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-0903802; DE-SC0010578

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

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

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

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

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.

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

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

[Bortnik et al., 2014]

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!

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

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

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

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

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.

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.

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.

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.

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.

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

BACK UPS

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

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=0.2-0.4 ω-k||v||=Ωe

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

Experimental setup ω-k||v||=Ωe

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 1807. 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 1779. 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 1807- rejected! [Phys. Today, 62(7) 2009]

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