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

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

Understanding the effects of data-driven repetitive chorus elements on the scattering characteristics of energetic radiation belt electrons

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]

Objective

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

USReality, somewhere in this

region …

When are nonlinear effects important?

2||

||||

||

sin2

sin2

w

w

dv qB v Bv

dt m B z

v vqBdv Bv v

dt m k B z

dkv

dt

adiabatic

phase

Example simple case: field aligned wave, non-relativistic particles

wave

When are nonlinear effects important?

“driving”force

“restoring”force

Conditions for NL:- Waves are “large”

amplitude- Inhomogeneity is “low”,

i.e., near the equator- Pitch angles are

medium-high

Large amplitude whistler waves

Cattell et al. [2008], First reports of large amplitude chorus, STEREO B~ 240 mV/m, ~ 0.5-2 nTMonotonic & coherent (f~0.2 fce, ~2 kHz)Oblique (~ 45 - 60), TransientL~3.5 – 4.8, MLT~2 – 3:45, Lat ~ 21°-26°, AE ~800 nT

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

Three representative cases

(a) small amplitude, pT wave(b) Large amplitude waves(c) Large amplitude, oblique, off-equatorial resonanceBortnik 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

•Non-relativistic form:

Resonant diffusion in velocity space

[Bortnik et al., 2014]

Subpacket structure: a Two-wave

model

Two-wave model

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.

Comparison with quaslinear theory

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

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.

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.

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.

Summary and conclusions• AIM: Bridge the ‘limiting’ paradigms:

1. Quasilinear theory: weak, broadband waves, linear scattering

2. Single-wave/test-particle: finite amplitude, narrowband & coherent, linear or nonlinear scattering

3. 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:1. High repetition rate & low amplitude: QL works well2. Low repetition rate & low amplitude: heavy tails, thin core 3. 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

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

1. Introduction to wave-particle interactions

2. Diffusion3. 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]

Amplitude threshold of QLT

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