1. Outline > does the presence of NL waves affect the conclusion that QL acceleration suffices? > it depends... Outline 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 wave- particle interactions Discussion & Conclusions SWG APL July 27-29, 2015

2. Large amplitude whistlers SWG APL July 27-29, 2015 Magnetic and electric field data from Van Allen Probe B

3. Occurrence rate fo 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

4. The schematic illustration of B w magnetic field perturbation structure in a vicinity of the wave source. Red/blue color indicates the amplitude of B w. Yellow arrows shows directions of wave normal for different wave packets. Wave transverse spatial scales SWG APL July 27-29, 2015 Magnetic field from Van Allen Probe A and B close approach event

5. 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] Coherence scales for chorus SWG APL July 27-29, 2015 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 even in a vicinity of the equator

6. Cattel et al. 2008 GRL Wilson et al. 2011 GRL Cully et al. 2008 GRL Large amplitude oblique whistlers SWG APL July 27-29, 2015

7. Large amplitude whistlers The critical wave amplitude is shown as a function of pitch- angle for several energies and three sets of system parameters [Artemyev et al., 2014] SWG APL July 27-29, 2015 log 10 (initial energy in keV) equatorial pitch-angle energy gain in keV 100 keV Landau resonance Cyclotron resonance 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.

8. Chorus Energy Budget Distribution of the energy of whistler waves in the Earth radiation belts. The distribution of the density of whistler wave energy W (in mV 2 m 2 ) is displayed in the (L,  ) space. Data are shown for two ranges of magnetic latitude (the near-equator region with | | in [0,20] and the high latitude region with | | in [20,40]), for day and night sectors, and for low (Kp 3) geomagnetic activity [Artemyev et al., Nature Communication 2015]. SWG APL July 27-29, 2015

9. Summary Large amplitudes wave are regularly observed during perturbed geomagnetic conditions (occurrence rate >10% for certain locations) 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 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