Magnetic Reconnection in Plasmas; a Celestial Phenomenon in the Laboratory

J Egedal, W Fox, N Katz,A Le, M Porkolab,

MIT, PSFC, Cambridge, MA

• The problem of magnetic reconnection

• Reconnection in the Versatile Toroidal Facility– Experimental setup

– Experimental observation

– Electron kinetic effects

• Wind satellite data from the deep magnetotail– Kinetic effects

• The new closed configuration in VTF

• Conclusions

Outline

The Versatile Toroidal Facility (VTF)

3.5 m

The Versatile Toroidal Facility (VTF)

The Versatile Toroidal Facility (VTF)

A new closed cusp by internal coil. Passing electrons &

spontaneous reconnection events.

Two different magnetic configurations

A open cusp magnetic field. Fast reconnection by trapped

electrons. Wind observation

Both configurations have Bguide and toroidal symmetry 2d

VTF open configuration plasmashave a trapping potential

Typical Parameters:ne ~ 2-3 1016 m-3

Te ~ 12 eV

Ti ~ 1 eV

Bt ~ 80 mT (800 G)

Bc ~ 0-10 mT

Open field lines intersect the vessel wall.

Electrons stream faster than ions, so plasma charges positive

Thermal electrons are electrostatically trapped

Reconnection drive

– Electric field induced by a central solenoid

– The solenoid is driven by an LC circuit

– Vloop ~ 100 V

Plasma response to driven reconnection

The electrostatic potential

Experimentalpotential,

+70 V

-70 V

2BE B

-v gB

Electron flow:

The electrostatic potential

Frozen in law isbroken where EB0

0 cusppolBE BE

Ideal Plasma:

BE

J Egedal et al., PRL 90, (2003)

The electrostatic potential

Frozen in law isbroken where EB0

0 cusppolBE BE

Ideal Plasma:

c

BE

eoc l

The size of the electron diffusion region is

δ

δ (c

m)

ρcusp

cgo BBl /

• Why is the experimental current density so small?

• Liouville/Vlasov’s equation: df/dt=0

• For a given (x0,v0), follow the orbit back in time to x1

• Particle orbits calculated using electrostatic

and magnetic fields consistent

with the experiment.

• Massively parallel code

evaluates f(x0,v0) = f(|v1|).

Kinetic modeling(1)

Computer Physics Communications , (2004)

0 – 12 kA/m2

• The current is calculated as

• Theory consistent with measurements

(B-probe resolution: 1.5cm)

Kinetic modeling(2)

3

|||| vv dfj

Theory

Experiment

• The problem of magnetic reconnection

• Reconnection in the Versatile Toroidal Facility– Experimental setup

– Experimental observation

– Kinetic effects

• Wind satellite data from the deep magnetotail– Kinetic effects

• The new closed configuration in VTF

• Conclusions

Outline

M. Øieroset et al. Nature 412, (2001)

M. Øieroset et al. PRL 89, (2002)

Wind satellite observations in distant magnetotail, 60RE

• Measurements within the ion diffusion region reveal: Strong anisotropy in fe.

M. Øieroset et al. Nature 412, (2001)

M. Øieroset et al. PRL 89, (2002)

Wind satellite observations in distant magnetotail, 60RE

• Measurements within the ion diffusion region reveal: Strong anisotropy in fe.

Log(f)

A trapped electron in the magnetotail

The magnetic moment:B

m

2

v 2

B

m

2

)v-v( 2||

2

• From Vlasov’s equation df/dt=0 f(x0,v0) = f(Eexit )

• Two types of orbits:

Drift kinetic modeling of Wind data

Passing: Trapped : =mv2/(2B)+… is constant

maxmin|| /1cos

v

vBBc

c

No cooling Cooling

• Applying f(x0,v0) = f(|v1|) to an X-line geometry consistent with the Wind measurements

• A potential, needed for trapping at low energies

• Ion outflow: 400 km/s, consistent with acceleration in

Drift kinetic modeling of Wind data

~ -300V~ -800V~ -1150V

Theory Wind

Phys. Rev. Lett. 94, (2005) 025006

• Applying f(x0,v0) = f(|v1|) to an X-line geometry consistent with the Wind measurements

• A potential, needed for trapping at low energies

• Ion outflow: 400 km/s, consistent with acceleration in

Drift kinetic modeling of Wind data

Theory Wind

Phys. Rev. Lett. 94, (2005) 025006

~ -1150V

f(x0,v0) = f(E0-q0), passing

= f(B), trapped

Cluster Obs.

• The problem of magnetic reconnection

• Reconnection in the Versatile Toroidal Facility– Experimental setup

– Experimental observation

– Kinetic effects

• Wind satellite data from the deep magnetotail– Kinetic effects

• The new closed configuration in VTF

• Conclusions

Outline

New closed magnetic configurations

A new reconnection drive scenario

Spontaneous reconnection

Phys. Rev. Lett. 98, (2007) 015003

Sweet-Parker is out, E ≠ *j !

Current channel expelled, J

Magnetic energy released

R

Bz

vA ~ 10 km/s

c/pi ~ 1m, s ~ 0.12m

4

-4

t [µs]d

/dt [

V]

What Triggers Reconnection? R

[m

]

t [µs]Mode at f=50 kHz

d/dt [V]R

Plasma outflows

Rough energy balance

• Magnetic energy released ~ 0.5 × 6 10-6 H × (500A)2 ~ 0.8 J

• Electron energization ~ 500 A × 80V × 2 10-5s ~ 0.8 J

• Ion flows: ~ 24 eV × 21018m-3 ×0.06m3 ~ 0.48 J

Strong energizations of the ions

Electrostatic (and magnetic) fluctuations observed during reconnection events

Loop voltage (V)

Fluctuation > 10 MHz (au)

Spectrogramf (MHz)

0 1t (ms)[Mar 22 shot 405,HPF 80kHz, scope B/W 150 MHz]

fLH ~ 10 MHz

fpi ~ 30 MHz

(off scale)

fpe ~ 10 GHz

fce ~ 1 GHz

800

0Plasma Current (A)

Conclusions– Fast, collisionless driven reconnection observed in the

open cusp configuration– Classical Coulomb collisions are not important– The width of the diffusion region scales with cusp

– Solving Vlasov’s equation (using the measured profiles of E and B) provides current profiles consistent with the VTF measurements; the current is limited by electron trapping.

– Wind observations consistent with fast reconnection mediated by trapped electrons

– New closed configuration in VTF provides exciting

new parameter regimes and boundaries for future study of collisionless magnetic reconnection & the trigger problem.

Thank you for your attention

Future studies with the new configuration• Fast, bursty reconnection with closed boundaries and in the

presence of guide magnetic field can be studied (for the first time)

• What controls the rate of reconnection?

• How is reconnection “triggered”

• Huge parameter regime available: Scans possible in Bcusp, Bguide, Te, Ne, Erec.

• Spans collisional to collisionless regimes: e = 0.1 – 103 m

• High plasma pressure (compared to magnetic field): ~ 1

• Warm and magnetized ions.

• 3D magnetic geometries are easily implemented

Upgrade of open Cusp

Existing configuration Fields of new in-vessel coils

Upgrade of open Cusp

New total field

Ionization region

Reconnection Experiments with a Guide Magnetic Field

J Egedal, W Fox, N Katz, A Le and M Porkolab

MIT, PSFC, Cambridge, MA