Does the presence of NL waves affect the conclusion that QL acceleration suffices ?

1. Does the presence of NL waves affect the conclusion that QL acceleration suffices? Jacob Bortnik Collaborators: Xin Tao, Richard M. Thorne Jay M. Albert, Wen Li

2. Basic problem • Quaslinear (QL) diffusion theory used to model dynamic evolution of radiation belt electrons • Assumes ‘small-amplitude’, incoherent, linear interactions • Recent observations of ‘large amplitude’, coherent chorus waves • Violates QL assumptions! • Nonlinear effects expected • Does QL theory still suffice to describe the acceleration process? Cattell et al. [2008], First reports of large amplitude chorus, STEREO B ~ 240 mV/m, ~ 0.5-2 nT Monotonic & coherent (f~0.2 fce, ~2 kHz) Oblique (~ 45 - 60), Transient L~3.5 – 4.8, MLT~2 – 3:45, Lat ~ 21°-26°, AE ~800 nT

3. When are nonlinear effects important? Example simple case: field aligned wave, non-relativistic particles wave adiabatic phase

4. When are nonlinear effects important? “restoring” force “driving” force Conditions for NL: • Waves are “large” amplitude • Inhomogeneity is “low”, i.e., near the equator • Pitch angles are medium-high

5. Three representative cases(a) small amplitude, ~1 pT wave(b) Large amplitude ~1 nT waves(c) Large amplitude, oblique, off-equatorial resonance Bortnik et al. [2008]

6. EMIC-electron Interactions Diffusion US Advection: to higher a, i.e., more trapped! Trapping: lower a, higher E Albert & Bortnik [2009]

7. [Bortnik et al., 2014]

8. Amplitude threshold of QLT Tao et al. [2012] Quasilinear diffusion coefficients deviate from test-particle results in a systematic way.

9. Resonant diffusion in velocity space [Bortnik et al., 2014]

10. QL modeling of Oct 8-9 2012 storm [Thorne et al., 2013, Nature]

11. Subpacket structure: full spectrum model Tao et al. [2012], GRL

12. Repetition rate of chorus elements Tao et al. [2014]

13. Example: rapidly growing tails: Relativistic turning acceleration Rapid acceleration on the scale of 10’s of minutes, to form a high-energy tail

14. Summary and conclusions • Does the presence of NL waves affect the conclusion that QL acceleration suffices? • The devil’s in the details! Depends on … • Wave amplitude: ~100 pT can be linear or NL, ~1 nT usually NL • Latitude of w-p interaction: equatorial NL, high latitude: becomes more linear • Electron energy: Most NL effects in 10’s-100’s keV range. Relativistic particles ~MeV usually fairly linear • Pitch Angle: small PA more linear, medium PA (~50-80 deg) most NL • Wave Normal: low WN most effective for NL effects, large WN not very effective • Harmonic content: subpackets linearize interactions somewhat • Repetition rate: more frequent chorus elements -> more linear • Look for rapidly growing (<1 hr) ‘tails’ in the electron distribution

15. BACK UPS

16. Subpacket structure: a Two-wave model Two-wave model Tao et al. [2013] subpacket structure modifies the single-wave scattering picture

17. Relativistic turning acceleration Rapid acceleration on the scale of 10’s of minutes, to form a high-energy tail

18. The wave environment in space Meredith et al [2004]

19. Objective Reality, somewhere in this region … 2. Quasilinear theory • Waves are all weak • Wideband & incoherent • Interactions uncorrelated • Global modeling US • 1. Single-wave/test-particle • Waves can be strong • Narrowband & coherent • Interactions all correlated • Microphysics

20. Current picture: Collective, incoherent wave effects • Particles drift around the earth • Accumulate scattering effects of: • ULF • Chorus • Hiss (plumes) • Magnetosonic • Characteristic effects of each waves are different and time dependent Thorne [2010] GRL “frontiers” review

21. Diffusion surfaces • Resonant interaction: Which particles are affected? • Non-relativistic form: • Relativistic form: • Resonant diffusion surface: confinement in velocity space • Non-relativistic form: