we can use the THEMIS network, and its data archive, to learn more about how much substorms heat up the atmosphere and how complicated and changeable this behaviour is.
For more information please see the paper below:
“How well can we estimate Pedersen conductance from the THEMIS white‐light all‐sky cameras?”, M. M. Lam , M. P. Freeman, C. M. Jackman, I. J. Rae, N. M. E. Kalmoni, J. K. Sandhu, C. Forsyth. Journal of Geophysical Research. https://doi.org/10.1029/2018JA026067
Figure caption: (a) Absolute difference between camera- and radar-derived 1 min Pedersen conductance (black solid) and the effect of different temporal smoothing (coloured broken). (b) As for a, but for the relative difference between camera- and radar-derived Pedersen conductance (normalised to the radar conductance). (c) Comparison of camera-derived and radar-derived Pedersen conductance values for days with different geomagnetic conditions as indicated by Kp: 1 min radar values (blue crosses), 1 min radar values smoothed over 10 min (red diamonds), and 1 min values derived from camera intensity (black squares).
by Martin Archer (Queen Mary University of London)
The abrupt boundary between a magnetosphere and the surrounding plasma, the magnetopause, has long been known to support surface waves which travel down the flanks. However, just like a stone thrown in a pond causes ripples which spread out in all directions, impulses acting on our magnetopause should also cause waves to travel towards the magnetic poles. It had been proposed that the ionosphere might result in a trapping of surface wave energy on the dayside as a standing wave or eigenmode of the magnetopause surface. This mechanism should act as a global source of magnetopause dynamics and ultra-low frequency waves that might then drive radiation belt and auroral interactions.
While many potential impulsive drivers are known, no direct observational evidence of this process had been found to date and searches for indirect evidence had proven inconclusive, casting doubt on the theory. However, Archer et al. (2019) show using all five THEMIS spacecraft during their string-of-pearls phase that this mechanism does in fact occur.
Figure: THEMIS observations and a schematic of the magnetopause standing wave.
They present observations of a rare isolated fast plasma jet striking the magnetopause. This caused motion of the boundary and ultra-low frequency waves within the magnetosphere at well-defined frequencies. Through comparing the observations with the theoretical expectations for several possible mechanisms, they concluded that the jet excited the magnetopause surface eigenmode – like how hitting a drum once reveals the sounds of its normal modes.
Hear the signals as audible sound here: https://www.youtube.com/watch?v=mcG03NBJf-s
For more information please see the paper below:
‘Direct Observations Of A Surface Eigenmode Of The Dayside Magnetopause’. M.O. Archer, H. Hietala, M.D. Hartinger, F. Plaschke, V. Angelopoulos. Nature Communications. | https://doi.org/10.1038/s41467-018-08134-5
by Samuel J. Wharton (University of Leicester)
The Earth’s magnetosphere is constantly being disturbed by ultralow frequency (ULF) waves. These waves transport energy and momentum through the system and can form standing waves on magnetospheric field lines. These standing waves have a resonant frequency which depends on the magnetic field strength and plasma distribution along the field line. The waves result in perturbations in the magnetic field and plasma in the ionosphere. These occur at the resonant frequency and can be directly observed with instruments on the ground. Being able to measure the resonant frequency can provide valuable information about the state of the magnetosphere.
Traditionally, this can be done by applying a cross-phase spectral technique to ground-based magnetometers. It works by finding the frequency where the phase change with latitude is most rapid. This occurs at the local resonant frequency.
The Super Dual Auroral Radar Network (SuperDARN) is a global consortium of 35 radars that observe radio waves backscattered from the ionosphere. The radars detect ULF waves by observing the movements of ionospheric plasma.
For the first time, we have applied the cross-phase technique to SuperDARN. These radars have a much greater spatial resolution and coverage and provide more detailed information than can be achieved with magnetometers alone. In this study, we have used some notable techniques, such as developing a Lomb-Scargle cross-phase technique for uneven data and exploiting an improved fitting procedure Reimer et al. (2018).
We have been able to apply these methods to several examples and validate the results with ground magnetometer estimations. When available, ionospheric heaters can be used to reduce the uncertainty in the backscatter location. However, the majority of SuperDARN data does not have a heater in the field of view and observes ‘natural scatter’. Figure 1 shows an example of the technique applied to natural scatter. The red band in Figure 1e lies at the resonant frequency. Hence, we can measure the resonant frequencies with and without an ionospheric heater.
This study demonstrates that SuperDARN can be used as a tool to monitor resonant frequencies and therefore the plasma distribution of the magnetosphere. This opens up a new application for the SuperDARN radars.
For more information, please see the paper below:
Wharton, S. J., Wright, D. M., Yeoman, T. K., & Reimer, A. S. (2019). Identifying ULF wave eigenfrequencies in SuperDARN backscatter using a Lomb-Scargle cross-phase analysis. Journal of Geophysical Research: Space Physics, 124. https://doi.org/10.1029/2018JA025859
Figure 1: This shows an example of the local resonant frequency being measured by SuperDARN. (a) and (b) show range-time-intensity plots for beams 12 and 15 of the Þykkvibær radar. (c) shows filtered line-of-sight velocities for range gates 10 and 9 on those beams respectively. (d) The cross-phase spectrum for data in (c). (e) The cross-phase spectrum from (d) smoothed.
by Carley J. Martin (Lancaster University)
Saturn’s rapidly rotating magnetosphere forms an equatorial current sheet that is prone to both periodic (i.e. flapping, breathing [see MIST nugget by Arianna Sorba]) and aperiodic movements (i.e. Martin & Arridge [2017]).
Although the current density of the sheet structure has been discussed by many previous authors, the current density in the middle to outer magnetosphere has not been fully explored. To this end we analysed aperiodic wave movements of Saturn’s current sheet, determined using Cassini’s magnetometer observations. The data were fitted to a deformed current sheet model in order to estimate the magnetic field value just outside of the current sheet, plus the scale height of the current sheet itself. These values were then used to calculate the height integrated current density.
We find a local time asymmetry in the current density, similar to the relationship seen at Jupiter, with a peak in current density of 0.04 A/m at ~ 3 SLT (Saturn Local Time). We then used the divergence of the azimuthal and radial current densities to infer the field-aligned currents that flow out from the equator pre-noon and enter the equator pre-midnight, similar to the Region-2 current at Earth. This current closure could enhance auroral emission in the pre-midnight sector by up to 11 kR.
Overall, the results provide important information into the asymmetries of the current sheet, and the characteristics of the current sheet suggest important field-aligned current systems that shape Saturn’s auroral emissions.
For more information, please see the paper below:
Martin, C. J., & Arridge, C. S. (2019). Current density in Saturn's equatorial current sheet: Cassini magnetometer observations. Journal Geophysical Researcher: Space Physics, 124, 279–292. https://doi.org/10.1029/2018JA025970
Figure: Divergence of height-integrated perpendicular current density (which infers the field-aligned current density). The coloured blocks show the average value of the divergence projected onto the X-Y plane in KSM (Kronocentric Solar Magnetospheric) coordinates. A range of magnetopause positions is shown using Arridge et at. (2006) along with the orbits of Titan (20 RS) and Rhea (9 RS), all shown in grey.