1. MHD and Kinetics Workshop February 2008 Magnetic reconnection in solar theory: MHD vs Kinetics Philippa Browning, Jodrell Bank Centre for Astrophysics, Manchester

2. MHD and Kinetics Workshop February 2008 Some books This talk is NOT a review of magnetic reconnection! For overview of current state of play on reconnection theory: “Magnetic reconnection” Priest and Forbes (2000) “Magnetic reconnection in plasmas” Biskamp (2005) “Reconnection of magnetic fields” Birn and Priest (2007)

3. MHD and Kinetics Workshop February 2008 Magnetic reconnection A restructuring of the magnetic field topology due to localised departures from frozen-in field condition Dissipation rates enhanced beyond simple Ohmic dissipation (or equivalent) due to interaction of flow field with dissipation Scale separation – global “ideal” region with inner “dissipative” region Causes changes in field connectivity and conversion of magnetic energy to thermal energy and kinetic energy (bulk flows and nonthermal particles)

4. MHD and Kinetics Workshop February 2008 Where does reconnection occur? Solar flares – reconnection likely to be primary energy release process Solar and stellar coronal heating Coronal mass ejections, prominence eruptions; flux emergence; magnetoconvection and dynamo

5. MHD and Kinetics Workshop February 2008 Magnetospheres Flare stars, magnetars Accretion discs and jets (AGNs, young stars etc) Protostar collapse, galactic and intergalactic magnetic fields, pulsars… Fusion plasmas e.g. tokamak sawteeth, spheromak formation Laboratory reconnection experiments e.g. MRX

6. MHD and Kinetics Workshop February 2008 Modes of reconnection Spontaneous reconnection – a linear instability of resistive plasma - tearing instability and variants Forced reconnection – triggered by external disturbance – Hahm and Kulsrud Steady state reconnection – Sweet-Parker, Petschek and variant models General time dependent reconnection – numerical simulations Most models of reconnection are 2D - current sheets and X lines Some significant differences in 3D - separators and separatrices, nulls, QSLs 3D reconnection usually 2D on local scale but global geometry is different

7. MHD and Kinetics Workshop February 2008 Tearing instability Furth et al, 1963 Spontaneous linear instability in current sheet (field reversal) or sheared field Outer ideal region matched to thin inner resistive layer Maximum growth rate

8. MHD and Kinetics Workshop February 2008 Steady state reconnection Sweet Parker, Petschek and variants Steady inflow (v i ), fields continually reconnect in current sheet Reconnection rate (Sweet Parker) (Petschek)

9. MHD and Kinetics Workshop February 2008 Current sheet forms at L z /2 where k.B 0 = 0 Boundary disturbance δcosky Forced reconnection Hahm and Kulsrud, 1985 Apply a transient sinusoidal disturbance to the boundary of a neutral sheet field or sheared field A current sheet develops which subsequently reconnects, releasing stored magnetic energy Allows reconnection in an initially stable field

10. MHD and Kinetics Workshop February 2008 Ohm’s Law Ohmic resistance (collisions) Electron inertia Hall Length scale of electron inertia – electron skin depth Length scale of Hall term – ion skin depth In Hall MHD, plasma is frozen to electron fluid – hence Hall term is not dissipative but can strongly affect reconnection dynamics – introduces two fluid effects

11. MHD and Kinetics Workshop February 2008 Approaches to reconnection modelling MHD – numerous! Hall e.g. Fitzpatrick, Arber and Haynes, Bhattarcharjee, Huba Hybrid – fluid electrons and particle ions Gyrokinetic Particle in Cell (PIC) e.g. Drake and co-workers Compare for simple model problem – tearing instability (GEM challenge – Birn et al, 2001) or forced reconnection variant (Newton challenge – Birn et al, 2005)

12. MHD and Kinetics Workshop February 2008 Newton challenge (Birn et al, 2005)

13. MHD and Kinetics Workshop February 2008 3D PIC simulation of reconnection (from Drake et al, 2006) Doubly periodic Harris current sheets Electron out of plane current at two successive times and temperature

14. MHD and Kinetics Workshop February 2008 Some numbers (solar corona) Typical length of coronal loop L = 10 7 - 10 8 m (widths of observed loops ≈ 10 6 m ) – the global scale length Take Lundquist number S =10 14 Mean free path Current sheet width in classical MHD tearing theory or Sweet Parker reconnection MHD valid for global scales but breaks down at local reconnection scales

15. MHD and Kinetics Workshop February 2008 Ion skin depth Ion gyroradius r Li ≈ 1 m Typical MHD simulation grid cell ≈ 10 5 - 10 6 m Typical kinetic simulation box size ≈ 10 3 m

16. MHD and Kinetics Workshop February 2008 Questions: MHD vs kinetics “Compare and contrast” or “link” What are similarities and differences between MHD and various kinetic models (Hall MHD, PIC etc)? How does reconnection rate depend on dissipation mechanism and on external conditions? Do net energy release and final state of reconnecting field depend on local dissipation process? What is the most appropriate form of Ohm’s law for modelling coronal plasmas?

17. MHD and Kinetics Workshop February 2008 How can we develop models (numerical or other) to incorporate wide range of length scales from kinetic to MHD? How are charged particles accelerated in reconnecting fields, and how do their properties depend on the parameters of the reconnection? What is “anomalous resistivity”? What is role of micro turbulence in reconnecting fields? What about other kinetic effects (beyond Ohm’s law) in reconnecting plasmas – heat transport, plasma waves etc?

18. MHD and Kinetics Workshop February 2008 Possible tools for linking MHD and kinetics Test particle models Beyond test particles to self-consistent models – hybrid codes? Comparison of simulations for “standard models” Coupled models Different models on different scales – local kinetic linked to global MHD Proper modelling of “ anomalous resistivity” ?

19. MHD and Kinetics Workshop February 2008 Links to other Workshop topics Strong electric fields in magnetic reconnection can be efficient particle accelerators – studies of generation of nonthermal particles in reconnecting fields requires some kinetic modelling Many reconnection models predict shocks (e.g. slow shocks in Petchsek) Reconnection is associated with turbulence on various scales – within dissipation region and globally Reconnection events may trigger waves and oscillations, also reconnection may be modulated or triggered by waves Reconnection causes strong localised heating, so heat transport needs to be properly modelled