Адиабатический нагрев электронов в хвосте магнитосферы.

1. Адиабатический нагрев электронов в хвосте магнитосферы. Зеленый Л.М., Артемьев А.В., Петрукович А.А. ИКИ РАН Физика плазмы в солнечной системе» 6 - 10 февраля 2012 г., ИКИ РАН

2. Model of electron heating in the course of Earthward convection and formation of electron temperature profiles Guiding center equation

3. Formation of electron temperature profiles Te z Magnetic field lines x 0 z, Bx Te x The growth of the electron temperature corresponds to the growth of Bz For particles with distant mirror points Tverskoy 1972 Lyons 1984

4. Adiabatic model z convection x The point of observation Bz x Electron heating during the earthward convection due to the conservation of the first and second adiabatic invariants Tverskoy 1972, Zelenyietal. 1990

5. Single electron dynamics Invariants Electrons with mirror points far from the neutral plane Near equatorial mirroring electrons

6. Evolution of electron distribution function Assumption Velocity distribution in the point of observation (Bz = Bz0) Integration of obtained function gives temperature profile Expressions obtained from m and JII conservation “In situ” observed values Velocity distribution in the neutral plane (Bx~0) Z Projection along field lines field line x as a function of z along field line tracing X x0 Point in the neutral plane downstream tail observation point Velocity distribution in dependence on Bx~z coordinate

7. The vertical profiles of electron temperature and anisotropy Electron anisotropy decays towards the Earth. Electron anisotropy is almost constant across the tail Anisotropic heating: Projection of velocity distribution along field lines gives the profiles of electron temperature anisotropy: TeII/Te ~ const Te/Temax IN THE EQUATORIAL PLANE TeII/Te profile downstream the tail Bz/Bn To Earth

8. Observed profiles of temperature anisotropy Profiles of electron anisotropy: TeII/Te TeII/Te is approximately constant Profiles of electron temperature: Te=(TeII+2Te)/3 Te decreases toward the TCS boundary

9. Comparison of model profiles Te(Bx) and observations Electron temperature asa function of the local magnetic field for four TCS crossings Spacecraft (Cluster 2) observations Model profiles Te(Bx) with h=-0.8

10. Electron energy distribution in TCS Anisotropy of temperature is produced by electron population with energy ~ 1keV. Cold core of distribution (<100 ev) and hot tails (>3 keV) are isotropic: f(a=0o)=f(a=90o) ke~1 ke~1 ke~1 Difference of energy distribution for a=90o and for a=0o For TCS

11. Statistics of observations Statistics for 70 TCS crossings Anisotropy of electron temperature is constant inside TCS Simple model based on conservation of adiabatic invariants explains: 1.Temperature anisotropy do exist 2. Anisotropy profile across the tail~ const Lyons 1984 Tverskoy 1969, Zelenyi et al. 1991 Isotropisation of electron distribution due to scattering at small-scale magnetic field fluctuations Anisotropic heating: Who is right? (SMALL ) ELECTRON ANISOTROPY DO !! EXISTS

12. The estimates of current sheet parameters from comparison of observations and model profiles Te(Bx) Input model parameters: B0 – amplitude of TCS magnetic field Bz – normal component of magnetic field Bext - magnetic field magnitude at the lobe Lz – current sheet thickness Lx – spatial scale along Earth-Sun direction direct observation direct observation direct observation ~B0/jcurl from mutlispacecraft observations free model parameter Output model parameters: Te(Bx) profiles Comparison of model Te(Bx) profiles and observed Te(Bx) can give estimates of Lx We vary the model input Lx to approximate the observed profiles Te(Bx) We use the statistics of 62 TCS crossings from 2001, 2002 and 2004 years As a result, we obtain the statistics of Lx

13. Distribution of Lx estimates Distribution of Lx The most TCSs have Lx [5, 20] RE. Distribution of Lx/Lz ratio The most TCSs have Lx/Lz~25

14. The ratio Lx/L and pressure balance in TCS 2D isotropic current sheetwith l=1 z l=2BzLx/B0Lz x Electrons help us to prove that Speiser ions are main players in pressure balance in thin current sheets! 1D TCSwith l>1 and nongyrotropic pressure z x Effect of ion nongyrotropy For 2D current sheet l =1, and longitudinal pressure balance could be maintained only by the gradient alongx (Schindler 1972, Lembege and Pellat 1982). For TCSl>1 and part of pressure balance corresponds to the inertia of Speiser ion motionwhich create the off-diagonal terms of the pressure tensor.

15. Conclusions: For particles with far mirror points For equatorial particles • Adiabatic electrons can gain energy during the Earthward convection with the rate: • The model of electron adiabatic heating during earthward convection can describe the observed profiles of Te(Bx) with the reasonable accuracy • The comparison between model and observed profiles Te(Bx) allows to estimate the longitudinal spatial scale of current sheetLx~(∂lnBz/∂x)-1: • Stretched magnetotail equilibria could be supported only by nongyrotropic ion distributions (Te<<Ti) and principal future task is the careful examination of ion pressure tensor 5 RE<Lx<20 RE <Lx/Lz>25 <2BzLx/B0Lz>~5