Figure 1: Image provided by Trond Trondsen, U. of Calgary.

Auroral Physics: Field-aligned electron acceleration by shear Alfvén waves#

The visible or "optical" aurora is the result of complex physical processes in Earth's magnetosphere. It is produced by high energy electron precipitation from the magnetosphere to the ionosphere, and is ultimately connected with the solar wind and hence the Sun's atmosphere. Exactly how electrons are accelerated along geomagnetic field lines to high energies is not well understood. In particular, some auroral displays consist of long-lived arcs or curtains which hang in the sky for many minutes, while other auroral displays are clearly more dynamic, moving rapidly across the sky, brightening and fading in complex patterns. Explaining the acceleration mechanism and the associated space and timescale variations is an active research area in auroral physics.

The image above shows a snapshot of dynamic aurora taken with the portable auroral imager (PAI, Trond Trondsen, University of Calgary). The auroral emissions are at ~110km altitude, implying an area of 14km by 10km at that height. Note the complicated structure with widths ~1km. These structures move and dance with timescales of the order of a second.

NEW: Do you want to use our model for scientific investigations? Find out details here#

Motivation and objective#

Some auroral displays consist of long-lived arcs or curtains which hang in the sky for many minutes. Other auroral displays are clearly more dynamic, dancing quickly across the sky, whilst brightening and fading in complex patterns.

Figure 2. Diagram of the basic shear Alfvén wave (SAW) interaction with electrons along geomagnetic field lines. Waves travel down field lines in response to activity in the magnetotail, and accelerate electrons in the auroral acceleration region. The resulting electron beams could be responsible for the dynamic aurora.

We are interested in dynamic auroral acceleration processes. There is much evidence from spacecraft and ground-based observations to suggest that wave-particle interactions between shear Alfvén waves and electrons along auroral field lines are responsible for many aspects of the dynamic aurora.

The aim of our auroral acceleration project is to design and implement a self-consistent Vlasov- Maxwell simulation model of electron dynamics along geomagnetic field lines in order to better understand the acceleration of auroral electrons by shear Alfvén waves. This also allows us to address one of the "Grand Challenge" science themes of the Canadian Geospace Monitoring Program (CGSM) "to elucidate the fundamental processes that cause and control auroral particle acceleration".

We have developed a sophisticated self-consistent simulation code named DK-1D (see Watt et al., 2004 and Watt and Rankin, 2008) to model dynamic acceleration processes which are energising electrons to create auroral displays.

FDAM personnel Clare Watt, Robert Rankin and Richard Marchand have all contributed to this project. Scott O'Donnell and Alex Degeling have contributed to visualisation of the simulation results, and we are grateful to Ed Sumbar of AICT at the University of Alberta for advice on how to optimise the simulation code.

Scientific Results#

We have used DK-1D to simulate auroral acceleration and shear Alfvén wave propagation along geomagnetic field lines above the auroral oval. These scientific results are explored in more detail below, and are summarised here. We have investigated:

• Electron trapping in shear Alfvén waves along auroral field lines at 4-7 Earth radii distance. These results can explain observations of shear Alfvén wave activity and electron acceleration from the Polar spaceraft. The results also show how shear Alfvén waves may persist in regions of warm plasma, where linear theory predicts they should be heavily damped.

• Auroral electron acceleration in regions close to the Earth (thousands of kilometres altitude) where the inertial effect is important in shear Alfvén waves. The simulation results indicate how to interpret the signatures of electron acceleration seen in spacecraft particle measurements, making a clear distinction between electron acceleration above the spacecraft and local electron acceleration to carry the parallel current of the wave.

• The wave and plasma parameters which affect auroral electron acceleration in regions where the inertial effect is important (~thousands of kilometres altitude)

Details of the simulation code are included below the science results.

Do magnetospheric shear Alfvén waves generate sufficient electron energy flux to power the aurora?#

Figure 3: Differential electron energy flux in the parallel direction towards the ionosphere at a distance of 0.5RE from the lower boundary of the simulation.

