Ions Heating During Magnetic Reconnection in the Reversed Field - - PowerPoint PPT Presentation

BINP seminar , Novosibirsk, 24 December 2008

Ions Heating During Magnetic Reconnection in the Reversed Field Pinch

Gennady Fiksel MST Group University of Wisconsin Madison, USA Center for Self-Organization in Laboratory and Space Plasmas

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In many lab and astro- plasmas ions are anomalously hot

• Hot ions in Solar plasma - much hotter than electrons
• In RFP ions are much hotter than expected from e/i

collisional heating

• In MST RFP, the ion heating is especially prominent

during magnetic reconnection and bursts of magnetic fluctuations

• We are trying to understand this connection

2

Outline

• Spontaneous magnetic reconnections in MST
• Ion heating - strong and robust; mechanism still not

understood

• Mass scaling of ion heating
• Well confined plasma with hot ions
• Conclusions

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Madison Symmetric Torus Reversed Field Pinch

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Neutral beam atoms scatter elastically from plasma ions Measure energy spectrum of scattered atoms arriving from one location along beam Spectrum shift and broadening => ion flow and temperature Measures bulk ions High intensity beam provides high time resolution Δr ~ 15 cm Δt ~ 30 μs

MST vessel Rutherford scattering (RS) - fast localized measurements of bulk ion dynamics

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Neutral beam atoms undergo CX with impurity ions in plasma Radiation from impurity ions localized to intersection of beam and viewing chord Doppler shift and broadening => ion flow and temperature Custom-built spectrometer provides high spectral and temporal resolution

Δr ~ 1 cm Δt ~ 10-100 µs

CHarge Exchange Recombination Spectroscopy (CHERS) - fast localized measurements of impurity ion dynamics

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Insertable Doppler spectroscopy probe - edge impurity ion dynamics

• Samples radiation from a small plasma volume
• Doppler shift of a radiation line (e.g. HeII) gives local measurement of ion

flow

• Doppler width gives temperature

Ti from Doppler width Vi from Doppler shift

Probe

Spectrometer

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Resistive tearing modes in RFP

• Resistive tearing modes are unstable - current driven
• Multiple resonant surfaces exist across the plasma

1,6 1,7 1,8 0,n

• 0.1

0.0 0.1 0.2 0.3 q 0.0 0.2 0.4 0.6 0.8 1.0 r/a

q = rBt RBp

Core modes

m,n

Edge modes

poloidal number toroidal number

q = m / n

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Magnetic activity has a relaxation character

∇J

 j,  b,  v

Current relaxation

Instability Current transport Free energy reduced Current peaking Current gradient - free energy source

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Bursts of magnetic fluctuation - magnetic reconnection

1,6 1,7 1,8 0,n

• 0.1

0.0 0.1 0.2 0.3 q 0.0 0.2 0.4 0.6 0.8 1.0 r/a

q = rBt RBp

q = m / n

Global reconnection - both core- and edge modes are excited

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Global reconnection results in a large change of stored magnetic energy

• Reconnection modifies the equilibrium magnetic field

profile

• Stored magnetic energy drops
• 1.0
• 0.5

0.0 0.5 1.0 160 165 170 175 180 Time to reconnection (ms) Stored magnetic energy (kJ)

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Strong and global ion heating is observed

• Bulk ion (D+) temperature measured with Rutherford

scattering.

• Ti quickly rises at all plasma radii
• Ti rise time ~ 100μs, τcoll ~ 1ms
• 1.0
• 0.5

0.0 0.5 1.0 Time reconnection (ms) 100 200 300 400 500 r/a=0.3 r/a=0.5 r/a=0.7

TD+ (eV)

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Impurities are heated stronger than bulk ions

• Similar to Solar plasma
• Possibly a clue to the heating mechanism, which is still

unknown

• 1.0
• 0.5

0.0 0.5 1.0 Time reconnection (ms) 100 200 300 400 500 r/a=0.3 r/a=0.5 r/a=0.7

TD+ (eV)

D+ C6+

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Recent measurements - heavier bulk ions are heated stronger as well

He D H

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Calculate thermal and magnetic energy Ti (eV) Emag (kJ)

T0

Ethermal = 3 2 kTi ne Zi dV

∫

Emag = B2 / 2µ0dV

∫

Since the density and temperature of the bulk ions is known we can calculate the total thermal energy and compare it with the released magnetic energy

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Heating efficiency ≈ (Mi)0.5 dependance on ion mass Weak dependence on Ip and ne

0.12 Mi

( )

0.51

H+ D+ He2+

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 1 2 3 4 5 Ion Heating Efficiency Ion Mass

α = ΔEthermal ΔEmag

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Include losses

Ti = T0 + T

1

3 2 ni dT

1

dt = α  Emag − 3 2 ni T

1

τ

Ti (eV) Emag (kJ)

T0 e−t/τ

Ethermal = 3 2 kTi ne Zi dV

∫

α - fraction of magnetic energy transferred into ion heating

Emag = B2 / 2µ0dV

∫

α = ΔEthermal + 3 2 ni τ T

1dt

∫

ΔEmag

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0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 1 2 3 4 5 Ion Heating Efficiency with Losses Ion Mass

0.15 Mi

( )

0.54

H+ D+ He2+

With losses

α = ΔEthermal + 3 2 ni τ T

1dt

∫

ΔEmag

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Global reconnection needed for ion heating - just a large amplitude mode is not enough

• Sometimes, very large core-resonant

mode m=1,n=6 is excited

• Other modes, in particular the edge-

resonant m=0,n=6 mode, are small.

• Similar to the RFX-machine QSH

(quasi-single helicity) mode.

• No change in the equilibrium

magnetic field profile. No change in the equilibrium magnetic energy

• No ion heating observed

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New regime of hot ion plasma - synergetic use of reconnection heating and improved confinement

• Reconnections “preheat” ions
• Following by auxiliary inductive current profile control reduces the tearing
• activity. Reduction of magnetic fluctuations and confinement improved, up to

ten-fold

• Hot ions (and electron) plasma with good confinement

B (gauss) ~ Ti (keV)

time (ms) 10 15 20 25 1.0 2.0 3.0 5 10 15 20 reconnection events improved confinement →

←

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Simultaneous hot electrons and ions

0.4 0.8 1.2 1.6 2.0

Te Ti

standard RFP

0.2 0.4 0.6 0.8 1 r/a

Te, Ti (keV)

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Simultaneous hot electrons and ions

0.4 0.8 1.2 1.6 2.0

Te Ti

standard RFP

0.2 0.4 0.6 0.8 1 r/a

Te, Ti (keV)

Te Ti

Improved confinement

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Summary

• Strong ion heating occur during reconnection events
• Magnetic energy release is a likely source for ion heating. However,

the mechanism is still unknown.

• Mass-scaling can be a constraint for choosing the heating

mechanism.

• Combination of reconnection heating and confinement improvement

results in hot ion, well confined plasma

• Future measurements will evaluate the heating anisotropy - another

constraint.

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Soon - add toroidal view to evaluate heating anisotropy Existing CHERS DNB

T⊥ T||

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The End

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′ vi = vi + 2v0 ′ vi

2 = vi 2 + 4viv0 + 4v0 2

′ vi

2 = vi 2 + 4viv0 + 4v0 2

Fermi-like acceleration - possible mechanism?

• Bouncing ball and a moving wall model

v0 ′ vi vi

Energy increases in the head-on collision and decreases in tail-on

v0 = v0 cos(ωt)

Suppose the wall oscillates

Δε = miv0

2

Rate of thermal energy change:

• proportional to (mi)1/2
• does not depend on Zi

ji Δε = n Ti mi miv0

2 ∝

mi

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