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
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, ~ 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
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.
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]
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]
[Bortnik et al., 2014]
Amplitude threshold of QLT Tao et al. [2012] Quasilinear diffusion coefficients deviate from test-particle results in a systematic way.
Resonant diffusion in velocity space [Bortnik et al., 2014]
QL modeling of Oct 8-9 2012 storm [Thorne et al., 2013, Nature]
Subpacket structure: full spectrum model Tao et al. [2012], GRL
Repetition rate of chorus elements Tao et al. [2014]
Example: rapidly growing tails: Relativistic turning acceleration Rapid acceleration on the scale of 10’s of minutes, to form a high-energy tail
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
BACK UPS
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
Relativistic turning acceleration Rapid acceleration on the scale of 10’s of minutes, to form a high-energy tail
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
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
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!