Laboratory Study of Plasma Space/Astrophysics:
Magnetic Reconnection and Magneto-Rotational Instability

Hantao Ji
Princeton Plasma Physics Laboratory, Princeton UniversityCollaborators:

Troy Carter
Jeremy Goodman (Princeton U.)
Scott Hsu
Akira Kageyama (NIFS)
Russell Kulsrud
Ethan Shoshan (Rutgers U.)
Fedor Trinchouk
Masaaki Yamada

ITC-12 & APFA’01
December 11-14, 2001 at Toki, Japan

Outline• A Growing Field: Plasma Astrophysics• Two Examples:– Magnetic reconnection• Magnetic Reconnection Experiment (MRX)– Magnetorotational instability (MRI)• Rotating Gallium Disk (RGD) Experiment• Relation to Fusion Science and Technology• Summary

A Growing Field: Plasma Space/Astrophysics
Space/Astrophysics

Plasma Physics••

Advanceddiagnostics
Powerful computersimulations••

TheorySimulation

Sophisticatedobservatories
Recognition ofimportance ofmagnetic field

ExperimentSignificant progress inunderstanding
dynamics of (hightemperature) plasmas

PlasmaSpace/Astrophysics

Strong demands inunderstanding plasma
dynamics inastrophysical systems

Many Elementary Processes Can Be Studiedin Laboratory• Magnetic field generation(dynamo)• Effects of magnetic field– Mixing process– Angular momentum
transport in accretion disks– Coronal activities onstellar/disk/galactic surfaces– Jet formation and particle
acceleration• Interactions between magnetic
field and plasma (magneticreconnection)

Evolution of Solar Flare(minutes to hours)
By TRACE satellitePhysics Issues for Understanding Fast
Magnetic Reconnection• Sweet-Parker versus Petschek models• Collisional versus collisionless reconnection– Classical collisions and nonclassical collisions (fluctuations)– Dissipation mechanism of magnetic energy• Local versus global– Global constraints (conservation of mass, flux…) provides
boundary conditions for local physics– Local physics decides global magnetic topology and relaxation
rate• Steady state versus transient reconnection• 2D versus 3D reconnection– 2D (w/o 3rd component) and 2.5 D (w/ 3rd component)– 3D dynamics in 2D symmetry– Reconnection through 3D null-point

Sweet-Parker Model vs. Petschek Model
Petschek Model

Sweet-Parker Model•••

2D & steady state
Imcompressible
Classical resistivity

VR= 1SVA•

In addition:– A much smaller diffusion region (L’<<L)– Shock structureS: Lundquest #diff /A

Prediction: a few months but can beshorter with anomalous resistivity

VR1≈
VA ln(S)Prediction: <1 hour but inconsistentwith uniform resistivity

Magnetic Reconnection Experiment

Experimental Setup in MRX

Realization of 2D Current Sheet and SteadyReconnection
Yamada et al. PRL (1997)

pull reconnection, no guide field• Formation ofstable 2D current
sheet (~20-30
τAlfven)• Quasi-steady state
reconnection
realized.

Parameters: B<2kG, Te~Ti=5-20eV, ne=(0.1-2)×1020/m3→S<1000

Diffusion Regions Qualitatively Consistentwith Sweet-Parker ModelAn example: Sweet-Parker like diffusion region

Measured Magnetic Profiles Agree Wellwith a Generalized Harris Solution
Yamada et al. PoP (2000)• Harris solution (generalized for the Te
predicts tanh form of B!

Ti case)Sheet Thickness Also Agrees Well WithHarris Model• Consistent withHarris solution.
• scales with c/ pi– Constant normalized
drift velocity– Not determined bySweet-Parkerthickness (L/ S)– Consistent withsimulations
Harris =c2Vspi Vdrift

Measurements Agree Only with aGeneralized Sweet-Parker ModelJi et al. PRL (1998); PoP (1999)

modelmodel

A generalized model:
Comparisons with classical
Sweet-Parker model
enhanced ηcompressible

slowedoutflow

Resistivity Determination andDependence on Collisionality
Ji et al. PRL (1998)

E + VR × BZ = j*E≡j

Significant enhancement in
low collisionality plasmas

Measurements of Perpendicular Resistivity
Extended Well into Collisional Regime
Trinchouk et al. PRL (2001)( mfp << )First experimental demonstration ofSpitzer perpendicular resistivity

How is the Resistivity Enhanced in MRX?
•Turbulent resistivity due to current driven micro-instabilities (i.e.,lower hybrid drift wave)– Wave-particle interactions to dissipate current/energy– Intensive works since ‘70– Not consistent with fluctuation measurement (Carter et al. 2001)•Facilitation by non-dissipative Hall terms– Formation of thin dissipative electron layer– Demonstrated in simulations and theories– Have not been detected (electric field, fine structures…)•“Speiser effect” or single-particle orbit– Loss of particle, current and energy– Not self-consistent and not likely•

Electron neutral collisions

Lower-Hybrid Drift Fluctuations
Measured in Current Sheet Region
Carter et al. PRL (2001)••

Both electrostatic andelectromagneticfluctuations detected
Frequency scales withlower-hybrid freq.

Measurements Consistent with Theory But
Inconsistent with Resistivity Enhancement

Radial profiles consistent
with linear theory

Time dependence inconsistent
with resistivity enhancement

Fast Reconnection Facilitated by Hall Effects
Drake et al. (1998)

Ion Current(ion skin depth,
similar to S-Pmodel)
Electron Current(similar toPetschek Model)

Generalized Ohm’s law:

J × B − ∇p me dVe
E+V×B = J++ 2
ene dtA combination of bothmodels throughelectric field!
Hall terms electron inertia

Resistivity Enhancement Depends on Collisionality•=2Experiments:*=1 0.5=⊥•= 1+Define:me ei=⊥e2 ne*⊥•*= 1+me= 2eei +ne

*

*
ei

Effective collision frequency:*•mfp

Vth,e=Vth,e≈3c / pi

Predicts ~9 hour flare time.

