1. Three Regions of Auroral Acceleration
Illustration of three regions of auroral acceleration: downward current regions, upward current regions, and the region near the polar cap boundary of Alfvénic acceleration (Courtesy C. Carlson, from Auroral Plasma Physics, International Space Science Institute)

2. Inverted-V and Alfvénic Acceleration Regions
Alfvénic acceleration: broad energy, narrow pitch angle
Overview of FAST passage through the auroral oval. Panels are (top to bottom): Magnetic field perturbation, electric field, electron energy, electron pitch angle, ion energy, and ion pitch angle.
Blue shading indicates upward current region, green is downward currents, and red is the Alfvenic acceleration region.
(Courtesy C. Carlson, from Auroral Plasma Physics, International Space Science Institute)
Inverted-V: quasi-static acceleration

3. What does “quasi-static” mean here?
Inverted-V electrons have roughly the same energy; thus, have fallen through the same potential drop.
So parallel electric field must be static on time scales of electron transit time through acceleration region (e.g., Block and Fälthammar, 1990)
A 100 eV electron has a velocity of roughly 1 RE/s, so “quasi-static” means < 1 Hz if scale size of acceleration region is ~ 1 RE.
Thus, parallel electric fields associated with field line resonances (periods of minutes) will be seen as quasi-static; E|| associated with ionospheric Alfvén resonator (periods of seconds) will give the characteristics of “Alfvénic arcs”

4. Ionospheric Alfvén Resonator
Alfvén speed rises sharply above ionosphere due to exponential fall of plasma density
Alfvén waves are partially reflected from this sharp gradient: wave can bounce between ionosphere and peak in speed: Ionospheric Alfvén Resonator (Periods 1-10 s)
Waves in this frequency range are commonly observed on ground and from satellites. Field-aligned acceleration can also be modulated at these frequencies.
Profiles of Alfvén speed for high density case (solid line) and low-density case (dashed line). Ionosphere is at r/RE = 1. Sharp rise in speed can trap waves (like quantum mechanical well). Note speed can approach c in low-density case.

5. IAR Response to a “turn-on” of field-aligned currentEx By
Simulation of Alfvén wave pulse driven by a turning on of the field-aligned current. Note that even a ramp-like turn on leads to oscillating fields in IAR.

6. Alfvénic Aurora as Transitional Phase
Changes of field-aligned current require the passage of shear Alfvén waves along field line.
Thus, Alfvénic nature of onset arc should not be surprising
Similarly, at polar cap boundary, plasma is convecting from open to closed field lines, requiring transitional readjustment.
Alfvénic aurora can also occur within inverted-V’s: may indicate smaller changes in current structure.
Speculation: Alfvénic interaction prepares system to allow for quasi-static aurora, especially by excavating density cavity (e.g., Chaston et al., 2006), creating low densities that are conducive to static parallel electric fields (Song and Lysak, 2006), and precipitating electrons into ionosphere to enhance conductivity and produce secondary and backscattered electrons.

7. Formation of Density Cavities by Alfvén Waves
Chaston et al. (2006) has recently shown FAST observations indicating strong Alfvén waves in density cavities, with outward phase propagation and inward group velocity, consistent with dispersion relation. (talk on Friday)
Ion heating and outflow are observed simultaneously, suggesting that Alfvén waves are in turn excavating the density cavity.
Low density regions are conducive to formation of quasi-static E|| (Y. Song, later)

8. Is Ionospheric structure imposed from tail or the result of M-I coupling?
Alfvénic aurora requires waves on electron inertial scale: 5 km for a density of 1 cm-3
Waves at this scale are damped at higher altitudes where ve > VA (Lysak and Lotko, 1996; right)
Thus, larger scale waves can couple structure from magnetosphere, but not on scale of individual arcs. (Exception: large Ti/Te decreases damping)

9. Wave energy input on large scales
Milling et al. (2008) show timing of Pi1 pulsations (~16 s period) from ground observations at substorm onset.
Waves must have scales ~ 100 km in order to be observed from ground due to atmospheric screening.
Results indicate propagation of signal at 1 hr MLT/20 sec, or about 30 km/s.
Initial location in region of downward FAC ( symbol) in substorm current wedge.
How do these large scale waves convert to small scale waves of Alfvénic aurora?

10. Production of Small Scales by M-I Coupling
Linear phase mixing at density gradients: Perpendicular variations of Alfvén speed can give rise to phase mixing, narrowing wave structures.
Ionospheric Feedback: Precipitation associated with upward field-aligned currents leads to enhanced ionization of the ionosphere. Secondary currents flowing at conductivity gradients can lead to positive feedback instability. Coupled with modes of ionospheric resonant cavity, this instability can lead to sub-kilometer scales.
Nonlinear and kinetic effects: Nonlinear effects can lead to cascade to smaller scales. Kinetic effects due to electron wave-particle interactions may also give rise to structure on inertial scale. Ionospheric instabilities important?

11. Phase mixing in Ionospheric Alfvén Resonator
Gradients in the Alfvén speed lead to phase mixing, producing smaller perpendicular scales (basic mechanism behind field line resonance.)
Time scale for phase mixing given to a scale L can be estimated by τ ~ (LA / L)T, where LA is perpendicular scale length of Alfvén speed and T is wave period. For 1 second wave in IAR, 100 km scale reduced to <10 km in less than a minute.
Suggests small-scale structure can be produced in presence of large-scale density gradients. VA

12. Simulations of Phase Mixing
Simulations of linear wave propagation including electron inertia effect were made in a overall perpendicular density gradient.
Alfvén speed
Density

13. Simulation results By Ex
Simulation initiated with uniform pulse across system oscillating at 1 Hz.
Interference between up and downgoing waves leads to structuring of fields.
Series of harmonics seen due to change of IAR eigenfrequencies.
Waves phase mix to ~ 1 km scale waves.

14. Ionospheric Feedback →
Precipitation of electrons in upward FAC regions enhanced conductivity; currents at conductivity gradients closed by secondary FAC.
Interaction not necessarily unstable, but instability occurs if response of ionosphere and magnetosphere reinforces initial perturbation.
Threshold for instability depends on drift, perpendicular wavelength and recombination damping.
Simulations (Lysak and Song; Streltsov et al) show instability stabilized above ~ 5 mho (background ΣP). →
(Lysak, 1990)

15. Nonlinear interactions
Alfvén wave nonlinear interactions due to v·v and jb can transfer energy between scales.
Chaston et al. (2008) show power law spectrum with breaks at inertial length and ion gyroradius, suggestive of turbulent cascade.
However, not classic cascade situation: E/B ratio decreases at large scales, indicative of ionospheric damping.
All processes (phase mixing, feedback, nonlinearity) may operate in concert.