reconnection in the solar corona: numerical simulationisss10/talks/buechner_isss10.pdf · why...

RECONNECTION IN THE SOLAR RECONNECTION IN THE SOLAR CORONA: NUMERICAL SIMULATIONCORONA: NUMERICAL SIMULATION

Jörg Büchner, Max-Planck-Institut für Sonnensystemforschung

Katlenburg-Lindau, Germany g , y

TSSSP group Katlenburg-Lindau: E Adamson and K -W LeeTSSSP group Katlenburg-Lindau: E. Adamson and K.-W. LeeCollaboration: N. Elkina (Munich University )

M Barta (Ondrejov Observatory Czech Academy of Sciences)M. Barta (Ondrejov Observatory, Czech Academy of Sciences)A.Otto (University of Fairbanks, Alaska)J Santos (INPE Sao Jose dos Campos)J. Santos (INPE, Sao Jose dos Campos)

J. Büchner et al. Simulation of Reconnection in the Solar Corona ISSS-10, Banff, July 25, 2011

MPS moves 2014 to GöttingenMPS moves 2014 to Göttingen2014: New

MPS building in Götti

2014: New MPS building in Götti

(since 1973 MPAewith Ian Axford as

(since 1973 MPAewith Ian Axford as

Göttingen -->Göttingen -->

with Ian Axford asdirector / since2003 MPS below)

with Ian Axford asdirector / since2003 MPS below)003 S be o )003 S be o )


Why simulate the solar corona?Why simulate the solar corona?• The 106 K hot solar corona and eruptions influence the

Space Weather near Earth in the interplanetary space• The 106 K hot solar corona and eruptions influence the

Space Weather near Earth in the interplanetary spaceSpace Weather near Earth in the interplanetary space. • Basic open questions: what causes

Space Weather near Earth in the interplanetary space. • Basic open questions: what causes

– the heating of the corona?– the acceleration of the solar wind? – the heating of the corona?– the acceleration of the solar wind? – eruptions (flares and coronal mass ejections)?

particle acceleration > X ray emission?– eruptions (flares and coronal mass ejections)?

particle acceleration > X ray emission?– particle acceleration -> X-ray emission?• Where, why, when? Triggering conditions?

– particle acceleration -> X-ray emission?• Where, why, when? Triggering conditions?-> Magnetic reconnection is a key process afterthin current sheets are formed in the corona-> Magnetic reconnection is a key process afterthin current sheets are formed in the coronathin current sheets are formed in the coronathin current sheets are formed in the corona


Challenges for simulationsChallenges for simulations1.) Non-ideal plasma effects & collisionless dissipation occur at

very small plasma scales (e g ion inertial length current sheets)1.) Non-ideal plasma effects & collisionless dissipation occur at

very small plasma scales (e g ion inertial length current sheets)very small plasma scales (e.g. ion inertial length current sheets)

2.) But solar phenomena including reconnection are often large

very small plasma scales (e.g. ion inertial length current sheets)

2.) But solar phenomena including reconnection are often large ) p g gscale processes, i.e. the energy has to be transfered from verylarge (observed sizes) to small (plasma-non-ideality) scales

) p g gscale processes, i.e. the energy has to be transfered from verylarge (observed sizes) to small (plasma-non-ideality) scales

3.) Specific coronal plasma conditionsSt P ti fl t ti f th h t h

3.) Specific coronal plasma conditionsSt P ti fl t ti f th h t h– Strong Poynting fluxes starting from the photosphere, crossthe chromosphere and transition region toward the corona

– A complicated structure of photospheric (source) B-fields

– Strong Poynting fluxes starting from the photosphere, crossthe chromosphere and transition region toward the corona