(*4=4×10)⊥Accretion Disks••

An accretion disk consists of gas, dust and plasmas
rotating around and slowly accreting onto a central
point-like object.
Many important astrophysical processes happen inaccretion disks:– Formation of stars and planets in proto-star systems– Mass transfer and energetic activity in binary stars– Release of energy (as luminous as 1015 of Sun) inquasars and AGNs

HH30
By HST

Magnetorotational Instability and AngularMomentum Transport in Accretion Disks•

A long-standing question is why the accretion is fast or angularmomentum outward transport is fast.
– Classical viscosity provides negligible transport– Hydrodynamically steady state disks (Keplerian disks) are stable satisfying
Rayleigh’s criterion d(R2 )/dR>0 since
1/R3/2 and R2
R1/2•

However, disks can be unstable in MHD: Magnetorotational Instability– Originally discovered by Velikhov (1959) and Chandrasekhar (1960)– Rediscovered by Balbus & Hawley (1991)•

MRI occurs when d /dR<0 with avertical B:– Radially displaced fluid elements arelinked by B.
– Fast part is slowed and slow part isaccelerated, angular momentum
transport.

•Stable if B is too strong or too resistiveA Rotating Gallium Disk Experiment toDemonstrate and Study MRI•

MRI exists so far only in theories and numerical simulations– Theories: Curry, Pudritz, & Sutherlan (1994), Blaes & Balbus (1994), Gammie(1996), Jin (1996), Sano & Miyama (1999)…
– Simulations: Brandenburg et al. (1995,1996), Matsmoto & Tajima (1995),Hawley et al. (1996,2000), Stone et al. (1996), Fleming & Stone (2000)…

•RGD experiment is to demonstrate
MRI for the first time:– In a short Couette flow geometry.
– Centrifugal force V2/R isbalanced by pressure force -dp/dR
from the outer wall, acting likegravity force in accretion disks.
– MRI can be destabilized withappropriate 1, 2 and Bz in atable-top size.

Bz<0.5TLocal and Global Analyses Predict MRI at
Moderate Speeds and Sizes
Ji et al., MNRAS (2001)

MRI(I): Unstable but can be stabilized by B
(II): Stable but can be destabilized by B: MRI(III): Always stableImportance of Boundary Conditions
Revealed by Global Analysis
Goodman and Ji, JFM (2001)••

Boundary layer forms at inner conducting wall
Ekman layers at top and bottom platesIncompressible Nonlinear MHD Simulations•

3-D code (periodic in axial direction)– Spectral method (Chebyshev-Fourier)–•Kageyama et al. (2001)

Time splitting scheme (Green function method for incompressibility)

2-D code (finite size in axial direction)– Ekman layer effects

2D linear run

3D nonlinear run

Concept Design of Rotating Gallium Disk
Drill press to drive
innner cylinder
Electromagnets

Disk vessel

motor to drive
turntable andouter cylinder

30 cm

Side view

3D electromagnetic analysis• 120kg of gallium and its alloy has been acquired.

Prototype Water Disk Experiments
Under Way• Establish hydrodynamic reference at fast rotations– Study effects of Ekman layers and its control– Examine effects of nonlinear instability• Seed particles to monitor stability and to measure flow

10cm
Potter’s wheel

Stability and Flow Measurements
Unstable flow

Couette solution

Stable flow

solution w/ end plates
but w/o Ekman layermeasurements• To modify end plates to optimize flow profiles

Laboratory Plasma Astrophysics Can
Contribute to Fusion Science and Technology• Reconnection experiments– Better understanding of reconnection help avoidanceof disruptive phenomena observed in fusion plasmas– Help develop innovative confinement concepts• A new way to formation of Field-Reversed Configuration(FRC) with large flux

Laboratory Plasma Astrophysics Can
Contribute to Fusion Science and Technology• Liquid metal experiments– Angular momentum transport due to MHD effects (Maxwellstress) relevant to flow dynamics in high- plasmas (e.g. RFP’s)– Related to new ideas utilizing flows (e.g. Centrifugal
Confinement, double-Beltrami flow, ITB physics, etc.)– Better understanding of (free-surface) liquid metal MHD helps
fusion concepts using liquid metal first walls
50403020100-101.0(a) 1˜ rB˜Br0(b) ∂∂ t

Vφ

0.50Den Hartog (1995)

slowdown time ~ 100µs at MST

-0.5
-1.0
-1.0

-0.5

00.5

1.0

Fiksel et al. (1999)

Liquid Metal Surface Wave ExperimentJi and Fox (2001)
surface waves in Ga without B
10 cm

data

surface waves in Ga with B

linear MHD
theoryTo study MHD surface waves relevant to astrophysical mixing andliquid metal wall application in fusion reactors

Summary• Plasma astrophysics is a growing field because of mutualinterests in plasma physics and astrophysics• Laboratory experiments, using plasmas or liquid metals,
represent a significant component of this field– Study basic physics mechanisms in controlled and systematic manners– Quantitative tests of theories and state-of-art numerical simulations• Two examples:– MRX has provided fundamental data on reconnection, impacting
theories and simulations of the observed disruptive phenomena– RGD experiment will test MRI for the first time and study angularmomentum transport• Better understanding of plasmas and liquid metals can promote
fusion research and can lead to better fusion concepts and technology