1. Адиабатический нагрев электронов в хвосте магнитосферы. Физика плазмы в солнечной системе» 6 - 10 февраля 2012 г., ИКИ РАН Зеленый Л.М., Артемьев А.В., Петрукович А.А. 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 z x Magnetic field lines z, B x TeTe 0 TeTe x Lyons 1984 Tverskoy 1972 For particles with distant mirror points The growth of the electron temperature corresponds to the growth of B z

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

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

6. Evolution of electron distribution function Velocity distribution in the point of observation (B z = B z0 ) “In situ” observed values Assumption Expressions obtained from  and J II conservation Velocity distribution in the neutral plane (B x ~0) Projection along field lines Point in the neutral plane x as a function of z along field line Velocity distribution in dependence on B x ~z coordinate X Z observation point tracing field line downstream tail Integration of obtained functiongives temperature profile x0x0

7. The vertical profiles of electron temperature and anisotropy Anisotropic heating: Projection of velocity distribution along field lines gives the profiles of electron temperature anisotropy: T eII /T e  ~ const B z /B n profile downstream the tail Electron anisotropy decays towards the Earth. Electron anisotropy is almost constant across the tail To Earth T eII /T e  T e /T emax IN THE EQUATORIAL PLANE

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

9. Comparison of model profiles T e (B x ) and observations Electron temperature Electron temperature as a function of the local magnetic field for four TCS crossings Spacecraft (Cluster 2) observations Model profiles T e (B x ) with h=-0.8

10. Electron energy distribution in TCS Difference of energy distribution for  =90 o and for  =0 o Anisotropy of temperature is produced by electron population with energy ~ 1keV. Cold core of distribution ( 3 keV) are isotropic: f(  =0 o )=f(  =90 o ) For TCS  e ~1

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

12. The estimates of current sheet parameters from comparison of observations and model profiles T e (B x ) Input model parameters: B 0 – amplitude of TCS magnetic field B z – normal component of magnetic field B ext - magnetic field magnitude at the lobe L z – current sheet thickness L x – spatial scale along Earth-Sun direction direct observation ~B 0 /j curl from mutlispacecraft observations free model parameter Output model parameters: T e (B x ) profiles Comparison of model T e (B x ) profiles and observed T e (B x ) can give estimates of L x We vary the model input L x to approximate the observed profiles T e (B x ) We use the statistics of 62 TCS crossings from 2001, 2002 and 2004 years As a result, we obtain the statistics of L x

13. Distribution of L x estimates Distribution of L x /L z ratio The most TCSs have L x /L z ~25 The most TCSs have L x  [5, 20] R E. Distribution of L x

14. The ratio L x /L and pressure balance in TCS For 2D current sheet =1, and longitudinal pressure balance could be maintained only by the gradient along x ( Schindler 1972, Lembege and Pellat 1982 ). >1 For TCS >1 and part of pressure balance corresponds to the inertia of Speiser ion motion which create the off-diagonal terms of the pressure tensor. =2B z L x /B 0 L z z z x x 1D TCS with >1 and nongyrotropic pressure 2D isotropic current sheet with =1 Effect of ion nongyrotropy Electrons help us to prove that Speiser ions are main players in pressure balance in thin current sheets!

15. Conclusions: 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 T e (B x ) with the reasonable accuracy The comparison between model and observed profiles T e (B x ) allows to estimate the longitudinal spatial scale of current sheet L x ~(∂lnB z /∂x) -1 : Stretched magnetotail equilibria could be supported only by nongyrotropic ion distributions (T e <<T i ) and principal future task is the careful examination of ion pressure tensor For equatorial particlesFor particles with far mirror points 5 R E  25 ~5