MIST
Magnetosphere, Ionosphere and Solar-Terrestrial
Nuggets of MIST science, summarising recent papers from the UK MIST community in a bitesize format.
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Distributions of Birkeland current density observed by AMPERE are heavy‐tailed or long‐tailed
Distributions of Birkeland current density observed by AMPERE are heavy‐tailed or long‐tailed
By John Coxon (Northumbria University)
Electric currents flow above Earth’s surface in the ionosphere; along the magnetopause; across the magnetotail; and in the same region of space as the radiation belts. These currents are all closed through currents flowing along the magnetic field lines in near-Earth space forming one large current circuit; the currents flowing along the field lines are known as field-aligned currents, or as Birkeland currents.
Birkeland currents are, therefore, the currents that communicate impacts from the solar wind (at the magnetopause) and from phenomena such as substorms (in the magnetotail) into the ionosphere, and a key part of the puzzle in understanding phenomena such as ground-based magnetic perturbations such as GICs.
In this paper, we analyse the distributions of the Birkeland current densities measured by a dataset called AMPERE. We find that the distributions are heavy-tailed, which means that they are more likely to display extreme behaviours than if they were distributed normally. We determine that the best model to describe the distributions is a q-exponential model, and we exploit this to find the probability of currents flowing above some given threshold.
We can use this to make maps of the probability of extreme current flows in the Northern and Southern Hemispheres (Figure 1). We can see that the most extreme currents are most likely to be on the dayside of Earth, and at a magnetic colatitude of ~20° (a latitude of ~70°), and we can see that extreme currents are much more likely in the Northern Hemisphere. This has important ramifications for space weather prediction, but also for the physical drivers of the currents; more details are available in the full paper.
Electric currents flow above Earth’s surface in the ionosphere; along the magnetopause; across the magnetotail; and in the same region of space as the radiation belts. These currents are all closed through currents flowing along the magnetic field lines in near-Earth space forming one large current circuit; the currents flowing along the field lines are known as field-aligned currents, or as Birkeland currents.
Birkeland currents are, therefore, the currents that communicate impacts from the solar wind (at the magnetopause) and from phenomena such as substorms (in the magnetotail) into the ionosphere, and a key part of the puzzle in understanding phenomena such as ground-based magnetic perturbations such as GICs.
In this paper, we analyse the distributions of the Birkeland current densities measured by a dataset called AMPERE. We find that the distributions are heavy-tailed, which means that they are more likely to display extreme behaviours than if they were distributed normally. We determine that the best model to describe the distributions is a q-exponential model, and we exploit this to find the probability of currents flowing above some given threshold.
We can use this to make maps of the probability of extreme current flows in the Northern and Southern Hemispheres (Figure 1). We can see that the most extreme currents are most likely to be on the dayside of Earth, and at a magnetic colatitude of ~20° (a latitude of ~70°), and we can see that extreme currents are much more likely in the Northern Hemisphere. This has important ramifications for space weather prediction, but also for the physical drivers of the currents; more details are available in the full paper.
Acceleration of Electrons by Whistler-Mode Hiss Waves at Saturn
By Emma Woodfield (British Antarctic Survey)
Whistler-mode hiss waves are well known for causing losses of energetic electrons from the radiation belts at the Earth through wave-particle interactions. The result of the interactions of charged particle with plasma waves, whether energy is transferred from wave to particle or vice-versa, is dependent on many factors including the background plasma conditions. In Saturn’s magnetosphere there is a torus of charged particles, the primary source of this plasma torus is neutral water particles emitted from the moon Enceladus which are then ionised. The combination of pressure, ambipolar electric field, centrifugal and gravitational forces on this moon sourced plasma creates a regime where density is highest near the magnetic equator and notably lower at higher latitudes. Consequently, the ratio of plasma frequency to electron gyrofrequency frequently falls below one at higher latitudes. This also coincides with the region where hiss mode waves are observed and our simulations show that this very low ratio leads hiss waves at Saturn to accelerate electrons rather than scattering them out of the radiation belt. This new finding has important implications for the radiation belt dynamics at Saturn since hiss waves are strong and frequently observed.
