Wave-particle interactions in dispersive shear Alfvèn waves

Transcription

1 Wave-particle interactions in dispersive shear Alfvèn waves R. Rankin and C. E. J. Watt Department of Physics, University of Alberta, Edmonton, Canada.

2 Outline Auroral electron acceleration in short parallel wavelength traveling shear Alfvèn waves Ion dynamics in the Ionospheric Alfvèn Resonator (IAR) Long paralel wavelength Standing wave field line resonances (FLRs) Electron trapping in FLRs long wave periods (minutes) imply nonlocal electron dynamics Conclusions

3 Alfvèn Waves Powering Aurora In-situ data from NASA POLAR and FAST missions suggests e.m. waves at altitudes ranging up to 4-5 R E on open field lines possess sufficient energy to power bright dynamic aurora. Wygant et al., JGR, 000 Courtesy of Trond Trondsen, University of Calgary

4 Alfvènic Electron Acceleration Complex interplay of plasma parameters: - Mirror force prevents components of e.d.f. from reaching low altitude, producing anomalous resistivity - E affected by mirror-force, geomagnetic field convergence and wavenumber - Variations in T and ρ affect wave speed, number of resonant e s available for interaction, and size of E Need self-consistent nonlinear kinetic models for wave-particle interactions

5 Electron acceleration wave E-parallel Inferred field line conductivity from observations n e = 1cm j "! 3 =, j E E = 1mV m ~ 10! 3 S m over 1R, e j = 1µ A Two-fluid wave conductivity: electron inertia e ne i E, " = 13. mhz,! 3S m " ~ = e 0 Two-fluid wave conductivity: finite T e m m, Much too high at low frequency eq! e n "! e # l " max VA 0 E ~ $% Pe en e,& ~ $ i ' (' 0. 03S / m for ~ 0. 1 m ( ( = ) e# *) VTe * VTe

6 1D Vlasov Model of Alfvèn Waves! f! f q "! A!$ #! f µ db! f + v + & v % ' % =! t! z m (! z! z )! p me dz! p "# " A + v = A 0 " t " z µ qf A =. k q Z / m 0 df! + µ 0 df p = v + qa /m Solve numerically using algorithm of Watt et al., JGR " $ s ( ) k v =1+ k # A 1+ % Z % " = # k v th The hot electron limit of the dispersion relation leads to " ~ k v A 1+ k # $ s Cold electron, zero ion-acousticgyroradius limit leads to " ~ k v A / 1+ k # $ e

7 Simulations with fixed k Sinusoidal short-duration (~ few s) pulse is introduced at the top of the simulation domain. Results are plotted as a function of time at fixed position. k λ e ~ 1 See Watt et al., JGR, 005, and Watt et al., GRL, R E 1R E

8 Simulations with fixed k Sinusoidal short-duration pulse (~ few s) is introduced at the top of the simulation domain. Results are plotted as a function of time at fixed position. k λ e ~ 1 Selfconsistent simulation shows nonlinear steepening of wave 3.5 R E 1R E

9 Simulations with fixed k Sinusoidal short-duration pulse (~ few s) is introduced at the top of the simulation domain. Results are plotted as a function of time at fixed position. k λ e ~ 1 Resonantly accelerated electrons 3.5 R E 1R E

10 Simulations with fixed k Sinusoidal short-duration (~ few s) pulse is introduced at the top of the simulation domain. Results are plotted as a function of time at fixed position. k λ e ~ 1 Locally accelerated and decelerated electrons needed to carry parallel current 3.5 R E 1R E

11 Varying k - Modeling NASA FAST Satellite Observation Resonantly accelerated electrons Locally accelerated and decelerated electrons needed to carry parallel current

12 Effect of mirror force varying k Down

13 IAR excited by shear Alfven pulse D color maps E ν, B φ E µ High altitude E ν B φ E ν, B φ E µ Time(s) Low altitude E µ IAR High altitude: the incoming pulse is mostly reflected off the Alfven speed gradient. Low altitude: the IAR is excited. Test particles: hydrogen and oxygen ions.

