1. Collaborators: Xin Tao, Richard M. Thorne
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, ~ 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
Albert [1993; 2000; 2002]; Bell [1984; 1986]; Dysthe [1970]; Ginet Heinemann [1990];
Inan et al. [1978]; Inan [1987]; Roth et al. [1999]; Shklyar [1986]; and many more.
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
Albert [1993; 2000; 2002]; Bell [1984; 1986]; Dysthe [1970]; Ginet Heinemann [1990];
Inan et al. [1978]; Inan [1987]; Roth et al. [1999]; Shklyar [1986]; and many more.

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!
Point out 3 regions similar to chorus, but alpha0 and E vary in opposite directions
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
Islands separate (nonoverlap), slightly overlapping (diffusion), and completely overlapping (degeneracy)
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]
Explain scales, f, t

19. Objective Reality, somewhere in this region … US 2. Quasilinear theory
Waves are all weak
Wideband & incoherent
Interactions uncorrelated
Global modeling
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
A lot of Eckersley’s work was published in Nature!