Magnetic Reconnection and Turbulence in Stellar-Convective ...

Magnetic Reconnection and Turbulence in Stellar-Convective-Zone-Relevant

Laboratory Plasmas

Jack D. Hare

MAGPIE

MAGPIE: S. V. Lebedev, L. G. Suttle, S. N. Bland, T. Clayson, J. W. D. Halliday, S. Merlini, D. R. Russell, F. Suzuki-Vidal, E. R. Tubman, V. Valenzuela-Villaseca

CERBERUS: R. A. Smith, S. Eardley, T. Robinson, N. StuartGORGON: J. Chittenden, N. Niasse

with N. F. Loureiro (MIT) and A. Ciardi (Sorbonne)

Summary

jack.d.hare@gmail.com PPPL 2020 2

Magnetic Reconnection with Plasmoids MHD Turbulence

New Diagnostics for Turbulence PUFFIN: A new pulser at MIT

Current sheet

Magnetic Reconnection

3jack.d.hare@gmail.com PPPL 2020

Current sheet

Magnetic Reconnection

Prediction: 1000 yrs. Reality: 10 minutes!

Plasmoids Lead to Fast Reconnection and Anomalous Heating

Stronglysheared flows

Multiple current sheets

Overview of recent theory:Loureiro, N. F., & Uzdensky, D. A. (2015). PPCF, 58, 014021

Current sheet

Plasmoids Lead to Fast Reconnection and Anomalous Heating

Multiple current sheetsBB

Current sheet

The Convective Zone is a Collisional Plasma (and so is a Z-Pinch)

• Collisionless: Solar Flares, MRX, TREX

𝐿 ≫ 𝜆𝑒𝑖 >𝑐

𝜔𝑝𝑖≫

𝜔𝑝𝑒≫

𝑣𝑇𝑒𝜔𝑝𝑒

𝐿 ≫𝑐

𝜔𝑝𝑖≫

𝜔𝑝𝑒> 𝜆𝑒𝑖 >

𝑣𝑇𝑒𝜔𝑝𝑒

• Collisional: Convective zone, Z-pinch

D. D. Ryutov, IEEE TPS (2015)

Kelvinsong / CC BY-SA

Outline

•What is magnetic reconnection?

•Reconnection and Diagnostics on the MAGPIE generator

•Anomalous heating and the Plasmoid Instability

•Creating turbulence through flux tube merging

•Diagnostics for turbulence

• The PUFFIN facility

Pulsed Power Driven Reconnection, jack.d.hare@gmail.com 8

Laboratory Reconnection Experiments

Reconnection Layer

Laserspot

BubbleExpansion

Magnetic Ribbon

Magnetically Driven:B=0.03 T, ne=5x1013 cm-3,

V=10 km/s, L= 10 cmTe= 10 eV, Ti= 10 eV

βth<<1, βdyn<<1Long lasting

Laser Driven:B=50 T, ne=7x1019 cm-3,V=500 km/s, L= 0.1 cm,Te= 650 eV, Ti= 250 eV

βth>>1, βdyn>>1Transient

Pulsed Power Driven:B=3 T, ne=5x1017 cm-3,V=50 km/s, L= 1 cm

Te= 100 eV, Ti= 500 eV,

βth ∼ 1, βdyn ∼ 1Long lasting

Reconnection layer

The MAGPIE Pulsed Power Generator

• Constructed 1993

• 4 Marx banks: 300 kJ

• 1.4 MA peak current

• 250 ns rise time

• 1 TW into 1 cm3

MAGPIE

Load goes here

Lebedev et al, Rev. Mod. Phys (2019)

Plasma Source: Exploding Wire Array

Current

I=1.4 MA, 240 ns rise time

Dime for scale

Plasma Source: Exploding Wire Array

Current

I=1.4 MA, 240 ns rise time

Magnetic Reconnection Setup: Double Exploding Wire Arrays

1.4 MA

Suttle, L.G. et al. PRL 2016Hare, J. D. et al. PRL 2017Suttle, L.G. et al. PoP 2017Hare, J. D. et al. PoP 2018Hare, J. D. et al. PoP 2018

• Sustained flows

• Quasi-2D

• Collisional

• No guide field

Pulsed Power Driven Reconnection, jack.d.hare@gmail.com

Magnetic Reconnection Setup: Double Exploding Wire Arrays

• Sustained flows

• Quasi-2D

• Collisional

• No guide field

Suttle, L.G. et al. PRL 2016Hare, J. D. et al. PRL 2017Suttle, L.G. et al. PoP 2017Hare, J. D. et al. PoP 2018Hare, J. D. et al. PoP 2018

14Pulsed Power Driven Reconnection, jack.d.hare@gmail.com

Overview of Diagnostic Suite

Diagnostic Setup

G. F. Swadling et al. RSI (2014)

Diagnostic Setup

End on Electron Density (Laser Interferometry)

A plasmoid

Magnetic Field Profile (Faraday Rotation Imaging)

x Pulsed Power Driven Reconnection, jack.d.hare@gmail.com

𝛼(𝑥, 𝑧) ∝ න𝑛𝑒𝑩. 𝑑𝒚

Harris Sheet:

𝛼(𝑥, 𝑧) ∝ න𝑛𝑒𝑩. 𝑑𝒚

Velocity and Temperature (Thomson Scattering)

Fibre Optic Bundle

Overall shift: Vfi

Collective scattering from Ion Acoustic Waves

Fibre Optic Bundle

Separation: ZTe

Overall shift: Vfi

Fibre Optic Bundle

Width: Ti

Separation: ZTe

Overall shift: Vfi

Fibre Optic Bundle

Width: Ti

Separation: ZTe

Overall shift: Vfi

[100 km/s]

Fibre Optic Bundle

Cold (50 eV)Fast movingΔλ=0.6 Å

V=50 km/s

Hot (600 eV)Stationary

Fibre Optic Bundle Cs= 30 km/s, VA= 70 km/s

Power Balance in the Reconnection Layer

𝑉𝑖𝑛𝐿ℎ 𝐸𝑚𝑎𝑔 + 𝐸𝑘𝑖𝑛 + 𝐸𝑡ℎ,𝑖 + 𝐸𝑡ℎ,𝑒 ≈ 𝑉𝑜𝑢𝑡𝛿ℎ 𝐸𝑘𝑖𝑛 + 𝐸𝑡ℎ,𝑖 + 𝐸𝑡ℎ,𝑒~50% ~25% ~25% ~40% ~60%

2L 𝑃𝑖𝑛

𝑃𝑜𝑢𝑡

Anomalous Heating in the Reconnection Layer

τ𝑣𝑖𝑠𝑐 ≈ 800 ns

τ𝑟𝑒𝑠 ≈ 350 ns

τ𝑒𝑥𝑝 ≈ 50 ns

Classical heating is too slow:

τ𝑒𝑥𝑝 ≪ τ𝑣𝑖𝑠𝑐, τ𝑟𝑒𝑠2δ

2L 𝑃𝑖𝑛

𝑃𝑜𝑢𝑡

Anomalous Heating in the Reconnection Layer

jack.d.hare@gmail.com JPP 2020

τ𝑣𝑖𝑠𝑐 ≈ 800 ns

τ𝑟𝑒𝑠 ≈ 350 ns

τ𝑒𝑥𝑝 ≈ 50 ns

Classical heating is too slow:

τ𝑒𝑥𝑝 ≪ τ𝑣𝑖𝑠𝑐, τ𝑟𝑒𝑠2δ

2L 𝑃𝑖𝑛

𝑃𝑜𝑢𝑡

Need a faster mechanism:Plasmoids?

Outline

Plasmoids Visible in Electron Density Maps

Region of enhanced density (a ‘plasmoid’): Vy=130 km/s

Uniformity of Inflows

Uniform inflow density near layer

Magnetic Structure of Plasmoids

43jack.d.hare@gmail.com JPP 2020

“B-dot” probe

Plasmoids lead to fast reconnection and anomalous heating

Overview of recent theory:Loureiro, N. F., & Uzdensky, D. A. (2015). PPCF, 58, 014021

Current sheet

Plasmoid instability depends on:• 𝑆 = 𝜇0𝐿𝑉𝐴/𝜂𝑆𝑝

[Lundquist number]• 𝐿/𝑑𝑖

[current sheet length]

Regimes of the Plasmoid instability: Collisional MHD

Collisional MHD

Plasmoids

PlasmoidsStronglysheared flows

Regimes of the Plasmoid instability: The Semi-Collisional Regime

Include two-fluid effects

The Semi-Collisional Plasmoid Instability

Baalrud et al. PoP 2011

Outline

Flux Tube Merging

Shading: out of plane currentBlack lines: magnetic flux surfaces

From Zhou, Y. et al. (2004). Rev Mod Phys, 76(4), 1015–1035

Flux Tube Merging

Anisotropy

Power Spectra

Intermittency

Pulsed-power driven Flux Tube Merging

Wire arrays produce flux tubes during initial ablation

From: Martin et al. PoP 2010

Wire cores

Flux tubes merge on axis to form a turbulent column

Pulsed-power driven Flux Tube Merging

Flux tubes

From: Martin et al. PoP 2010

Optical Self Emission: Formation of a Turbulent Column

Axial imaging

Long lasting, confined column

Optical Self Emission: Formation of a Turbulent Column

Axial imaging

Dimensionless Parameters

L = 5 mm

DimensionlessParameters

EstimatedParameters

140 nsne= 5 x 1018 cm-3

Te = 100 eVTi = 200 eVB = 5 TV = 200 km/s

λei/L ≈ 0.01β ≈ 1Re ≈ 2500ReM ≈ 250Pr < 0.1

Axial Interferometry shows cellular structures

s0327_185 mm

355 nm laser probing: 200 ns after current startCellular structures

Side on Shadwography shows cellular structures

Cellular turbulentstructures

Imploding Wire Array

Outline

Pulsed Power Driven Turbulence, jack.d.hare@gmail.com 64

A simple experiment: Plasma flow into a planar obstacle

Imaging Refractometry: Density Fluctuations

https://arxiv.org/abs/2007.04682

Flow into planar obstacle

Imaging Refractometry: Density Fluctuations

Flow into planar obstacleReverse shock forms

Planar shock experiment: Aluminium, stable

Flow into planar obstacleReverse shock forms

Planar shock experiment: Tungsten, Turbulent

Flow into planar obstacle???? forms

New Diagnostics: Imaging Refractometer

eflection

angle (m

Space 73jack.d.hare@gmail.com PPPL 2020

eflection

angle (m

Measuring the Spectrum of Deflection Angles

Undeflected raysDeflected rays

0.8 0.6 0.4 0.2Intensity (a.u.)

eflection

angle (m

FWHM D ≈ 0.75 degrees

Spatialscale

Deflectionangle

Need a theory to link distribution of total deflection angles to the spectrum of density fluctuations

Random walk -> Gaussian

0.8 0.6 0.4 0.2Intensity (a.u.)

eflection

angle (m

FWHM D ≈ 0.75 degrees

Spatialscale

Deflectionangle

Need a theory to link distribution of total deflection angles to the spectrum of density fluctuations

Random walk -> Gaussian

But - deflection spectrum notGaussian!

0.8 0.6 0.4 0.2Intensity (a.u.)

eflection

angle (m

Faraday Rotation Imaging: Out of Plane Magnetic Fields

No axial fields in inflowsAxial interferometry

Out of planefields

Local measurements from Thomson Scattering

Ion Feature:Collective scattering, 28-points

Electron Feature:Collective and non-collective scattering

Probebeam

Bulk Flow,Electron and iontemperatures

Electron temperature,density

jack.d.hare@gmail.com PPPL 2020

Outline

Long drive times required to study instabilities and turbulence

Flux tube mergingPlasmoid Instability

Emperor Penguin:

4 ft/1.2 m

1.5 MA peak current, 1.5 µs rise time

[MAGPIE: 1.4 MA, 0.25 µs]

Starting January 2021 at MIT

Instabilities and turbulence need time to develop.

Vacuum coaxtransmission lines

Vacuum chamber

PUFFIN: A long drive pulser for fundamental plasma physics

Conclusions

• Reconnection and turbulence in collisional HED plasmas

• Sub-Alfvénic reconnection, anomalous heating, plasmoid unstable

• Magnetised turbulence with Pr < 1, 𝛽 ∼ 1

• New diagnostics to study turbulence in unprecedented detail

• PUFFIN: a new long drive pulser for magnetised HED plasmas at MIT

Magnetic Reconnection and Turbulence in Stellar-Convective ...

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