2014 LWS/HINODE/IRIS Workshop, Portland OR, Nov 2-6, 2014

1. Understanding the effects of data-driven repetitive chorus elements on the scattering characteristics of energetic radiation belt electrons 2014 LWS/HINODE/IRIS Workshop, Portland OR, Nov 2-6, 2014 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-0903802; DE-SC0010578

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]

4. 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

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

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, ~ 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

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 • Non-relativistic form:

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

12. Subpacket structure: a Two-wave model Two-wave model 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.

16. Comparison with quaslinear theory Model the chorus wave power with a fitted Gaussian, and use SDE approach to simulate the “diffusive spread”

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.

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.

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.

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 W-P interaction 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 = 168.3 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) Fourier’s monograph on heat diffusion was submitted handwritten to the Institut de France in 1807- 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.