j. büchner+collaborators, at different times, were:

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

Consequences of LHDI for three-dimensional collisionless reconnection through thin current sheets

J. Büchner+collaborators, at different times, J. Büchner+collaborators, at different times, were: were:

J. Kuska, B. Nikutowski, I.Silin, Th.Wiegelmann J. Kuska, B. Nikutowski, I.Silin, Th.Wiegelmann

all at: Max-Planck Institut für Sonnensystem-all at: Max-Planck Institut für Sonnensystem-forschung in Katlenburg-Lindau, Germany forschung in Katlenburg-Lindau, Germany

(for „Solar System Research“ starting 1.7.2004 (for „Solar System Research“ starting 1.7.2004 after being „for Aeronomy“ the last 40 years)after being „for Aeronomy“ the last 40 years)

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

Topics• Gradient and current-driven plasma instabilities in

current sheets • Initiation of 3D collisionless reconnection (PIC->Vlasov-

simulation approach) in / through– anti-parallel magnetic fields– creation / annihilation of helicity density– non-anti-parallel, finite guide magnetic field case– asymmetric (magnetopause) current sheet case

• „Anomalous resistivity“ approach to introduce kinetic results into large scale MHD

• EUV Bright Points (BP): MHD modeling of the dynamic evolution (photospheric flows) + anomalous transport=> Null point <or> finite B <or> QSL reconnection ???

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

3D current sheet instabilities• 1970th: quasi/linear theory: LHD-instability at the edges

(Drake, Huba, Davidson, Winske, Tanaka & Sato ... )• 1996: 3D PIC simulations showed: global (kink/sausage)

mode current sheet instabilities can initiate reconnection

(Pritchett et al.; Zhu & Winglee; Büchner & Kuska 1996)• 1998...now: New theory - and simulation results about

current-driven and drift instabilities at sheet center

(Horiuchi & Sato; Büchner, Kuska & Silin; Daughton et al.)• Our latest move:

From PIC to Vlasov-codes to test wave-particle

interactions, resonances etc. which can initiate

current sheet instabilities and reconnection

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

Vlasov equation: 0)(1

v

fBv

cE

m

e

r

fv

t

f j

j

jjj

Linear perturbation of distribution functions

tdv

fBvEc

cm

etf

tj

j

jj

0111 )(

Resulting perturbation of density and current

vdfvej

vdfe

jjj

jjj

11

11

Maxwell equations for the fields or wave equation for the potentials

121

2

21

121

2

21

41

41

jct

A

cA

tc

Kinetic stability investigation

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

-> > 20o: Eigenmodes are linearily stable(k=k0 cos ex +k0 sin ey)

Linear stability of oblique eigenmodes at current sheet center

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

Vlasov simulation code

vdfvej

vdfe

ei

Veijei

V

eieij

ei

3,

,,

3,

,,

121

2

21

121

2

21

41

41

jct

A

cA

tc

0)(1 ,

,

,,,

v

fBv

cE

m

e

r

fv

t

f ei

ei

eieiei

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

Nonlinear LHDI (anti-parallel fields: Vlasov kinetic simulation)

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

Non-local penetration of LHD unstable waves

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

Simulation shows: the Ey fluctuations grow also at the center

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

Drift-resonance instability (DRI)

1D ion distribution in the current direction

1D electron distribution in the current direction

Ions drive waves → plateau-formation → electron-heating

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

DRI: 3D distribution function

3D Ion distribution function 3D electron distribution

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

3D current sheet instability

(Plasma density perturbation; case of antiparallel fields) (Plasma density perturbation; case of antiparallel fields)

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

Current sheet thickness C1<->C4 (7.9.01, 19:00>23:00)

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

Current sheet waves ~21:00 UT

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

Current sheet waves –observed by Cluster as predicted

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

Waves initiate 3D reconnection

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

Mechanism:Wave- reconnection coupling:

Dashed: LHDI (edge) ; Solid: LHDI at the center; Dashed-dotted: reconnecting mode

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

3D reconnection island:

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

2.) Helicity density evolution:a.) 3D antiparallel

reconnection

0 const. B)d (A H 3M x

Spheres: quadrants 1 and 4

Squares: quadrants 2 and 3

Solid line - total helicity:

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

Antiparallel -> finite guide field By

guide field By -> flux ropesguide field By -> flux ropesQuadrupolar By fieldQuadrupolar By field

-> Bending of B-fields-> Bending of B-fields

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

Finite guide field case -> non 180o magnetic shear Guide fields change the shear angle between the ambient B-fields

