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)


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 ???


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


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


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

Linear stability of oblique eigenmodes at current sheet center


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


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


Non-local penetration of LHD unstable waves


Simulation shows: the Ey fluctuations grow also at the center


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


DRI: 3D distribution function

3D Ion distribution function 3D electron distribution


3D current sheet instability

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


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


Current sheet waves ~21:00 UT


Current sheet waves –observed by Cluster as predicted


Waves initiate 3D reconnection


Mechanism:Wave- reconnection coupling:

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


3D reconnection island:


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:


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


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


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

oi t = 1 oi t = 25


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

Dotted: quadrants 1 and 4

Dashed: quadrants 2 and 3


0d B) (E2- H 3M

xdt

d


oi t = 1

oi t = 23

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


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

Dotted: quadrants 1 and 4

Dashed: quadrants 2 and 3


0d B) (E2- H 3M

xdt

d


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.


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


Result: patchy reconnection in the

non-anti-parallel, guide field case:

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


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 //


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:


Magnetopause observation (Cluster)

A. Vaivadset al., 2004


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

(Davidson and Gladd, Phys. Fluids, 1975)


Anomalous momentum exchangedue to nonlinear DRI in a current sheet:


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


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)


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


But: dynamical footpoint motion:

-> currents are driven into the chromosphere/corona


Model, starting with extrapolated B-fields ...


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


Density Evolution -> t=128


Parallel electric fields and parallel currents at t=128


Transition region parallel electric fields


Transition region reconnection


Reconnection due to resistivity switched on enhanced current (velocity)


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

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


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“)

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

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