Electric fields in the Corona: Linking Kinetic and

Magnetohydrodynamic Scales

Electric fields in the Corona: Linking Kinetic and

Magnetohydrodynamic ScalesJörg Büchner,

Max-Planck-Institut für Sonnensystemforschung Katlenburg-Lindau, Germany

in collaboration withM. Barta (Ondrejov Observatory, Czech Academy Sciences),

A.Otto (University Fairbanks, Alaska), J. Santos (University Brazilia),

F. Jenko (IPP Garching) and M. Püschel (University Madison)

Contribution to the RAS Specialist Discussion Meeting "Kinetic Processes and Radiophysics of the Sun“ London, October 12, 2012

OutlookOutlook• Radio and X-ray observations -> more and more details

about the electron acceleration in the corona• While the corona accumulates energy at large scales for

electron acceleration small, plasma scales are relevant, e.g.– for resonant wave-particle interaction, – for stochastic acceleration in magnetic islands, shocks– for B-field dissipation and reconnection at current sheets

• Here: concentration on the latter • Prediction by magnetic topology (Nulls, separatrices, QSL)• Perpendicular acceleration near B-Nulls (ideal MHD E-fields)• Parallel in current channels of crossing separatrices in 3D• Problem of building up parallel E-fields in the corona• Consequences of turbulence and cascading reconnection

• Radio and X-ray observations -> more and more details about the electron acceleration in the corona

• While the corona accumulates energy at large scales for electron acceleration small, plasma scales are relevant, e.g.– for resonant wave-particle interaction, – for stochastic acceleration in magnetic islands, shocks– for B-field dissipation and reconnection at current sheets

• Here: concentration on the latter • Prediction by magnetic topology (Nulls, separatrices, QSL)• Perpendicular acceleration near B-Nulls (ideal MHD E-fields)• Parallel in current channels of crossing separatrices in 3D• Problem of building up parallel E-fields in the corona• Consequences of turbulence and cascading reconnection

Topology Predictions by Nulls, Separatrices and QSL (finite B case)Nulls and separatrix-footprintsobtained for a monopoles([D. Longcope‘s] MPole) ->Green dots: Main polaritiesRed dots: Main magnetic nullsas they survive in a smooth B-field extrapolation (see below)

Topology Predictions by Nulls, Separatrices and QSL (finite B case)Nulls and separatrix-footprintsobtained for a monopoles([D. Longcope‘s] MPole) ->Green dots: Main polaritiesRed dots: Main magnetic nullsas they survive in a smooth B-field extrapolation (see below)

Regions of small or vanishing B fields (Nulls) predict thelocation of currentconcentrations

3D Coronal Null case3D Coronal Null case

A 3D coronal null resulting from a quadrupolar photospheric B-fieldvia its fan and spine field lines it isconnected to the B-maxima

A 3D coronal null resulting from a quadrupolar photospheric B-fieldvia its fan and spine field lines it isconnected to the B-maxima

Eigenvalues of the Jacobian of B around the null: {+2; -1.7; -0.3}

{Spine, Fan; Fan}.

According to [Priest & Pontin 2009]: whether torsional Spine / Fan or Shear flow reconnection -> Is decided by flows!

Büchner et al. Fields and flows around 3D reconnection DPG Bonn 18.3.10

Null-point reconnection simulationNull-point reconnection simulation

3D magnetic null-related reconnection dynamics [from Büchner 2008]

Eperp of ideal MHD can accelerate only de-magnetized particlesas near Nulls with their strong Böfield gradients and curvatures.Analyitcal models (see later talk by the Manchester group):

Eperp acceleration near a Null

Electron acceleration by Eperp in a simulated (ideal MHD) magnetic Null

Electron acceleration in the Eperp of ideal MHD is not at all efficient from [Guo, Büchner et al., 2010]

For Epar a non-ideal, resistiveMHD description is neededFor Epar a non-ideal, resistiveMHD description is needed

+ closing energy equation+ closing energy equation

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

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

Possible energy equationPossible energy equation

Cross -fan clockwise motionCross -fan clockwise motion

Shown are thevelocity vectorsof a clockwiseplasma motionnear thefootpoints ofthe two fansout of themagnetic null -> velocityshear in thecenter.

