Some books

MHD and Kinetics Workshop February 2008MHD and Kinetics Workshop February 2008

Magnetic reconnection Magnetic reconnection in solar theory:in solar theory:

MHD vs KineticsMHD vs Kinetics

Philippa Browning, Philippa Browning, Jodrell Bank Centre for Astrophysics, ManchesterJodrell Bank Centre for Astrophysics, Manchester

MHD and Kinetics Workshop February 2008

Some booksSome 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)


Magnetic reconnectionMagnetic 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)


Where does reconnection occur?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


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


Modes of reconnectionModes 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


Tearing instabilityTearing instabilityFurth et al, 1963Furth et al, 1963

1 2 1tear aS t

•Spontaneous linear instability in current sheet (field reversal) or sheared field

•Outer ideal region matched to thin inner resistive layer

•Maximum growth rate


Steady state reconnectionSteady state reconnectionSweet Parker, Petschek and variantsSweet Parker, Petschek and variants

lnrec At t S

Steady inflow (vi) , fields continually reconnect in current sheet

Reconnection rate

(Sweet Parker)

(Petschek)

1 2 1 2r A Dt t S t S

1

8 lni

A

v

v S

1 2i

A

vS

v


Current sheet forms at Lz/2 where k.B0 =

0

Boundary disturbance δcosky

Forced reconnectionForced reconnectionHahm and Kulsrud, 1985Hahm 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


Ohm’s LawOhm’s Law

2

1

te

e

mp

ne ne

j jE v B j B

1 2

02

1 2

0

2

ee

pe

pi

pi

mccne

mccne

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


Approaches to reconnection modellingApproaches 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)


Newton challenge (Birn et al, 2005)Newton challenge (Birn et al, 2005)


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


Some numbers (solar corona)Some numbers (solar corona)

Typical length of coronal loop L = 107 - 108 m (widths of observed loops ≈ 106 m ) – the global scale length

Take

Lundquist number S =1014

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 3 2 610 , 10 , 10n m B T T K

410coll m

1 2 10 100l S L m


Ion skin depth

Ion gyroradius rLi ≈ 1 m

Typical MHD simulation grid cell ≈ 105 - 106 m

Typical kinetic simulation box size ≈ 103 m

10 mi


Questions: MHD vs kineticsQuestions: 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?


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?


Possible tools for linking MHD and kineticsPossible 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” ?


Links to other Workshop topicsLinks 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

Documents

Some books