14 Complex ion dynamics at high altitude Phase space parallel velocity and E-parallel Hydrogen Oxygen Hydrogen: narrow orbits, ExB drift velocity is faster than the gyrorotational velocity, centrifugal force dominates. Oxygen: wide orbits, fast gyro-rotation, mirror force dominates.

15 Energy of e s resonantly accelerated by SAW depends upon wave amplitude and phase velocity. Phase velocity much higher at ~5R E, but e s are warm (T e ~1keV):resonant waveparticle interactions take place at high velocities, resulting in high energy e s. At ~5R E, v A ~ v th,e, and electrons can easily be accelerated to ~kev energies E ~ 60mV/m, k λ e =1.7 Phase velocity must be reduced by short perpendicular scale lengths in inertial regime (~R E ) to allow interaction between waves and cold electrons. SAW At ~R E v A >>v th,e and electrons can only be accelerated when k λ e >1, which reduces wave phase velocity: E ~ 50mV/m, k λ e =3.4

16 IPELS007 How does this work for FLR s? Rankin et. al, Phys. Plasmas 004 Keogram shows evidence of phase mixing FLR frequency of f~1.4mhz at L~14, neq~0.38amu/cm-3 E is modulating precipitation even though it is small according to two-fluid theory

17 Fixed k - driven FLR in kinetic Regime Φ (Volts) T e =60eV, v th /v A =3., ρ s > λ e ω t Wave potential driven for 3 periods Trapped electrons detune FLR, producing beats and nonlinear saturation

18 Explaining the island width Nonlinear electron (wave) trapping (damping) is important when many electrons exist at the trapping velocity defined by: v tr ~ ee /mk T e =60eV, v th /v A =3., ρ s > λ e From simulations: E ~0.1mV/m, E ~0.1µV/m v tr ~10 6 m/s agrees with island width

19 Φ (Volts) Φ (Volts) IPELS ω t ω t Driven FLR Inertial Regime L /λ e =59 L /λ e =1 L /λ e =8 Φ (Volts) ω t T e =0.5eV, f~8mhz v th /v A =0.3, ρ s < λ e Damping rate much higher than linear theory: c.f., Lysak and Lotko, JGR, 1996.

20 Φ (Volts) Φ (Volts) IPELS L /λ e =59, T e =0.5eV ω t L /λ e =59, L /ρ s =40, T e =ev ω t! Cold plasma behavior: E " k k # $ e E # v tr " k # $ e Damping depends only on the perpendicular scale of the wave, i.e., in agreement with simulations Warm plasma behavior: E " k k # $ e v th /v A E # Additional dependence of E-par on T e means damping should be more effective at larger spatial scale, i.e., at high altitudes on a real flux tube.

21 Consequences for a real flux tube? Strongly driven case Trapping width increases with T e. At high altitude, entire distribution function is heavily damped. At low altitude, in cold plasma, v th <<v A, damping is strong when L /λ e ~8-10. Beams form on the edges of the distribution function Suggestive of a region of auroral acceleration ranging from the ionosphere to an altitude where v th ~O(v A ).

22 Conclusions Electron acceleration by short parallel wavelength Alfven waves is reasonably well understood. The opposite is true for long parallel wavelengths. Damping rates due to electron trapping in dispersive FLRs are much larger than for linear Landau damping. Phase-space vortices form with a characteristic width defined by v tr =(ee /mk ) 1/ In cold plasma, v th <<v A, damping is strong when L /λ e ~8-10 In warm plasma, v th >>v A, damping is effective even for L >>ρ s due to the increase of E with T e (altitude) Electron beams form in FLRs at low T e (low altitude) At high T e (high altitude) beams do not form due to island width broadening. However, the bulk distribution is heavily damped at widths that are large compared to the ion-acoustic gyroradius.