ELECTRON ACCELERATION BY TIME DOMAIN STRUCTURES (TDS) by Mozer, F.S., O.V. Agapitov, A.V. Artemyev, V. Krasnoselskikh, and I. Vasko OUTLINE 1.Experimental examples of TDS and Electron Acceleration 2.Acceleration by the Landau Resonance 3.Fermi Acceleration 4.The ? Mechanism Mozer, F.S., O.V. Agapitov, A.V. Artemyev, J.F. Drake, V. Krasnoselskikh, S. Lejosne, and I. Vasko, Time domain structures: what and where they are, what they do, and how they are made, 2015, Geophys. Res. Lett., Geophys. Res. Lett., 42, doi: /2015GL

Time Domain Structures (TDS) are short (~1 msec) spikes of parallel electric field that occur in bunches with as many as hundreds of spikes in a single second. Electromagnetic and electrostatic electron holes, double layers, solitary waves, and non-linear whistlers are examples of TDS Each plot consists of 6 panels, 3 E and 3 B. Plots are in field-aligned coordinates with Epar in panel c and Bpar in panel f. TOP LEFT PLOT Non-linear whistlers BOTTOM LEFT PLOT Electrostatic electron holes TOP RIGHT PLOT Electromagnetic electron holes BOTTOM RIGHT PLOT Electron holes that evolve into double layers. 2

- Large FAC appear 3 times with deltaB/B ~0.2 - TDS are consistent with generation by FAC -Ratio>2 consistent with acceleration by TDS -FAC, TDS and Ratio >1 are sometimes associated with injections, sometimes not. CONCLUSION 1. Free energy in FAC makes TDS 2. TDS accelerates electrons to several keV 3. Injection sometimes, but not always provides the free energy in the FAC EXAMPLE OF FIELD-ALIGNED CURRENT WHOSE FREE ENERGY PRODUCES TDS AND PARALLEL ELECTRON ACCELERATION BY THE TDS 3

1.Large field-aligned currents (ΔB/B~0.3) appear, (panel b) sometimes near injections (panel e), sometimes not. 2.Field-aligned currents cause TDS (panel c) [Roberts and Berk, 1967; Morse and Nielson, 1969a, 1969b; Lashmore-Davies, 1973; Joyce and Hubbard, 1978; Hubbard and Joyce, 1979; Yamamoto and Kan, 1985; Omura et al, 1996, 2008; Berthomier et al, 1998; Miyake et al, 1998; Goldman et al, 1999; Newman et al, 2001; Oppenheim et al, 2001; Singh 2003; Wu et al, 2011] 3.Parallel electron acceleration by TDS causes field- aligned electron distributions (panel d) [Artemyev et al, 2014; Osmane et al, 2014; Mozer et al, 2015] (note the absence of higher frequency electric field power at these times) 4.Field-aligned electrons cause electron precipitation to make auroras (panel a). 4

PARALLEL ELECTRON ACCELERATION BY THE LANDAU RESONANCE The idea - Time domain structures overtake electrons - Electrons are accelerated by the parallel electric field in the time domain structure - The electrons move into a converging magnetic field so some v_par is converted to v_perp - This increases the dwell time of the electrons in the TDS so they are further accelerated. 5

SIMULATION OF THE LANDAU RESONANCE ASSUMES 1.Electrons interact with a single time domain structure. 2.Time domain structure is electrostatic 3.Time domain structure has no net potential. RAN 1000 PARTICLES FOR EACH OF 4 ENERGIES AND 45 PITCH ANGLES TO SHOW THAT ELECTRONS CAN GAIN ~10 keV THROUGH INTERACTION WITH A SINGLE TIME DOMAIN SPIKE Artemyev, A.V., O.V. Agapitov, F.S. Mozer, and V. Krasnoselskikh, Thermal electron acceleration by localized bursts of electric field in the radiation belts, Geophys. Res. Lett, 2014, DOI: /2014GL

PARALLEL ELECTRON ACCELERATION BY THE FERMI PROCESS The idea - An electron traveling along the magnetic field line is reflected by the potential barrier represented. by a TDS traveling in the opposite direction - TDS is electrostatic with no net potential 7 Vasko, I.Y., O.V. Agapitov, F.S. Mozer and A.V. Artemyev, Thermal electron interaction with electric field spikes in the outer radiation belt: acceleration and formation of field-aligned pitch angle distributions, J. Geophys. Res., in publication In the simulation, 5 pairs of packets, each containing 50 TDS having amplitudes of mV/m, move from the equator in a dipole B and damp out at 35degrees. The simulation lasts one bounce period for 10 eV electrons.

