Outline
> does the presence of NL waves affect the
conclusion that QL acceleration suffices?
> it depends...
• Large amplitude whistler waves
• Limitations for NL wave-particle interactions
• spatial scales of whistler waves: coherence and source
region scale
• Large amplitude oblique waves and peculiarities for NL waveparticle interactions
• Discussion & Conclusions
SWG APL July 27-29, 2015
Outline
Magnetic and electric field data
from Van Allen Probe B
SWG APL July 27-29, 2015
Large amplitude whistlers
The occurrence rate of large amplitude chorus type whistler waves. Occurrence rate for the waves with averaged
magnetic field amplitudes Bw > 100 pT (means ~5-10 times larger) are indicated by red circles. The occurrence rate
for waves, with average magnetic field amplitudes Bw > 10 pT are indicated by black circles. Panels b and c present
the distribution of the occurrence rate of Bw > 100 pT waves in the L-shell/MLT frame for two ranges of Kp
SWG APL July 27-29, 2015
Occurrence rate fo large amplitude whistlers
The schematic illustration of Bw magnetic field
perturbation structure in a vicinity of the wave
source. Red/blue color indicates the amplitude of
Bw. Yellow arrows shows directions of wave
normal for different wave packets.
Magnetic field from Van Allen Probe A and B
close approach event
SWG APL July 27-29, 2015
Wave transverse spatial scales
Coherence scales for chorus
Source region size ~ 3000 km at L~9
~600 km at L~4-5
Coherence scale ~300 km at L~9
~70-80 km at L~4-5
[Agapitov et al., 2010, 2011]
Coherence Scale << Chorus Source Scale
SWG APL July 27-29, 2015
Spectrograms of magnetic field fluctuations captured aboard four
THEMIS spacecraft. Panels (from top to bottom) show data from
THB, THC, THD, and THE [Agapitov et al., 2010]
even in a vicinity of the equator
Large amplitude oblique whistlers
Cully et al. 2008 GRL
Wilson et al. 2011 GRL
SWG APL July 27-29, 2015
Cattel et al. 2008 GRL
Cyclotron resonance
Landau resonance
100 keV
100 keV
equatorial pitch-angle
equatorial pitch-angle
energy gain in keV
The critical wave amplitude is
shown as a function of pitchangle for several energies and
three sets of system
parameters [Artemyev et al.,
2014]
Energy gain for a single trapping (time scale of such trapping is less than 1/4
of bounce period) is shown for two resonances as function of initial energy
(vertical axis) and initial equatorial pitch-angle (horizontal axis). Particles
with initial ~100 keV are indicated by horizontal red lines.
SWG APL July 27-29, 2015
log10(initial energy in keV)
Large amplitude whistlers
Distribution of the energy of whistler waves in the Earth radiation belts. The distribution of the density of whistler wave
energy W (in mV2m2) is displayed in the (L, l) space. Data are shown for two ranges of magnetic latitude (the near-equator
region with |l| in [0,20] and the high latitude region with |l| in [20,40]), for day and night sectors, and for low (Kp<3) and
high (Kp>3) geomagnetic activity [Artemyev et al., Nature Communication 2015].
SWG APL July 27-29, 2015
Chorus Energy Budget
Summary
• Large amplitudes wave are regularly observed during perturbed
geomagnetic conditions (occurrence rate >10% for certain locations)
• Decrease of the amplitude threshold (as well as particles energy treshold)
for NL interactions
• Nonlinear trapping (and acceleration) is limited by losing of the
phase coherence for waves propagating in a randomly
inhomogeneous plasmas - necessary to quantify for the cyclotron
and Landau resonances! -> wave amplitude is not the single
parameter to test the applicability conditions for QL and NL
approaches
SWG APL July 27-29, 2015
• The significant part of whistler waves energy is contained in oblique
waves and global energy budget is dramatically underestimated if
the parallel waves approach is used