Ion pickup and acceration in magnetic reconnection exhausts

J. F. Drake

University of Maryland

• M. Swisdak University of Maryland• T. Phan UC Berkeley• E. Quatert UC Berkeley• R. Lin UC Berkeley• S. Lepri U Michican• T. Zurbuchen U Michican• P. Cassak University of Delaware• M.A. Shay University of Delaware

Ion acceleration during magnetic reconnection

• In solar flares energetic ions up to GeVs have been measured– In impulsive flares have enhancements of ions

over coronal abundances linked to Q/M • In the solar wind see energy proportional to mass• Heated ions in solar wind reconnection events

(Gosling et al, 2005; Phan et al 2006)• Ubiquitous v-5 energetic ion distribution in the quiet

solar wind (Fisk and Gloeckler 2006)

Heavy ion data from Ulysses

• The thermal spread of the various ion species is nearly mass independent (von Steiger and Zurbuchen 2006)– Energy proportional to mass

Wind observations of solar wind exhaust

• 300RE event (Phan et al., 2006)

Tp ~ 7eV)

T ~ 30eV)

TαΔTp

=mαmp

10-11

10-9

10-7

10-5

10-3

10-1

101

103

1 10 100

tail retail 2:40:15 PM 1/22/06

*FWtail*tail+SWSW distribution1FWFW<FW>meanFWnetFWbkgsum core+tail quietFWPI upFW -26day to TS LECPFW -20day to TS LECPFW -26day to TS LECPFW -20day to TS LECPFW(Vr broadened)Tail with cutoff

Phase Space Density (s

3 /km

6 )

W Ion Speed/Solar Wind Speed

f(w) = fow -5

(in solar wind frame)

H+

quiet timetails

Solar wind protons

<R> = 4.86 AU

SWICS

ULEIS

1 AU

4.23 AU

94 AU

Core pickup protons

• Proton spectra of the form f v-5 are often observed• What about the anisotropy of energetic ions?• Similarity to spectra from the Fermi mechanism is striking

Universal ion spectrum in the quiet solar wind

Gloeckler et al, 2006

Impulsive flare energetic ion abundance enhancement

• During impulsive flares see heavy ion abundances enhanced over coronal values

• Enhancement linked to Q/M

∝Q

M⎛⎝⎜

⎞⎠⎟

−3.26

Mason, 2007

Ion pickup in reconnection exhausts

• Ions moving from upstream cross a narrow boundary layer into the Alfvenic reconnection exhaust

• The ion can then act like a classic “pick-up” particle, where it gains an effective thermal velocity equal to the Alfvenic outflow cA

• The result is roughly energy proportional to mass (Fujimoto and Nakamura, 1994)

Ion acceleration during anti-parallel

reconnection

• PIC simulation with mi/me=25

• Focus on ion heating well downstream of the x-line

• Sharp increase of Ti in region of large Hall fields– The Hall fields drive the

outflow exhaust

Vx =cEyBz

B2

Test particle trajectories

• Ions cross a narrow boundary layer into the region of large Hall electric field Ey that drives the outflow

• Initial motion along Ey

rather than in E B direction (e.g., Wygant et al 2005)– acts likes a pickup ion

in the solar wind

– Gains a non-zero magnetic moment

Fields and frame transformation in the

outflow

• The boundary layer that bounds the outflow exhaust is not a switch-off slow shock– Never seen in PIC simulations

• Move to the local field-line frame to eliminate the electric fields (vx = -1.35cA)

moving framemoving frame

Particle motion in 1-D fields

• Similar to Buechner and Zeleny ‘86– Additional sharp

boundary from the Hall field Bz

• Particles see a sharp kink in B as enter exhaust– Generates finite

• Within the layer Speiser-like orbit

Ion temperature in reconnection outflows:anti-parallel case

• Speiser-like Fermi reflection

conservation violation at the outflow boundary

• Total temperature change

– Similar to Krauss-Varban and Welsch (2007)

• Note energy proportional to mass as is typically seen in energetic particles in the solar wind

TiP = micAx

2 Bx2

B2

Ti⊥ =1

2micAx

2 Bz2

B2

Ti =

1

3ΔTiP + 2ΔTi⊥( ) =

1

3micAx

2

Wind solar wind exhaust data

• Data from 22 solar wind reconnection exhaust encounters– All with small guide fields

• Proton temperature increase in exhaust is given by

mpv2(eV)

3Tp(eV)

3Tp ; 0.74mpv2

Heavy ions from SWICS

1 23

Lepri and Zurbuchen, 2008

• Heliospheric current sheet reconnection event (Gosling et al 2007)

Mass dependence of temperature increase

*Fe has low statistics at this time resolution

Ion acceleration with a guide field

• Structure of electric field changes dramatically from anti-parallel case– Large Ey drives the outflow (cEy/Bz=cAx)

• Large guide field can magnetize the protons conserved for protons

• Can’t eliminate E everywhere with a frame transformation

Bz0 = 5.0

Test particles in Hall MHD reconnection fields

• Protons and alpha particles remain adiabatic ( is conserved)– Only mass 6 and above behave like pickup particles because of large guide field

Ey

Bz0 = 5.0

Ion energy gain• Ion energy gain– Irreversible portion

• The ions that act like pickup particles -- those with high M/Q -- gain much more energy

• What is the threshold for acting like a pickup particle?