We asked this question in a recent publication - and the answer is a resounding yes. For shear Alfvén waves with amplitudes which have been observed in the plasma sheet and plasma sheet boundary layer, we find that they can accelerate electrons to sufficient energies to account for visible auroral brightening. Figure 3 shows the downwards differential energy flux of the precipitating electrons for four different simulations with different initial wave amplitudes. In all but the smallest amplitude case, the resulting energy flux was >1mW/m2, which is sufficient to cause a a visible auroral display.

References

1. C. E. J. Watt and R. Rankin, Do magnetospheric shear Alfvén waves generate sufficient electron energy flux to power the aurora?, Journal of Geophysical Research, 115, A07224, doi:10.1029/2009JA015185.

Electron Trapping#

We investigated the propagation of shear Alfvén waves through the warm plasma of the plasma sheet boundary layer (PSBL) between 2-8 Earth radii from the Earth. Observations (e.g. Wygant et al., 2002) indicate that during times when shear Alfvén waves are observed at ~5 earth radii radial distance, electrons are accelerated both parallel and anti-parallel to the ambient magnetic field. Work on the linear dispersion relation of shear Alfvén waves in warm plasma (Lysak and Lotko, 1996) indicates that they should be heavily damped in regions where the thermal speed of the plasma is greater than the Alfven speed, conditions which are observed in this very region.

Figure 4: Snapshots of the distribution function (top) and parallel electric field (bottom) showing electron trapping near to the top of the simulation domain which escape the wave around z=4 Earth radii. The velocity axes extend from -15,000km/s to +15,000km/s and the parallel electric field axes extend from -1.5mV/m to +1.5mV/m.

The simulation uses a dipolar ambient magnetic field model and has initial number density (1/cc) and temperature (200eV). A monochromatic wavepacket of period 2s is added to the scalar potential at the upper boundary. The figure above shows electron trapping in the wave near the top of the simulation domain, where the thermal velocity is greater than the Alfvén velocity. This trapping prevents the wave from damping away completely, allowing it to persist through this region. Below z~4 Earth radii, the ratio of thermal to Alfvén velocity Rv reduces, causing the wave parallel electric field to reduce dramatically, since it varies as Rv squared.

The electrons, now freed from the trapping parallel electric field, may stream down the field line towards the ionosphere unimpeded. Note that although the parallel electric field has reduced dramatically due to the changing magnetic field, the perpendicular electric and magnetic field perturbations have only decreased slightly.

The comparison below is between observations from the Polar spacecraft (left) and the results from the simulation (right). Electron acceleration is seen both parallel and anti-parallel to the magnetic field. The simulation indicates that the acceleration in parallel direction is due to electron trapping (electrons which will form field-aligned beams closer to the Earth) and the acceleration in the anti-parallel direction is due to the parallel current requirements of the shear Alfvén wave.

Figure 5: (left) Polar observations of electron distribution function (Figure 6(a), Wygant et al., 2002); (right) Simulation distibution function averaged over the integration time of the Polar Hydra instrument.

References:

1. Watt and Rankin (2009), 'Electron trapping in shear Alfvén waves that power the aurora', Physical Review Letters, 102, 045002.
2. Wygant et al., (2002), 'Evidence for kinetic Alfvén waves and parallel electron energization at 4–6 RE altitudes in the plasma sheet boundary layer', Journal of Geophysical Research, 107, 1201, doi:10.1029/2001JA900113.
3. Lysak and Lotko (1996), 'On the dispersion relation for shear Alfvén waves', Journal of Geophysical Research, 101, 5085.

Suprathermal "Bursts"#

In-situ spacecraft and rocket measurements of auroral electron energisation display a rich variety of acceleration signatures along auroral field lines. Figure 6 shows a short interval of data from the Fast Auroral SnapshoT mission. Panel (a) shows the downward (<+/- 30deg from the ambient magnetic field direction) differential electron energy flux; panel (b) shows the electric field in the spacecraft direction (close to perpendicular to the ambient magnetic field direction); panel (c) shows the electric field near to the ambient magnetic field direction and panel (d) shows the perpendicular magnetic field perturbation. Whilst this data was being collected, the FAST satellite was flying through the dayside magnetosphere (9MLT) at ~3200km altitude.

