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“)