Shown are thevelocity vectorsof a clockwiseplasma motionnear thefootpoints ofthe two fansout of themagnetic null -> velocityshear in thecenter.

[Santos,Büchner,Otto,11] (from the title page ofAstronomy& Astrophys., January 2011)

If the the plasma atthe footpoints of thefan field lines ismoved clockwise -> strong central shear-> Formation of a current channelbelow the Null

If the the plasma atthe footpoints of thefan field lines ismoved clockwise -> strong central shear-> Formation of a current channelbelow the Null

• Parallel electric fields can accelerate particles to high energies, up to run away, if strong enough.

• Test particle simulations, e.g. by [Litvinenko 1996, Bruhwiler & Zweibel 1992, Mori el al. 1998, Browning & Vekstein 2001, Zharkova & Gordovskyy 2004, Hamilton el al. 2005, Hannah & Fletcher 2006, Turkmani et al. 2006, Liu et al. 2007]

• But: – All these calculations used ad hoc (resistive) electric

fields, whose generation and strength in the corona, which are due to on microscopic plasma effects, are is not well-understood, yet.

• Parallel electric fields can accelerate particles to high energies, up to run away, if strong enough.

• Test particle simulations, e.g. by [Litvinenko 1996, Bruhwiler & Zweibel 1992, Mori el al. 1998, Browning & Vekstein 2001, Zharkova & Gordovskyy 2004, Hamilton el al. 2005, Hannah & Fletcher 2006, Turkmani et al. 2006, Liu et al. 2007]

• But: – All these calculations used ad hoc (resistive) electric

fields, whose generation and strength in the corona, which are due to on microscopic plasma effects, are is not well-understood, yet.

Epar test particle acceleration

Epar in the collisionless coronaEpar in the collisionless corona

If e & i are both considered -> generalized Ohm`s law:If e & i are both considered -> generalized Ohm`s law:

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

dissipationdue toplasmaturbulence

<-

electron inertia

electron- iondecoupling,„Hall“ term“

off-diagonal elements of the pressure tensor

Jpne

BJne

BvEdtJd

eipe

rrrrrrr

114

2

Ensemble averaging:

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

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

-> Correlations due to wave-particle i.a.; cannot be taken fromtheory (e.g. quasilinear) -> kinetic simulations are needed!

Ensemble averaging:

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

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

-> Correlations due to wave-particle i.a.; cannot be taken fromtheory (e.g. quasilinear) -> kinetic simulations are needed!

Self-consistent E-fields solar in the collisionless corona

Self-consistent E-fields solar in the collisionless corona

Epar in large-β plasmasEpar in large-β plasmas

O-type Null

Spiraling field lineout of a X-type Null

Separsurfac

Fan field lines outof a X-type Null

Spine fline ouX-type

Note: withoutinitial guide field, i.e. plasma beta ~ unity like nearmagnetic Nulls

3D Kinetic (micro-) turbulent reconnectioncoupled to due toLHD/kink-sausageturbulence

3D Kinetic (micro-) turbulent reconnectioncoupled to due toLHD/kink-sausageturbulence

For smaller β: transition LH -> IAFor smaller β: transition LH -> IA

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

For very small β: most unstable are B-field aligned compressional waves

electro staticpotential

fe(forwardcurrent)

fi [Büchner, Elkina, 2006; Munoz, Lee,

Büchner, 2012]

electro staticpotential

fe(forwardcurrent)

fi [Büchner, Elkina, 2006; Munoz, Lee,

Büchner, 2012]

Nonlinear evolution - small β case

Very small plasma-β limit: very thin and turbulent sheets

[From Jenko, Büchner et al., 2012]

Large scaleobservedconvection, extrapolatedmagnetic fields-> Eperp

The overall picture so far:

What are theacceleratingfields?

