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

[email protected] PPPL 2020 2

Magnetic Reconnection with Plasmoids MHD Turbulence

New Diagnostics for Turbulence PUFFIN: A new pulser at MIT

Current sheet

BB

Magnetic Reconnection

[email protected] PPPL 2020

Current sheet

BB

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

BB

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≫

𝑐

𝜔𝑝𝑒≫

𝑣𝑇𝑒𝜔𝑝𝑒

𝐿 ≫𝑐

𝜔𝑝𝑖≫

𝑐

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, [email protected] 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

B

V

I=1.4 MA, 240 ns rise time

Magnetic Reconnection Setup: Double Exploding Wire Arrays

1.4 MA

13

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, [email protected]

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, [email protected]

Overview of Diagnostic Suite


2 m

Diagnostic Setup

17

y

x

y

x

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


Diagnostic Setup

18

y

x

y

x



Diagnostic Setup

19

z

x

z

x

y

x

y

x



End on Electron Density (Laser Interferometry)


y

x 20

Wires



y

x 21



y

x

A plasmoid

22


Magnetic Field Profile (Faraday Rotation Imaging)

23

z

x

10 mm


24

z

x Pulsed Power Driven Reconnection, [email protected]

10 mm


B B

25

z

x Pulsed Power Driven Reconnection, [email protected]

𝛼(𝑥, 𝑧) ∝ න𝑛𝑒𝑩. 𝑑𝒚

B B


Harris Sheet:

1 mm

z

x


𝛼(𝑥, 𝑧) ∝ න𝑛𝑒𝑩. 𝑑𝒚


Velocity and Temperature (Thomson Scattering)

27

Fibre Optic Bundle

Fibre Optic Bundle


Overall shift: Vfi

Collective scattering from Ion Acoustic Waves


28

Fibre Optic Bundle

Fibre Optic Bundle


29

Fibre Optic Bundle

Fibre Optic Bundle


Separation: ZTe

Overall shift: Vfi



30

Fibre Optic Bundle

Fibre Optic Bundle


Width: Ti

Separation: ZTe

Overall shift: Vfi



31

Fibre Optic Bundle

Fibre Optic Bundle


Width: Ti

Separation: ZTe

Overall shift: Vfi



[100 km/s]


λ0

32

Fibre Optic Bundle

2 mm



λ0

33

Fibre Optic Bundle

2 mm

Cold (50 eV)Fast movingΔλ=0.6 Å

V=50 km/s

Hot (600 eV)Stationary

Δλ



λ0

34

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

2 mm



λ0

35

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

2 mm


Power Balance in the Reconnection Layer


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

2δ

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

[email protected] 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?

38

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




“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

BB

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



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

Wires

5 mm

Long lasting, confined column


Optical Self Emission: Formation of a Turbulent Column

Axial imaging

Wires

5 mm



Dimensionless Parameters

Wires

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

Wires

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








B

V

Pulsed Power Driven Turbulence, [email protected] 64

A simple experiment: Plasma flow into a planar obstacle

Imaging Refractometry: Density Fluctuations


Flow

https://arxiv.org/abs/2007.04682

Flow into planar obstacle

B


Imaging Refractometry: Density Fluctuations


Flow


Flow into planar obstacleReverse shock forms

B


Planar shock experiment: Aluminium, stable


Flow


Flow into planar obstacleReverse shock forms


Planar shock experiment: Tungsten, Turbulent


Flow


Flow into planar obstacle???? forms


New Diagnostics: Imaging Refractometer


Ray d

eflection

angle (m

rad)

30

-30

Space

0


Flow


Flow



Flow


Space [email protected] PPPL 2020

Flow


Ray d

eflection

angle (m

rad)

30

-30

0


Measuring the Spectrum of Deflection Angles

Undeflected raysDeflected rays


Flow

0.8 0.6 0.4 0.2Intensity (a.u.)

Flow


Ray d

eflection

angle (m

rad)

30

-30

0




L

n

n

n

Ln

cr

e

cr

e

22

1

=

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


Flow

0.8 0.6 0.4 0.2Intensity (a.u.)


Ray d

eflection

angle (m

rad)

30

-30

0




L

n

n

n

Ln

cr

e

cr

e

22

1

=

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!


Flow

0.8 0.6 0.4 0.2Intensity (a.u.)


Ray d

eflection

angle (m

rad)

30

-30

0


Faraday Rotation Imaging: Out of Plane Magnetic Fields

77

No axial fields in inflowsAxial interferometry

Out of planefields

Local measurements from Thomson Scattering

78

Ion Feature:Collective scattering, 28-points

Electron Feature:Collective and non-collective scattering

Probebeam

Bulk Flow,Electron and iontemperatures

Electron temperature,density


Outline








Long drive times required to study instabilities and turbulence


Flux tube mergingPlasmoid Instability

5 mm

Wires

5 mm


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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