– A complicated structure of photospheric (source) B-fields– A complicated structure of photospheric (source) B-fields– A considerable inhomogeneity of the coronal plasma,

structured by the solar gravity and magnetic fields

– A complicated structure of photospheric (source) B-fields– A considerable inhomogeneity of the coronal plasma,

structured by the solar gravity and magnetic fieldsy g y g– Heat conduction, radiative losses, radiation transfer

y g y g– Heat conduction, radiative losses, radiation transfer


One hour of X-ray and three -l h SDO b ti

One hour of X-ray and three -l h SDO b tiwavelengh SDO observationswavelengh SDO observations

Top graph: X-ray fluxTop graph: X-ray fluxp g p yat geostationary orbit (GOES-15)

p g p yat geostationary orbit (GOES-15)Main movie: SDO composite observations at 211

Main movie: SDO composite observations at 211observations at 211 Å, 193 Å and 171 ÅEUV wavelengths

observations at 211 Å, 193 Å and 171 ÅEUV wavelengths(21.1, 19.3, 17.1 nm) taken on June 7 (21.1, 19.3, 17.1 nm) taken on June 7 between 6:10 UT and7:13 UT (Blast: 6:20 –6 41)

between 6:10 UT and7:13 UT (Blast: 6:20 –6 41)6:41)6:41)


ProcessesProcesses andand theirtheir scalesscalesEnergyaccumulation &

Energy transfer, Inertial range, self-i il h

Energy dissipation, e.g. by plasma

ideal evolution, similar over howmany decdes?

e.g. by plasmamicro-turbulence

sity

Energy Input Scale

Energ

y den

sit Inertial ranEn nge

Dissipation range

Coronal phenomena:

range

Wave number kD

Coronal phenomena:Mega-Meters … …at least 6 decades… … to the ion inertial length

scale: MetersJ. Büchner et al. Simulation of Reconnection in the Solar Corona ISSS-10, Banff, July 25, 2011

Natural coronal length scalesNatural coronal length scales

0 BBvB

t

MHD induction equation:MHD induction equation:t

As soon as we introduce the size of phenomena as aAs soon as we introduce the size of phenomena as a physical length scale -> for typical l in the collisionlesscorona the magnetic Reynolds numbers become Rm ~ 108 i e B field / j cannot simpl b dissipated!108 - i.e. B-field / j cannot simply by dissipated! Since v ~ 10 km/s there are two ways to decrease Rm:

) f1.) Decrease l e.g. the width of thin current sheets2.) Enlarge the resistivity - e.g. by plasma

b l d i i bili iturbulence due to micro-instabilitiesJ. Büchner et al. Simulation of Reconnection in the Solar Corona ISSS-10, Banff, July 25, 2011

Inherent plasma length scalesInherent plasma length scalesIf e & i are considered as fluids->generalized Ohm`s law:If e & i are considered as fluids->generalized Ohm`s law:

< spatial > <

c/pic/pe i<- spatial -><- scales ->

dissipation

<-

off-diag dissipationdue to high-frequency

electron inertia

electron- iondecoupling

off-diagonal elements y

micro-turbulence

decoupling,„Hall“ term“

of the pressure ttensor


Physical scales in the coronaPhysical scales in the coronaCurrentsheetsCurrentsheets

Most of the plasma ofth l t h iMost of the plasma ofth l t h ithe solar atmosphere isideal (Rm~108 )the solar atmosphere isideal (Rm~108 )

cmcmcmcm


Microscale dissipation physicsMicroscale dissipation physicsEnsemble averaging:Ensemble averaging:

-> Modified Vlasov equation, after velocity averaging> momentum exchange in the parallel direction

-> Modified Vlasov equation, after velocity averaging> momentum exchange in the parallel direction-> momentum exchange in the parallel direction-> momentum exchange in the parallel direction

-> correlation of e/m fluctuations and plasma density /current fluctuations-> correlation of e/m fluctuations and plasma density /current fluctuations

-> Correlations due to wave-particle i a can rarely be taken from-> Correlations due to wave-particle i a can rarely be taken from-> Correlations due to wave-particle i.a. can rarely be taken fromtheory (e.g. quasilinear) -> kinetic simulations are needed!