In between:inertial range- E_par = ???

At smallest scales: Selfconsistent Epardue to non-idealityby microturbulence

Energ

y den

sity

Energy Input Scale

Inertial range

Dissipation range

Wave number kD

Epar in chromosphere & coronaEpar in chromosphere & corona

In the (lower) chromosphere:by binary particle collision rate [Spitzer-Härm–Braginski Theory 1958-63]

Epar via current density and resistivityparametrized by an effective „collisionfrequency“, which is dominated:

In the TR / corona:by plasma turbulence as obtained by Vlasov code simulationsfor coronal conditions, Te~Ti etc:[Büchner & Elkina 2006/2007]– for higher beta plasma -> 1D: IA double layers– for lower beta plasma –> 2D: LH turbulenceBut: as threshold: a large current carrier driftvelocity j/ne > v_te (-> thin sheets!)

LHLH

Epar in RMHD by resistivityEpar in RMHD by resistivityBackground eta0 Spitzer- level> Rm ~ 10^9 in the coronaWhile current-carrier-velocity dependent anomalous resitivityin the corona: etaeff =10^6 times the Spitzer resistivity !

etaeff is due to high frequency plasma turbulence , obtained byVlasov code simulations for coronal conditions (Te~Ti et c.) in [Büchner & Elkina 2005-2008]:- for low beta conditions -> 1D: IA double layers- for higher beta plasma –> 2D: LH turbulence

Note: large velocities j/ne -> Vte needed -> thin sheets c/ pi, not resolved by MHD – „Filling factor“ and smoothed current sheets

LHLH

Multiple current sheet tearing

Multiple tail current sheet tearing obtained by 2.5 D adaptive grid MHD simulation [Bárta, Büchner et al., 2011, ApJ paper 1]

After islands are formed -> coalescence continues the cascade -> smaller scale islands [Bárta, Büchner et al. 2011, ApJ paper 1])

•

… followed by island coalescence

-> many small magnetic islands, where electrons are accelerated

Due to cascading reconnection (tearing+coalescence) -> wider acceleration regions rather than the original currentssheets, a large number of particles can become accelerated!

Observable: size spectrum

Simulated island size spectrum

In our simulation the cascade ends atthe smallest dissipation scale whichstill can be resolved.The spectral index of the island sizedistribution is about 2.14, is now comparedto observations [Bemporad et al. 2012]

Cascading reconnection: Acceleration in the 3D islands

… and after their coalescence

-> Particles are ejected out of the islands parallel to the magneticfield letting them precipitate down to the chromosphere

Flare-ribbon structure ofthe mappedacceleration

regions

Derived Observables

from [Bárta, Büchner et al., 2011, ApJ 2]

Flare-ribbons structures observed by the Ondrejov MCF Spectrograph, fom [Kotrč et al. 2009]

Comparison to radio observations

Flare-ribbon X-ray / accelerated electron structures as observedby RHESSI, from [Nishizuka et al., ApJ, 2009]

… and RHESSSI X-ray observations

SummarySummary

• Ideal MHD E-fields near Nulls do not provide efficient acceleration

• Instead: parallel, non-ideal MHD E-fields due to current concentrations, e.g. by 3D separatrixcrossings

• But: non-ideal E-par fields form at small scales, coronal energy is accumulated by large scale motion

• Solution: Cascading and turbulent reconnection• Signatures: e.g. ribbons already found in radio- and

X-ray observations

• Ideal MHD E-fields near Nulls do not provide efficient acceleration

• Instead: parallel, non-ideal MHD E-fields due to current concentrations, e.g. by 3D separatrixcrossings

• But: non-ideal E-par fields form at small scales, coronal energy is accumulated by large scale motion

• Solution: Cascading and turbulent reconnection• Signatures: e.g. ribbons already found in radio- and

X-ray observations