1 8 0 °

M S P M S HJ

1 2 5 °

M S P M S H

J

2 1 0 °

M S P M S HJ

180o

(J = direction of sheet current and of reconnection E- field)

Negative Co-

helicity HMo < 0

Positive Co-helicity

HMo > 0 0 B)d (A H 3Mo x

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

3D guide field reconnection: initially positive co-helicity case

oi t = 1 oi t = 25

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

2D / 3D positive co-helicity reconnection („pull reconnection“)

Dotted: quadrants 1 and 4

Dashed: quadrants 2 and 3

Solid line - total helicity:

0d B) (E2- H 3M

xdt

d

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

oi t = 1

oi t = 23

3D guide field reconnection: initially negative co-helicity case

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

2D / 3D negative co-helicity reconnection („push reconnection“)

Dotted: quadrants 1 and 4

Dashed: quadrants 2 and 3

Solid line - total helicity:

0d B) (E2- H 3M

xdt

d

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

3.) Resonant DRI in the guide field case:

The growth rate of the instability decreases proportionally to the number of resonant ions.

For stronger guide fields the cross-field

propagation direction turns

further away from the current direction.

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

Reconnection wave in a non- anti-parallel (guide field) current sheet

Bz in linear presentation for the polarity of magnetic bubbles

Bz in log presentation turbulence -> structure

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

Result: patchy reconnection in the

non-anti-parallel, guide field case:

The B field opens the boundary throug local patches (blue: below, red: above)

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

Simulation model

The pressure being locally balanced; drift Maxwellians,

drifts

currents

4: Non-symmetric case (MP)

-> fields rotate through a tangential magnetic boundary

Bc

j

4

eiei TTuu //

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

Instability of a non-symmetric magnetic boundary current sheet

LHD instability first on magnetospheric side (z<0) -> penetrates to the magnetosheath side (z>0) and triggers reconnection - island formation

Magnetic

field Bz:

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

Magnetopause observation (Cluster)

A. Vaivadset al., 2004

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

5.) Quasilinear estimate of the WP momentum exchange (-> “anomalous collision frequency;-> “... resistivity”)

(Davidson and Gladd, Phys. Fluids, 1975)

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

Anomalous momentum exchangedue to nonlinear DRI in a current sheet:

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

6.) X-ray & EUV Bright Points (BPs): quiet-sun reconnection

- XBP are formed inside diffuse clouds, which grow at 1 km/s up to 20 Mm and then form a bright core 3 Mm wide, they last, typically, 8 h

Vaiana, 1970: rockets; Golub et al. 1974-77: Skylab More recently: SOHO and TRACE observations

-Later (Soho...) : also many EUV BP investigated

-> BP are assumed to be prime candidates for reconnection: they well correlate with separated photospheric dipolar (opposite polarity) photospheric magnetic fluxes

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

Soho-MDI and EIT: EUV BP

MDI line-of sight magnetic

field

( 40” x 40”)

EIT (195 A) same field of

view

17-18.10.1996 (M. Madjarska et al., 2003)

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

Reconnection models for BP

- Due to the B separation in the photosphere -> Reconnection between bipoles

assumed to take place in the corona, -> magnetohydrostatic models, e.g.

- Newly Emerging Flux Model (EMF) Heyvaerts, Priest & Rust 1977

- Converging flux model Priest, Parnell, Martin & Gollup, 1994- Separator Reconnection in MCC

Longcope, 1998

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

But: dynamical footpoint motion:

-> currents are driven into the chromosphere/corona

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

Model, starting with extrapolated B-fields ...

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

... and footpoint motion (here after 1:39 ...and density-heightUT 18.10.96): profile (VAL):

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

Density Evolution -> t=128

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

Parallel electric fields and parallel currents at t=128

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

Transition region parallel electric fields

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

Transition region reconnection

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

Reconnection due to resistivity switched on enhanced current (velocity)

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

Not at a null, but between two nulls (separator through 35,20,5 ?)

<- Iso-surfaces of a smalltotal magnetic field, henceembedding the nulls

Magnetic Reconnection Theory, Newton Institute Cambridge, August 20, 2004

Further work planned on:• Current sheet instabilities for more

realistic current and field models and their consequences for reconnection

• resulting anomalous transport as an approach toward quantifying the coupling between MHD and kinetic scales for solar and magnetospheric applications

• Reconnection at neutral points vs. separator reconnection vs. quasi-separatrix layer - reconnection in the course of the dynamically evolving „magnetic carpet“ („tectonics“)