Another result of the high latitude occurrence of hiss (> 25 degrees) is that only electrons which bounce a good distance along the magnetic field lines will encounter these particular wave-particle interactions. Therefore, the energy increase in the electrons due to the hiss waves is only seen in these particles. We can describe how far along the magnetic field a particle will reach using the equatorial pitch angle, which is the angle between the particle velocity and the magnetic field at the magnetic equator. An electron with an equatorial pitch angle of 90 degrees is confined to the equator whereas one of 0 or 180 degrees will reach all the way down to the planet in different hemispheres. The result of the hiss wave interactions is to drive the pitch angle distributions of the electrons towards a “butterfly shape” with peaks at low (and very high) equatorial pitch angle reflecting the hiss interactions at high latitudes in both hemispheres. The strength and speed of the interaction also varies with electron energy, the figure shows how our simulations of the electron pitch angle distributions at different L-shells (radial distance along the magnetic equator of a magnetic field line) progress after one Earth day for three typical radiation belt energies. These simulations consider only the effect of the hiss waves to isolate their effect from radial diffusion and transport and any other wave-particle interactions or collisional losses. Highly anisotropic pitch angle distributions (with the peak at lowest and highest pitch angle) are apparent in all three energies in even this relatively short timescale simulation.
![Equatorial pitch angle distributions from 2D model runs at a given L-shell after 24 hours with a resolution of 0.1L. Each run considers the energy and pitch angle diffusion, no radial diffusion or radial transport is included. Each pitch angle distribution is normalised to the flux value at 90 degrees. (a) initial condition for all energies, (b,c,d) flux at 0.4, 1.0 and 3.0 MeV respectively. From: Emma Woodfield - BAS Sent: 27 January 2022 13:50 To: Walach, Maria <m.walach@lancaster.ac.uk> Subject: RE: [External] MIST Nugget Hi Maria, Will do 😊 There’s a BAS news twitter – I’ll double check the twitter handle. Thanks Emma From: Walach, Maria <m.walach@lancaster.ac.uk> Sent: 27 January 2022 12:36 To: Emma Woodfield - BAS <emmwoo@bas.ac.uk> Subject: Re: [External] MIST Nugget Hi Emma, Great! Could you prepare one within the next 1-2 weeks? I also advertise new nuggets via the MIST twitter page. Please let me know if you have any twitter account(s) that you would like me to tag in the post or any suggested wordings. Thanks, Maria On 27 Jan 2022, at 12:29, Emma Woodfield - BAS <emmwoo@bas.ac.uk> wrote: This email originated outside the University. Check before clicking links or attachments. Hi Maria, That was a quick spot – I haven’t even checked the online version myself yet! :-) Yes happy to do a nugget, when would you like it by? Kind regards Emma From: Walach, Maria <m.walach@lancaster.ac.uk> Sent: 27 January 2022 12:28 To: Emma Woodfield - BAS <emmwoo@bas.ac.uk> Subject: MIST Nugget Hi Emma, I hope all is well with you! I am contacting you on MIST Council business, due to your recent article (https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2021GL096213?campaign=wolacceptedarticle). MIST nuggets are short, 1-2 paragraphs (100 - 300 words) accompanied by a figure/animation that describes the importance and some key result/aspect of your work, as well as a caption for the figure and any references.. For some examples please see http://www.mist.ac.uk/nuggets. They are aimed to be understandable for the general MIST audience - at the level of a 1st year PhD student, with a focus on clear language and the wider impact of the results. We would like to invite you to contribute to the series of MIST nuggets and provide a short nugget on your recently published work. Hopefully this should not take much time to write, and it is a great way to advertise your work to the wider MIST community! Please would you be able to let me know whether or not you will be able to contribute at your earliest convenience. Many thanks, Maria On behalf of MIST council -------------------------------------------------- Maria-Theresia Walach Senior Research Associate Space and Planetary Physics Group Physics Department Lancaster University Lancaster LA1 4YB UK This email and any attachments are intended solely for the use of the named recipients. If you are not the intended recipient you must not use, disclose, copy or distribute this email or any of its attachments and should notify the sender immediately and delete this email from your system. UK Research and Innovation (UKRI) has taken every reasonable precaution to minimise risk of this email or any attachments containing viruses or malware but the recipient should carry out its own virus and malware checks before opening the attachments. UKRI does not accept any liability for any losses or damages which the recipient may sustain due to presence of any viruses.](/images/Emma_Woodfield_20220204.png)
Figure Caption: Equatorial pitch angle distributions from 2D model runs at a given L-shell after 24 hours with a resolution of 0.1L. Each run considers the energy and pitch angle diffusion, no radial diffusion or radial transport is included. Each pitch angle distribution is normalised to the flux value at 90 degrees. (a) initial condition for all energies, (b,c,d) flux at 0.4, 1.0 and 3.0 MeV respectively.