Panels (b) and (d) show a strong perturbation at 0833:27.0 UT in the perpendicular electric and magnetic field components. This perturbation is identified as Alfvénic in Su et al., (2004). We are interested in the field-aligned electron behavior associated with the Alfvén perturbation. Immediately preceding the perturbation, we can see a beam in the downwards direction (0833:26.4 - 0833:27.0 UT ). This beam contains high energy electrons which have previously interacted with the perturbation, been accelerated, and are now streaming down the field line ahead of the perturbation.

Figure 6: (a) Downward differential electron energy flux, (b) quasi-perpendicular electric field, (c) electric field near to ambient magnetic field direction and (d) perpendicular magnetic field perturbations from FAST spacecraft.

During the perturbation, we see an enhancement of the differential electron energy flux for all energies less than the lowest beam energy. This is often referred to in the literature as a suprathermal burst.

Figure 7 shows the evolution of simulation parameters with time at a distance of 1RE from the lower boundary of the simulation domain. Panel (a) shows the differential electron energy flux of the downward moving electrons, panel (b) shows the perpendicular electric field perturbation; panel (c) shows the parallel electric field perturbation and pansel (d) shows the perpendicular magnetic field perturbation.

Figure 7: (a) Downward differential electron energy flux, (b) perpendicular electric field, (c) parallel electric field and (d) perpendicular magnetic field perturbations from self-consistent simulation code.

The simulation was initiated with uniform plasma parameters (number density, temperature and drift velocity) in a uniform magnetic field. The drift velocity was initially zero at all spatial locations. A Gaussian-shaped pulse was added to the scalar potential at the top end of the simulation domain, and then the pulse was allowed to travel down the field line, interacting with the plasma as it went. We can see from the electromagnetic field information that the pulse has steepened from its original, symmetric Gaussian form.

The simulation electron flux shows the same features as the data: before the pulse arrives, we can see a beam of electrons; coincident with the pulse we can see a similar enhancement in electron energy flux for all energies less than the beam energy. The beam electrons are accelerated at the top of the simulation domain, and are now travelling at velocities faster than the wave, so once accelerated, the beam electrons have no more interaction with the pulse in the uniform magnetic field simulation. Analysis of the burst electrons reveal them to be locally accelerated electrons. They are accelerated to carry the parallel current associated with the wave. After the pulse has passed, these electrons are decelerated again, since they are no longer required to carry the parallel current at that position, and so they do not precipitate in the same way as the beam electrons.

References:

1. C. E. J. Watt, R. Rankin, I. J. Rae, and D. M. Wright, (2005) 'Self-consistent Electron Acceleration due to Inertial Alfvén Wave Pulses', Journal of Geophysical Research, 110, A10S07, doi:10.1029/2004JA010877.
2. Su et al. (2004), 'Modeling of field-aligned electron bursts by dispersive Alfvén waves in the dayside auroral region,' Journal of Geophysical Research, 109, doi:10.1029/2003JA010344

Electron Conics#

Another observational feature of electron acceleration due to shear Alfvén waves which is seen in the FAST dataset is the electron conic. We studied these features using the self-consistent simulation code with a non-uniform magnetic field (results obtained in previous section used a uniform magnetic field). The number density and temperature were uniform along the field line. A sinusoidal pulse was introduced at the top of the simulation domain (~2.5RE altitude) and travelled towards the lower boundary (~800km altitude).

Figure 8 shows a comparison between snapshots of the differential electron energy flux from FAST (b-e) and snapshots from the simulation (f-i). The snapshots show the differential electron energy flux as a function of both parallel and perpendicular velocity, downwards velocities are at the bottom of each panel, and upwards velocities are at the top.

