1. 2014 LWS/HINODE/IRIS Workshop, Portland OR, Nov 2-6, 2014
Understanding the effects of data-driven repetitive chorus elements on the scattering characteristics of energetic radiation belt electrons
Jacob Bortnik, Xin Tao, Wen Li, Jay M. Albert, Richard M. Thorne
Many thanks to the NSF/DOE partnership in basic plasma physics, award # ATM ; DE-SC

2. Radiation belt dynamics: Collective, incoherent wave effects
Particles drift around the earth
Incoherently accumulate scattering effects of:
ULF
Chorus
Hiss (plumes)
Magnetosonic
Characteristic effects of each waves are different and time dependent
Thorne [2010] GRL “frontiers” review

3. The wave environment in space
Meredith et al [2004]
Explain scales, f, t

4. 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

5. 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

6. 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.

7. Large amplitude whistler waves
Li et al. [2011], Burst mode observations from THEMIS: Large amplitude chorus is ubiquitous, midnight-dawn, predominantly small wave normal angles
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

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

9. [Bortnik et al., 2014]

10. 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!

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

12. 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

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

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

15. Sequence of chorus elements
Tao et al. [2014]: Model a sequence of chorus elements, chosen at random from THEMIS observation, randomly chosen initial phase, initiated at equator.
Put in 2000 particles, 100 keV, 45 deg PA, uniformly distributed in gyrophase and bounce phase. run for one unperturbed bounce period.
Chorus element: from THEMIS D, 11/16/2008.

16. Comparison with quaslinear theory
Model the chorus wave power with a fitted Gaussian, and use SDE approach to simulate the “diffusive spread”
Put in 2000 particles, 100 keV, 45 deg PA, uniformly distributed in gyrophase and bounce phase. run for one unperturbed bounce period.
Chorus element: from THEMIS D, 11/16/2008.

17. Case 1: high repetition, low amplitude
Repetition rate δt/τ=0.4 , BRMS=10 pT. Test particle and SDE (QL-diffusion) results agree very well.
Put in 2000 particles, 100 keV, 45 deg PA, uniformly distributed in gyrophase and bounce phase. run for one unperturbed bounce period.
Chorus element: from THEMIS D, 11/16/2008.

18. Case 2: low repetition, low amplitude
Repetition rate δt/τ=1.2 , BRMS=10 pT. Test particle and SDE (QL-diffusion) results disagree: spreading is non-Gaussian, heavy tails and thin core.
Put in 2000 particles, 100 keV, 45 deg PA, uniformly distributed in gyrophase and bounce phase. run for one unperturbed bounce period.
Chorus element: from THEMIS D, 11/16/2008.

19. Case 3: low repetition, med. amplitude
Repetition rate δt/τ=1.2 , BRMS=80 pT. Test particle and SDE (QL-diffusion) results disagree: spreading is non-Gaussian, large positive bias and thin core.
Put in 2000 particles, 100 keV, 45 deg PA, uniformly distributed in gyrophase and bounce phase. run for one unperturbed bounce period.
Chorus element: from THEMIS D, 11/16/2008.

20. Summary and conclusions
AIM: Bridge the ‘limiting’ paradigms:
Quasilinear theory: weak, broadband waves, linear scattering
Single-wave/test-particle: finite amplitude, narrowband & coherent, linear or nonlinear scattering
Reality: somewhere inbetween?
Subpacket structure: periodicity of amplitude modulation relative to Bw defines mode of interaction. “Realistic” wave packet tends to linearize response.
Repetitive chorus elements:
High repetition rate & low amplitude: QL works well
Low repetition rate & low amplitude: heavy tails, thin core
Low repetition rate & med. amplitude: large +ve bias, thin core

21. BACK UPS

22. Large Plasma Device at UCLA
Operated under Basic Plasma Science Facility (NSF/DOE)
18m long, 60 cm diam
B up to 3.5 kG (0.35 T) 10 independent power supplies
Plasma by diode switch ~1 MW, Ne>2x1012 cm-3, Te=6-15 eV
450 radial ports, computer controlled scanning probes
20 kHz-200 MHz wave generator with 20 kW tuned RF amplifier

23. Experimental setup ω-k||v||=Ωe W-P interaction
- Talk about some challenges to this experiment!
10 cm diameter energetic electron beam, Lanthanum Hexaboride LaB6 source, with series of grids separated by ceramic insulating spacers.
Heated up >1500deg C, and biased negatively wrt machine walls (Earth), such that 0.5 kV < V_beam < 3 kV (i.e., correct resonant energies for our whistler).
Whistler wave antenna is 6.4 m away from beam source.
Antenna is a 1 cm diameter balanced loop, with normal perpendicular to B0. Powered by a 2 kW RF amplifier, broadband up to 220 MHz. Whistlers in range: f/f_ce=
ω-k||v||=Ωe

24. 5. Single particle motion example
Wave:
Bw = 1.4 pT
 = 0°
2 kHz (~0.28 fce)
Constant with latitude
Particle:
E = keV
eq = 70°
0 = 
Cumulative changes when d/dt~0, i.e., resonance

25. Experimental setup
ω-k||v||=Ωe

26. Outline Introduction to wave-particle interactions Diffusion
The wave-particle interaction experiment at the LAPD (Large Plasma Device)
Joseph Fourier’s monograph on heat diffusion was submitted handwritten (top) to the Institut de France in Among the four referees were Joseph Lagrange and Pierre Simon Laplace, who rejected the monograph out of mistrust of Fourier’s use of trigonometric series. It was never published. Laplace expressed probabilities associated with random variables as partial difference equations as early as This 1809 excerpt (bottom) from Journal de l’École Polytechnique shows his solution to a partial differential RT equation analogous to the heat equation.
Fourier’s monograph on heat diffusion was submitted handwritten to the Institut de France in rejected! [Phys. Today, 62(7) 2009]

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