See full paper for details:
Woodfield, E. E., Glauert, S. A., Menietti, J. D., Horne, R. B., Kavanagh, A. J., & Shprits, Y. Y. (2022). Acceleration of electrons by whistler-mode hiss waves at Saturn. Geophysical Research Letters, 49, e2021GL096213. https://doi.org/10.1029/2021GL096213
Publication URL: https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2021GL096213
Weak Turbulence and Quasilinear Diffusion for Relativistic Wave-Particle Interactions Via a Markov Approach
By Oliver Allanson (Exeter University)
Quasilinear diffusion theory forms the basis of much of the modelling and interpretation of particle transport and energization due to interactions with electromagnetic waves; at terrestrial and planetary radiation belts; in the solar atmosphere and solar wind; and for the dynamics of cosmic rays.
We present a derivation of weak turbulence and quasilinear diffusion theories in energy and pitch-angle space that differs from the most standard methods of derivation (based upon the Vlasov equation [1]). We
- start from solutions to the single-particle Lorentz force equation
- expand the relevant equations of motion up to second order in a small parameter (magnitude of magnetic perturbations to background field)
- ensemble average the solutions to obtain the diffusion coefficients.
The approach used in this paper builds upon the work by [2], in which only pitch-angle dynamics were considered.
The main conclusions and results of this paper are as follows:
- A derivation and discussion of the general Fokker-Planck equation to describe stochastic charged particle dynamics. This equation includes all possible advective and diffusive dynamics, in principle. The form of the drift and diffusion coefficients are then to be determined on a system-by-system basis. We solve for the diffusive dynamics only, and leave investigations of the drift coefficients and drift-diffusion relations for future works
- The weak turbulence diffusion coefficients: i) display an interesting dependency on time (see Figure1); ii) and also explicitly incorporate the effects of non-resonant particles, as well as the standard effects of cyclotron-resonant particles
- We recover the standard form as used in the resonant-diffusion limit of relativistic quasilinear theory [3], when we consider elapsed timescales much greater than a gyroperiod
- Our new derivation has a number of benefits, including: 1) the relationship between a more general weak turbulence theory and the standard resonant diffusion quasilinear; 2) the general nature of the Fokker-Planck equation that can be derived without any prior assumptions regarding its form; 3) the clear dependence of the form of the Fokker-Planck equation and the transport coefficients on given specific timescales.
See paper for full details: Allanson O, Elsden T, Watt C and Neukirch T (2022) Weak Turbulence and Quasilinear Diffusion for Relativistic Wave-Particle Interactions Via a Markov Approach. Front. Astron. Space Sci. 8:805699. doi: 10.3389/fspas.2021.805699
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1: C. F. Kennel and F. Engelmann , "Velocity Space Diffusion from Weak Plasma Turbulence in a Magnetic Field", The Physics of Fluids 9, 2377-2388 (1966)
2: Don S. Lemons , "Pitch angle scattering of relativistic electrons from stationary magnetic waves: Continuous Markov process and quasilinear theory", Physics of Plasmas 19, 012306 (2012)
3: Glauert, S. A., and Horne, R. B. (2005), Calculation of pitch angle and energy diffusion coefficients with the PADIE code, J. Geophys. Res., 110, A04206
Magnetopause ripples going against the flow form azimuthally stationary surface waves
By Martin Archer (Imperial College London)
Like waves on water, surface waves on the outer boundary of Earth’s magnetosphere, the magnetopause are thought to always travel in the direction of the driving solar wind. Indeed, many observations of the global dynamics of the magnetosphere show that disturbances travel tailward, i.e. with the wind, for both steady and impulsive driving. However, we find that the lowest-frequency magnetopause surface waves, which form standing waves along the terrestrial magnetic field, actually propagate against the flow outside the boundary.