-> Correlations due to wave-particle i.a. can rarely be taken fromtheory (e.g. quasilinear) -> kinetic simulations are needed!


Strong β : 1D plasma instabilitieselectrostatic double layersStrong β : 1D plasma instabilitieselectrostatic double layerselectrostatic double layerselectrostatic double layers

Inset: electrostatic potential around the double layer. The ion holesmerge into the double layer while the electron motion becomesmerge into the double layer while the electron motion becomeshighly turbulent behind the layer [from Büchner & Elkina, 2006].J. Büchner et al. Simulation of Reconnection in the Solar Corona ISSS-10, Banff, July 25, 2011

-> effective „collision rates“-> effective „collision rates“


Moderate β: transition to 2D /LH Moderate β: transition to 2D /LH

β = 0 01 β = 0 1β = 0.01 β = 0.1 Linearily unstable modes γ > 0 (colors) in kpar vs. k

Only for very small β the most unstable waves are B-field aligned, y y β g ,but in the corona often β ~ 0.1 - 1


2D Vlasov & 1D fluid simulation2D Vlasov & 1D fluid simulation

• Vlasov solver: Unsplit finite volume conservative central scheme [Elkina and Büchner, 2007; Büchner et al, 2008]

• Velocity- and real space grid (Debye length resolution):

• Vlasov solver: Unsplit finite volume conservative central scheme [Elkina and Büchner, 2007; Büchner et al, 2008]

• Velocity- and real space grid (Debye length resolution):• Velocity- and real space grid (Debye length resolution): . 128 x 128 x 128 x 128 x 128

• Mass ratios Mi/me = 25, 100, 1800

• Velocity- and real space grid (Debye length resolution): . 128 x 128 x 128 x 128 x 128

• Mass ratios Mi/me = 25, 100, 1800• Performance tested, e.g., on a 62.3 TFlop/s and 17 TBytes

shared memory Altix 4700 (9728 Montecito dual-core CPUs)• Now to be extended to 3D: PIC codes on 5 Pflops and

• Performance tested, e.g., on a 62.3 TFlop/s and 17 TBytesshared memory Altix 4700 (9728 Montecito dual-core CPUs)

• Now to be extended to 3D: PIC codes on 5 Pflops and• Now to be extended to 3D: PIC codes on 5 Pflops and100.000 processor computers (IBM)

• Now to be extended to 3D: PIC codes on 5 Pflops and100.000 processor computers (IBM)


High beta-> LH waves take overHigh beta-> LH waves take over2D time-evolution of the electric wave-fieldelectric wave-field Ex(x,y): First ion-acoustic field-aligned modes are excited. After t _pe ~ 300 oblique LH modes takeoblique LH modes take over [Büchner et al. 2008]. But needed:3D PIC d ( fi fPIC codes (see fig for older results)-> but with many particles 1012y psince high res. Vlasovcodes are too expensive [see posterexpensive [see posterK.W.Lee]


Micro-turbulent dissipationMicro-turbulent dissipation„Effective resistivity“ - for RMHD parametrized

by an effective collision frequency“:

In the (lower) chromosphere:by the binary particle collision rate

by an effective „collision frequency :

... by the binary particle collision rate [Spitzer-Härm–Braginski Theory 1958-63]

I th l t i ti i dIn the solar transistion region and corona:… by an effective rate due to plasma turbulence as obtained byVlasov code simulations for coronal conditions (Te~Ti et c ):Vlasov code simulations for coronal conditions (Te Ti et c.):[Büchner & Elkina 2006/2007]– for higher beta plasma -> 1D: IA double layersg p y– for lower beta plasma –> 2D: LH turbulenceNote: the threshold is a large „current carrierd ift l it “ j/ > t > thi h t !

LHLH

drift velocity“ j/ne > v_te -> thin sheets!


