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“Ambipolar Diffusion” and Magnetic Reconnection Tsap Yu.T. , Stepanov A.V. Crimean Astrophysical Observatory Central (Pulkovo) Astronomical Observatory 1. Diffusion and dissipation of the magnetic field in the partially ionized plasma is an important physical process in many cosmic objects Star formation Mestel&Spitzer (1956) - magnetic force prevent star formation if the mass of the magnetic cloud M < 500 Msun since magnetic flux is conserved. 2. Dynamo – alpha-effect due to the magnetic reconnection 3. Flare energy release on the Sun and stars Zaitsev-Stepanov (1991) circuit model of flares Giardini Naxos 2010 What is the “ambipolar diffusion” in the weakly ionized plasma according to Mestel&Spitzer? Three-fluid approximation ene dVe ene E Ve B ne m ea (Va Ve ) ne m ei (Vi Ve ); ne m dt c eni dVi n M en E V B n M ( V V ) n m ( V i i i i ia a i i ei e Vi ); dt c dVa n M n M ( V V ) n M ( V a a ai i a a ae e Va ). dt ene j eni (Vi Ve ) equation for the electric current ene E c Ve B 0; en E eni V B n M (V V ) 0. i i ia i a i c j B Vi Va cnM but ia Vi B E c “Ambipolar diffusion” (collisional plasma) is the motion of ions through a gas of neutral particles under action of Ampere’s force but classical (real) diffusion is caused by the inhomogenity (two types of diffusion) Mestel and Spitzer (1956) considered star formation in magnetic dust cloud due to gravity • Main problem: since the field is frozen into the contracting cloud the star formation becomes impossible because of the magnetic forces • Solution: the distorted magnetic field is able to straighten itself, dragging the ions and electrons with it , while the bulk of the cloud contracts across the magnetic energy This scenario suggests that the magnetic field is frozen into ions, i.e. B rotVi B t Very popular expression beginning from Parker (1963) cloud What is the Joule dissipation in the collisional plasma? The Joule dissipation is the work of the electric field on electric current without the mechanical energy caused by Ampere’s fоrсe, which is equal to the thermal energy release due to ion-neutral, electron-neutral, and ionelectron collisions, i.e. jB V B V E j E j c c nM in (Vn Vi ) 2 nm ei (Vi Ve ) 2 nn m ni (Vn Ve ) 2 Q Ej Mestel&Spitzer(1956), Parker(1963) and others. On the Magnetic Flux Conservation jB V V i a cnM en ia i V B jB eni E c i c eni en E V B n M (V V ) 0 i i ia a i c i B jB rotV B rot i t en i But Parker (1963) B rotVi B t Magnetic flux does not conserved due to Joule dissipation Cowling Conductivity (1957) The degree of ionization is not important as distinguished from Mestel&Spitzer(1956) Main suggestions: 1. Collisional plasma na maVa ni miVi ne meVe v na ma ni mi ne me v vk Vk v vk 2. Plasma must be non-stationary over time or space dv v ( v )v 0 dt t Generalized Ohm’s Law j eff ( E v B) , C S c Mn in ne eff , S , C . 2 2 C S m( ei en ) B F 2 2 Cowling conductivity Sweet-Parker magnetic reconnection Sweet-Parker [Sweet 1958, Parker 1957] Main features: 1. L>>l – the current sheet is long and thin; 2. Plasma is evacuated from the current sheet because of the gas (magnetic) pressure. Plasma evacuation may be caused by Lorentz force due the strength of the magnetic field lines (effect of slingshot) B0 – perpendicular component Scaling Laws and the Slingshot Effect LV lV0 0 - mass balance equation B2 p p0 - pressure balance across the magnetic field 8 V02 0 p0 p - coponent of the momentum equation along the sheet 2 B VB С - induction equation uniform elctric field l V02 BBL 0 p0 p 0 2 8 l VB V0 B0 continuity equation for electric field - Å const B B0 continuity of the magnetic field lines - divB 0 L l B B0 L l VB 0V0 B0 - contradict ion LV lV0 Energy Balance of Plasma j2 B 2 VA 4 L 3nkT J 2 B / 4 0 - energy releace rate due to Joule dissipatio n L L - heating time VA VA 0 L - dynamical plasma cooling V A 0 J d d Qr nnH F (T ) radiative losses 7 negligibly small T 2 Qt 2 losses caused by thermal conductivi ty L Thickness of the Current Sheet under Solar Chromospheric Conditions L l ~ C VA 11 3 nH 10 cm 7 F 1 l ~ 10 cm T 10 4 K L 108 cm B 30G Solar Chromospheric Ejections observations with SOT/Hinode in lineСа Shibata etal.07, De Pontieu et al.07 H Spicules Chromospheric jets Thickness < 200 km thickness - 150-300 km, Hinode Ca H Models Shibata et al. 1992 Shock waves push plasma Proposed model Magnetic pressure pushes plasma Токовый слой Conclusions 1. There are two types of ambipolar diffusion in plasma physics – real and formal. 2. The Joule dissipation in partially ionized plasma is determined by collisions between neutrals and ions too. 3. Approach proposed by Cowling (1959) is more adequate than approach proposed by Meste& Spitzer~(1956) in the case of the collisional plasma. 4. Plasma evacuation is an effective cooling mechanism of the current sheet. 5. The Sweet-Parker reconnection in partially ionized plasma can play an important role in the solar chromosphere. Thank you! RT-22, Crimea