8 Fermi acceleration simulation Experiment COMPARISON BETWEEN THEORY AND EXPERIMENT The mechanism picks a narrow range of energies to accelerate

9 COMPARISON BETWEEN THEORY AND EXPERIMENT The mechanism picks a narrow range of energies to accelerate a Before simulation b After simulation c Before TDS in data d After TDS in data

Mozer, F.S., O.V. Agapitov, V. Krasnoselskikh, S. Lejosne, G.D. Reeves, and I. Roth, Direct observation of radiation belt electron acceleration from electron-volt energies to megavolts by nonlinear shistlers, Phys. Rev. Lett. 113, , keV ELECTRONS CAN BE THE SEED PARTICLES ACCELERATED TO RELATIVISTIC ENERGIES BY UPPER BAND CHORUS WAVES

11 PROBLEM The Landau and Fermi mechanisms can only accelerate electrons to ~10 keV. But 100 keV field-aligned distributions are observed about 10% of the time. STATISTICS OF 200 FIELD-ALIGNED EVENTS OBSERVED IN THE PRESENCE OF ONLY TDS

OBSERVATION OF KEV FIELD-ALIGNED ELECTRON DISTRIBUTIONS Fifteen examples of keV field-aligned electron distributions were observed during the first year of Van Allen Probe operations. Examination of the waves in the vicinity of each observation revealed that the field-aligned electrons were all associated with only three- dimensional, magnetized, electron holes. None were observed in the near vicinity of whistler waves or any mode other than low frequency magnetic noise that is present most of the time and that may be due to kinetic Alfven waves. It is suggested that the energetic field-aligned electrons arise largely from pitch angle scattering of perpendicular electrons rather than parallel acceleration of lower energy electrons. The ratio of the parallel electric field to the parallel magnetic field in the time domain structures is the order of times c. Any simulation that explains this data must take into account the three-dimensional nature of the electric field spikes and the curl of the electric field that arises from dB/dT THE FOLLOWING SLIDES GIVE SIX EXAMPLES OF THE ELECTRON PITCH ANGLE DISTRIBUTIONS AND THE WAVES THAT OCCURRED IN THEIR VICINITY. Proton pitch angle distributions were also checked and nothing unusual was found. 12

POINTS 1.Occur with TDS and fac, sometimes near injections, sometimes not. 2.No other high frequency waves are observed at these times. 3.Durations of energetic field-alignment is 10 or a few tens of seconds 4.Nothing happens to the protons during these times. 5.Associated with electromagnetic TDS 6.Our existing mechanisms can’t make >100 keV TDS. So we need a new mechanism. This can be either the effect of dB/dt or pitch angle scattering of 90 degree electrons. I should plot a case to show this. It should include pitch angle distributions immediately before, during, and after the event.***** 13

Maximum field-aligned energy = 168 keV. Maximum Eparallel = 40 mV/m. Maximum Bparallel = 60 pT 14 Field-aligned current makes electromagnetic TDS TDS makes field-aligned electron distributions, to 170 keV No other VLF wave is present

Maximum field-aligned energy = 168 keV. Maximum Eparallel = 20 mV/m. Maximum Bparallel = 120 pT

Maximum field-aligned energy = 134 keV. Maximum Eparallel = 100 mV/m. Maximum Bparallel = 150 pT

17 POSSIBLE MECHANISM FOR MAKING 100 KEV FIELD-ALIGNED ELECTRONS - The TDS that make the 100 keV field-aligned electrons are three-dimensional - The TDS that make the 100 keV field-aligned electrons have a significant component of parallel magnetic field Perhaps the perpendicular electric field and/of the parallel magnetic field cause rapid pitch angle scattering so the original 90 degree electrons become field aligned with little actual acceleration.

18