2.) 2.) InertialInertial rangerange investigationsinvestigations: : 2D AMR2D AMR--MHDMHD simulationsimulation2D AMR2D AMR MHD MHD simulationsimulation

2.5 D high-resolution adaptice-mesh refinement MHD, tearing mode instability lets islands grow (see [Bárta, Büchner et al. y g ( [

ApJ, 2011, paper 1]J. Büchner et al. Simulation of Reconnection in the Solar Corona ISSS-10, Banff, July 25, 2011

SecondarySecondary currentcurrent sheetssheets andandccascadascadinging reconnectionreconnectiongg

Coalescence also contributes to the direct cascade !(High-resolution MHD AMR [Bárta, Büchner, Karlicky and(High resolution MHD AMR [Bárta, Büchner, Karlicky and

Kotrc, ApJ, 2011, paper 1]J. Büchner et al. Simulation of Reconnection in the Solar Corona ISSS-10, Banff, July 25, 2011

Cascading Cascading reconnectionreconnection ––schematicsschematics

C di ( f t l“) ti d t b tCascading („fractal“) reconnection due to subsequent tearing-mode and coalescence instabilities createsstructures at smaller and smaller scales in a self-similarmanner -> energy is transfered to smaller scales


EnergyEnergy cascadecascade toto smallsmall scalesscales


3.) Large scales: RMHD3.) Large scales: RMHD

(the index(the index(the index„0“ indicateschromosph. neutrals

(the index„0“ indicateschromosph. neutralsneutralscoupled tothe plasma)

neutralscoupled tothe plasma)

+ closing energy equation+ closing energy equation


Energy equationEnergy equation

))

For a conservative energyequation in the ideal MHD limitq


LINMOD3D - code• Non-diffusive discretization scheme:

• Leapfrog, 2nd order accuracyF 2 d d d i ti ( i th i d ti )• For 2nd order derivatives (e.g. in the induction eq.):

• Dufort-Frankel method• Initial time step (required by the staggered grid)• Initial time step (required by the staggered grid)

• Lax-Wendroff method• Optimized Fortran77 OpenMP parallelizationOptimized Fortran77 OpenMP parallelization• SGI-ALTIX: Numatools bind threads to processors• 3D grid, non-equidistant in z (radial direction)g ( )• e.g.

• x*y*z = 46.5 * 46.5 * 31 Mm3

107 id i t (260*260*170)• 107 grid points (260*260*170)• Highest resolution along z => 150km


Initial force-balancedplasma-pressure equilibriumInitial force-balancedplasma-pressure equilibriumplasma pressure equilibriumplasma pressure equilibrium

-Initial height-stratified equilibriumstratified equilibrium- added B-field, extrapolated fromextrapolated fromobserved LOS - Energy input:- Energy input: Plasma motion in thephotospherephotosphere- Rescaling of currentdensities to the

Plasma density [height] temperature

densities to theplasma scales, not resolved by MHDy [ g ] p

and pressure in the solar gravitationresolved by MHD(„sub-grid“)


+extrapolated B + plasma motion+extrapolated B + plasma motion

The solar magneticis complexThe solar magneticis complexis complex. It evolves due tothe photospheric

is complex. It evolves due tothe photosphericthe photosphericplasma motionaway from thel t

the photosphericplasma motionaway from thel tlowest energystate. This causes

lowest energystate. This causesThis causescurrents includingnon-force-free

This causescurrents includingnon-force-freeones - and, finally, reconnection.ones - and, finally, reconnection.