Multi-spacecraft observations of the resonant surface waves excited by an isolated magnetosheath jet show that the speed of the waves’ energy flow is comparable, but in opposition, to the magnetosheath velocity. Global MHD simulations of the magnetospheric response to a pressure pulse reveal the inward/outward boundary motion is azimuthally stationary across a wide local time range (09-15h). This is despite significant flows being present that should otherwise advect the waves tailward. We show in the figure this is possible since the surface waves’ Poynting flux (panel a) exactly balances the flow's advective effect (panel b) leading to no net energy flux (panel c) over this local time range. Further down the equatorial flanks, however, advection dominates hence the waves travel downtail, seeding fluctuations at the resonant frequency which subsequently grow in amplitude via the Kelvin-Helmholtz instability. Our findings are also in excellent agreement with simple analytic theory. We, therefore, illustrate our overall conclusions in the right panel of the figure.
These unexpected results reveal that magnetopause surface waves can persist longer than was previously expected, which will have implications upon radiation belt, ionospheric, and auroral dynamics. Furthermore, since surface waves drive dynamics in many space, astrophysical and laboratory plasma systems, the results made possible by in situ measurements, may have applications to other environments where these are not possible, for example coronal loops.
Please see paper for full details: Archer, M.O., Hartinger, M.D., Plaschke, F. et al. Magnetopause ripples going against the flow form azimuthally stationary surface waves. Nat Commun 12, 5697 (2021). https://doi.org/10.1038/s41467-021-25923-7
The Roles of the Magnetopause and Plasmapause in Storm-Time ULF Wave Power Enhancements
By Jasmine Kaur Sandhu (Northumbria University)
The Earth’s magnetosphere experiences extreme and dramatic changes during geomagnetic storms due to strongly enhanced solar wind conditions. One impact of the elevated solar wind conditions is the increased occurrence and amplitude of Ultra Low Frequency (ULF) waves across the dayside magnetosphere. These ULF waves are of particular interest due to their implications for transporting and coupling energy within the magnetosphere. However, the radial distribution of ULF wave power is complex – controlled interdependently by external solar wind driving and the internal magnetospheric structuring.
In this study, we explored how ULF wave power is distributed radially in the dayside magnetosphere. We conducted a statistical analysis of storm-time ULF wave power observations from the Van Allen Probes. The results showed that accounting for the plasmapause and (especially) the magnetopause locations reduce statistical variability and improve parameterisation of spatial trends over and above using the L value, highlighting the importance of these boundaries in controlling where and when enhanced ULF wave power is present.
A key finding was the importance of local plasma density. We find that during geomagnetic storms, high density patches in the afternoon sector (e.g. plasmaspheric plumes) act to “trap” ULF waves, leading to spatially localised patches of very high ULF wave power. Figure 1 shows one example of high ULF wave power confined within a patch of enhanced density. The results have critical implications for understanding how ULF waves propagate within the terrestrial magnetosphere, and highlights the importance of the highly distorted storm-time cold plasma density distribution on wider geomagnetic processes.
Figure 1. Timeseries for 27 August 2015 showing the (a) Sym-H index [nT], (b) Earthward component of the solar wind speed, |vX| [km s-1], and (c) Southward IMF component, BZ [nT]. Panels (d-i) show time series for the Van Allen Probes A (pink) and B (blue). We show (d) L value and (e) MLT [h] of the spacecraft location, and (f) total electron density, ne [cm-3]. Panels (g) and (h) show power, P(f) [nT2 Hz-1], as a function of frequency, f [mHz], and time for Probe A and Probe B, respectively. Panel (i) shows the power, P [nT2 Hz-1], summed over the ULF wave band.
Please see the paper for full details:
, , , , , , & (2021). The Roles of the Magnetopause and Plasmapause in Storm-Time ULF Wave Power Enhancements. Journal of Geophysical Research: Space Physics, 126, e2021JA029337. https://doi.org/10.1029/2021JA029337