• For coronal parameters (n ~ 3 109/cm3, T ~ 3 106 oK) proton threshold is 60G

rvi =

rvi −

rvE×B

viy≈0.1cApx

ρsp

>Ωi ⇒mi

Zimp

>10cps

cApx

Ion temperature in reconnection outflows:guide field case

• Shift to moving frame in exhaust to eliminate electric fields there– Calculate dynamics in adiabatic and non-adiabatic limits

• Non-adiabatic ions same as no guide field

• Adiabatic ions

– Very small for a strong guide field

Ti =1

3micApx

2

Ti =1

3micApx

2 Bx2

B2

Production of energetic ions during flares

• Pickup in solar wind exhausts can seed ions to Alfvenic velocities.

• Ions must interact with many reconnection exhausts magnetic islands to reach GeV energies

A multi-island acceleration model

• Narrow current layers spawn multiple magnetic islands in guide field reconnection

– The generic case

• Secondary islands seen in observations

– FTEs at the magnetopause

– Magnetotail– Downflow blobs in the

corona

• In 3-D magnetic islands will be volume filling

• Explore particle acceleration in a multi-island environment

Multi-island acceleration

• Consider a reconnection region with multiple islands in 3-D with a stochastic magnetic field

• Electrons are accelerated through Fermi reflection as each island undergoes contraction(Kliem, 1994, Drake, et al., 2006)

• Thermal ions are too slow too slow to undergo many bounces– Ions accelerated through pickup seed the ions so they can be accelerated through Fermi

reflection. Evidence that pickup is important?

uin

CAx

CAx

Abundance enhancements in impulsive flares

• Ion pickup criterion can be rephrased as a threshold on magnetic island width wc.

– Higher M/Q ions have lower island width thresholds

• Rate of production of pickup ions

– Take powerlaw distribution of island widths: P(w) ~ w-

– Match the observations if ~ 6.26 reasonable

miZimp

>10csp

cAxp cAxp ; ′cAxpwc >10csp

Zimp

mi

⎛

⎝⎜⎞

⎠⎟

dNidt

: 0.1w>wc

∑ cAxLw : w2

w>wc

∑ : dwwc

∞

∫ w2P(w)

dNidt

: wc3− :

Zimp

mi

⎛

⎝⎜⎞

⎠⎟

3−

Fermi acceleration for super-Alfvenic particles

• Steady state kinetic equation for electrons or ions in 2-D reconnection geometry

• Energy gain linked to release of magnetic energy• Powerlaw distributions of energetic particles with spectral indices that

depend on the incoming plasma

r∇•

ruf −

r∇ • κ (v)

r∇f =

1

3A 1 −

8πW

3B2

⎛

⎝⎜⎞

⎠⎟

1/2dcAxdy

∂

∂vvf

–For the solar corona

v2f ~ E-1.5

f ~ v-5

• Universal spectrum for low • Consequence of firehose marginal stability due to anisotropy of accelerated particles

Implications for the solar wind observations

• Do these ideas about ion acceleration translate to the solar wind observations?– Is dissipation in solar wind turbulence dominated by local

reconnection processes?

– Bent field lines accelerate ions in reconnection. Do similar processes occur in Alfvenic turbulence?

• If so then marginal firehose condition should also play a role in Alfvenic turbulence

– Source of the v-5 velocity distributions?

Conclusions• Ions entering magnetic reconnection exhausts can act like

pickup particles– Produces Alfvenic thermal spread on with energy proportional to mass

-- confirmed with Wind and ACE observations– During reconnection with a guide field small Q/M ions much more

easily behave like pickup particles and are more easily accelerated than large Q/M ions

• High energy particle production during magnetic reconnection typically involves the interaction with many magnetic islands– Not a single x-line– Using the pickup threshold for heavy ions can explain impulsive flare

heavy ion abundance enhancements with a simple model

• Fermi acceleration within contracting magnetic islands can energize super-Alfvenic ions seeded by the pickup process– Produces f(v) ~ v-5 distributions consequence of firehose marginal

stability