MIST

 By Frankie Staples (formerly at MSSL UCL, now at UCLA)

Loss mechanisms act independently or in unison to drive rapid loss of electrons from the radiation belts. Electrons may be lost by precipitation into the Earth’s atmosphere, or through the magnetopause into interplanetary space – a process known as magnetopause shadowing. The mechanisms by which electrons are lost may be identified through changes to electron phase space density (PSD). This method considers the number of particles at given adiabatic coordinates (𝝁, K, and L*), which relate the electron energy, pitch angle, and location in the magnetic field. The characteristics of PSD evolution as a function of L* can be used to identify which loss mechanism is acting. However, the rapid nature of electron flux dropouts make it extremely difficult to resolve PSD dynamics at the necessary timescales to identify the contributions of either loss mechanism.

In this study we used a new multimission dataset of PSD observations from 36 satellites to resolve the dynamics of a magnetopause shadowing induced flux dropout in September 2017. We showed that by using Van Allen Probe data alone, the physical processes causing the dropout could be misinterpreted due to limited time and/or spatial resolution. Using multimission observations provided unprecedented time and spatial resolution necessary to correctly interpret PSD dynamics. 

The labelled Figure shows the magnetopause shadowing characteristics identified in PSD observations. Each panel shows PSD as a function of L* for fixed μ = 900 MeV/G and K = 0.1 G0.5RE at 1-hour intervals through phases of the storm. Symbol colours indicate when measurements were taken within the hour period, and dotted lines show the minimum and maximum L* of the last closed drift shell (LCDS) before the magnetopause. 

Please see paper for full details: 

Staples, F. A., Kellerman, A., Murphy, K. R., Rae, I. J., Sandhu, J. K., & Forsyth, C. (2022). Resolving magnetopause shadowing using multimission measurements of phase space density. Journal of Geophysical Research: Space Physics, 127, e2021JA029298. https://doi.org/10.1029/2021JA029298

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.

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

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

1. start from solutions to the single-particle Lorentz force equation
2. expand the relevant equations of motion up to second order in a small parameter (magnitude of magnetic perturbations to background field)
3. 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:

1. 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
2. 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
3. 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
4. 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