Localization of the dissipationb t i t bilitLocalization of the dissipationb t i t bilitby current instabilityby current instability

Current density Current carrier velocity Vccv = j / (e n)Current density Current carrier velocity Vccv = j / (e n)Vccv= j / (e n), the current carrier velocity, is enhanced mainly near theVccv j / (e n), the current carrier velocity, is enhanced mainly near thetransition region, where the plasma density drops (Shown is Vccv > Vcrit)


Resulting 3D reconnectionResulting 3D reconnection

Finite-B 3D reconnection due to l i h h QS

3D reconnection is characterized by E (E fi ld ll l B)plasma motion through a QSL strong Epar (E-fields parallel to B)


Heating case X-ray Bright PointHeating case X-ray Bright Point

Japanese HinodeJapanese Hinodes/c observation:Four X-ray imagesy gobtained by theXRT telescopebetween 23:00 UTand 24:00 UTand 24:00 UTon December12, 2006,


Energy input by various types of h t h i l ti

Energy input by various types of h t h i l tiphotospheric plasma motionphotospheric plasma motion

•23:27 –23:32UT

•23:22 –23:27UT

•23:17 –23:22UT

•23:12 –23:17UT

•23:07 –23:12UT

•23:02 –23:07UT •23:32UT •23:27UT •23:22UT •23:17UT •23:12UT•23:07UT


Heating and bulging out ofth t iti iHeating and bulging out ofth t iti ithe transition regionthe transition region

The figure showsThe figure showsThe figure showsthe resulting abovethe Bright Point

i

The figure showsthe resulting abovethe Bright Point

iregion newtransition region –with an asimuthal

region newtransition region –with an asimuthalwith an asimuthalstructure on top ofthe usually

d di l

with an asimuthalstructure on top ofthe usually

d di lassumed radial inhomogeneityonly!

assumed radial inhomogeneityonly!only!For details: seePoster of Eric

only!For details: seePoster of Eric


Adamson et al.Adamson et al.

The 3D structure of the corona

Confirmed by simulation: scheme of the 3D solar atmosphere - photosphere -Confirmed by simulation: scheme of the 3D solar atmosphere photospherechromosphere- transition region as envisioned by [Schrijver et al., 2001]J. Büchner et al. Simulation of Reconnection in the Solar Corona ISSS-10, Banff, July 25, 2011

To be confirmed by data …To be confirmed by data …

Now: SDO data, but2017, hopefullya closer looka closer lookinto the solar polar regions b SOLARby SOLAR ORBITER

SummarySummaryKi ti di l id l MHD d l l RHMDKi ti di l id l MHD d l l RHMDKinetic, medium scale non-ideal MHD and large scale RHMD

simulations are all together needed to advance the understanding of the multi-scale solar reconnection

Kinetic, medium scale non-ideal MHD and large scale RHMD simulations are all together needed to advance the understanding of the multi-scale solar reconnectionunderstanding of the multi scale solar reconnection

1.) For the time beeing small scale dissipative processes canbe described only for small systems, the next step are

understanding of the multi scale solar reconnection1.) For the time beeing small scale dissipative processes can

be described only for small systems, the next step arebe desc bed o y o s a syste s, t e e t step a e– 3D PIC-code simulations over 3 decades using 1012

macroparticles on 104x104x103 grids at 5-10 Petaflops

be desc bed o y o s a syste s, t e e t step a e– 3D PIC-code simulations over 3 decades using 1012

macroparticles on 104x104x103 grids at 5-10 Petaflopsp g p2.) For their inter-scale coupling to large scales:

– large fluid systems in which kinetically derived

p g p2.) For their inter-scale coupling to large scales:

– large fluid systems in which kinetically derivedg y ytransport properties quantify the dissipation

3.) AMR-MHD simulations for the intermediate scales

g y ytransport properties quantify the dissipation

3.) AMR-MHD simulations for the intermediate scales– have to be extended to 3D over a range of up to 106 to

get the limits of the self-similar behaviour right, e.g. of– have to be extended to 3D over a range of up to 106 to

get the limits of the self-similar behaviour right, e.g. ofcascading reconnection towards the dissipation scale. cascading reconnection towards the dissipation scale.


reconnection in the solar corona: numerical simulationisss10/talks/buechner_isss10.pdf · why...

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