We have shown that the details of the FAST observations can be reproduced in the simulation, with no prescribed density profiles, potential drops or conditions on the reflection properties of the waves. The electron conic signature is a natural by-product of the progress of the accelerated electron beam through regions of increasing mirror force. Eventually, those beam electrons with non-zero perpendicular velocity will find themselves at an altitude where the mirror force overcomes the parallel electric field force which keeps them moving ahead of the wave. These mirroring particles form the conic signatures seen in the simulation and the observations.

Figure 8, From Watt et al., 2006: (a) Comparison between FAST observations of an electron acceleration event during orbit 3568 and the results from the simulation code. (a) Differential electron energy flux of the down-going electrons; (b)-(e) full two-dimensional plots of FAST differential electron energy flux for time intervals indicated with red vertical lines in (a); (f)-(i) two-dimensional plots of differential energy flux for time intervals of 0.3 s duration taken from the simulation.

References:

1. C. E. J. Watt, R. Rankin, I. J. Rae, D. M. Wright (2006), Inertial Alfvén waves and acceleration of electrons in nonuniform magnetic fields, Geophysical Research Letters, 33, L02106, doi:10.1029/2005GL024779.

Full list of FDAM publications on shear Alfvén waves and electron acceleration#

1. C. E. J. Watt and R. Rankin (2010), Do magnetospheric shear Alfvén waves generate sufficient electron energy flux to power the aurora?, Journal of Geophysical Research, 115, A07224, doi:10.1029/2009JA015185.
2. C. E. J. Watt and R. Rankin (2009), Electron trapping in shear Alfvén waves that power the aurora, Physical Review Letters, 102, 045002.
3. C. E. J. Watt, and R. Rankin (2009), Comment on “Role of dispersive Alfvén waves in generating parallel electric fields along the Io-Jupiter fluxtube” by S. T. Jones and Y.-J. Su, Journal of Geophysical Research, 114, A04212, doi:10.1029/2009JA014083.
4. C. E. J. Watt and R. Rankin (2008), Electron acceleration and parallel electric fields due to kinetic Alfvén waves in plasma with similar thermal and Alfvén speeds, Advances in Space Research, 42, 964-969, doi:10.1016/j.asr.2007.03.030.
5. C. E. J. Watt and R. Rankin (2008), DK-1D: A drift-kinetic simulation tool for modelling the shear Alfvén wave and its interaction with collisionless plasma, Plasma Physics and Controlled Fusion, 50, 074008.
6. R. Rankin, C. E. J. Watt and J. Samson (2007), Self-consistent wave-particle interactions in dispersive scale long-period field-line-resonances, Geophysical Research Letters, 34, L23103, doi:10.1029/2007GL031317.
7. C. E. J. Watt, R. Rankin (2007), 'Parallel electric fields associated with inertial Alfvén waves', Planetary and Space Science, 55, 714-721.
8. R. Rankin, C. E. J. Watt, K. Kabin, R. Marchand, J. Y. Lu and A. Degeling (2006) 'Theoretical aspects of kinetic and inertial scale dispersive Alfvén waves in Earth's magnetosphere' in Magnetospheric ULF Waves: Synthesis and New Directions, Geophysical Monograph Series, 169, edited by Kazue Takahashi, Peter J. Chi, Richard E. Denton, and Robert L. Lysak, AGU, Washington, D.C.
9. C. E. J. Watt, R. Rankin, I. J. Rae, D. M. Wright (2006), Inertial Alfvén waves and acceleration of electrons in nonuniform magnetic fields, Geophysical Research Letters, 33, L02106, doi:10.1029/2005GL024779.
10. C. E. J. Watt, R. Rankin, I. J. Rae, and D. M. Wright, (2005) 'Self-consistent Electron Acceleration due to Inertial Alfvén Wave Pulses', Journal of Geophysical Research, 110, A10S07, doi:10.1029/2004JA010877.
11. C. E. J. Watt, Rankin, R. Marchand (2004), 'Kinetic simulations of electron response to shear Alfvén waves in magnetospheric plasmas', Physics of Plasmas, 11, 1277-1284.