liquid metal and stellarator research at columbia...

Liquid Metal and Stellarator Research at Columbia UniversityFrancesco A. VolpeDept. Applied Physics & Applied Mathematics, Columbia University, New York

with special thanks to:CNT students: K.C. Hammond, A. Anichowski, R.R. Diaz-Pacheco, Y. WeiCIRCUS students: B.Y. Israeli, J. Li, J. Mann, A. Clark, M. Doumet et al.Former TARALLO collaborator: C. CaliriLiquid metal post-doc: S.M.H. Mirhoseini

Seminar at University of Illinois, Urbana-ChampaignNovember 8, 2016

Tokamaks and Stellarators are the two main approaches to magnetic confinement of plasmas

• Inductive or non-inductive current in plasma– Ohmically heats the plasma– generates a poloidal field

• Disadvantage: disruption

2

•Rotational transform is entirely generated by external coils

•Steady state

•No current-driven instabilities

•Resilient to pressure-driven instabilities

• Disadvantages: complexity & mm precision

ITER in Cadarache and W7-X in Greifswald are the next largest tokamak and current largest stellarator in the world

3

Nuclear fusion power plants should…

• …be steady state and not disrupt– Stellarators!

• …make clean plasmas, and walls should withstand heat and neutrons– Liquid metal walls!

4




5

But do they have to be so complicated?Can we invert 3D measurements?Can we heat them at high density?Are stellarators stable at high pressure?Can they teach how to start a tokamak

without a solenoid?Do they have non-fusion applications?




6

But do they have to be so complicated?Can we invert 3D measurements?Are stellarators stable at high pressure?Can we heat them at high density?Can they teach how to start a tokamak


• CNT and CIRCUS only use planar circular coils.• With 4 coils, CNT is ideal to test techniques to infer and

correct coil misalignments after construction.• CIRCUS could be generalized to axisymmetric stellarator.

7

Long-exposure photograph

Plane for cross-sections

IL coils

PF coils

Electron gun

Flux surfaces are measured with an electron beam and a phosphor-coated rod

8

IIL/IPF = 3.68 IIL/IPF = 3.18

Initial agreement between measured and predicted flux surfaces was poor

9

X(p) can be determined with a field line tracer

Finding p for a given X requires an iterative method

X p

Objective: deduce IL coil misalignments based on observed Poincaré cross sections

10

Define discrepancy vector: F(p) = X(p) – X*

Newton step δp satisfies F = – J δp� Jacobian:� δp1 ⟶ p1 = p0 + δp1 ⟶ X(p1) ⟶ F(p1) ⟶ δp2 ⟶ …

Best linear unbiased estimator for δp:� Minimize: �

�

Use Newton-Raphson method to find p* such that X(p*) = X*

� PF coils assumed to be displaced according to photogrammetry

� All 10 IL parameters free

� Reduction of 𝜒2 by factor > 100

11

IL coil displacements were optimized to fit experimental data for IIL/IPF = 3.68

12

I IL/I P

F=

3.68

I IL/I P

F=

3.18

Nominal coil positions Optimized coil positions

Cross sections for optimized parameters exhibit significantly improved qualitative agreement

CNT concept can be generalized to more than 2 tilted interlinked circular coils.

3 6 92 (CNT)

1 (LDX)

D. Spong (ORNL)13

18 coil device more axisymmetric than 18 coil tokamak

Needs less Ip than tokamak, for same rotational transform Æless violent disruptions.

14

Tilted coils need less current to achieve same transform. Also, have lower effective ripple than equivalent tokamak.

15

Fieldline tracing suggests generation of rotational transform and compact aspect ratio

16

Aspect ratioA≈8

Sharp boundaries correspond to island chains exiting LCFS

6 tilted TF coils were interlinked

17

Coil set was inserted in acrylic vessel

• Installed 1kW, 2.45 GHz magnetron.

• Installing two paraboloidalmirrors, of which one steerable.

• Coils tested.

• Vacuum tested (210-5 Torr).

18

e-beam from filament biased at -100 V in gas at 10-5-10-4 torr

follows rotationally transformed field line

Bird’s-eye view

Electron gun can be scanned in 3D, for fine scans of flux surfaces in field-line mapping

Sliding feedthrough mounted on tiltable bellow




22

But do they have to be so complicated?Can we invert 3D measurements?Are stellarators stable at high pressure?Can we heat them at high density?Can they teach how to start a tokamak


Onion-peeling concept

• Discrete layers of emissivity e(r)

• A layer contributes to pixel brightness p in proportion to distance L travelled by line-of-sight across layer

• p = Le • L from topology,

p from fast camerae ≈ (LTL)-1LTp

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e5

L21

e4

L22

e3

L11

e2e1

p2

p1

ej = emissivity of jth layer Lij = length of ith line-of-sight through jth layerpi = brightness of ith pixel

Concept was tested by illuminating single layer with hot catode

24

r = 2.3 cm r = 3.3 cm r = 5.7 cm

Images from glow discharges were inverted. Peak of emissivity moves with source.

25

Reconstructed images agree with experiment

26

Reconstructed images agree with experiment and emissivity peaks at edge of microwave plasmas, as expected

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• CNT has low BÆ low magnetic pressure• Small volume Æ high heating power density• Overdense heating Æ high n and high T

Since Dec.2012, CNT confines neutral, microwave-heated plasmas for tens of seconds

29

Waveguide axis (cm)-20 -10 0 10 20 30 40 50

Fiel

d-pe

rpen

dicu

lar a

xis (

cm)

-20

-10

0

10

20

O-mode propagation2D 5% power contoursBeam radius1st and 2nd harmonic

Waveguide axis (cm)-20 -10 0 10 20 30 40 50

Fiel

d-pe

rpen

dicu

lar a

xis (

cm)

-20

-10

0

10

20

O-mode propagation2D 5% power contoursBeam radius1st and 2nd harmonic

� Circular waveguide; approaches plasma edge

� Interior held at atmosphere to avoid breakdown

� Enters obliquely through port

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Launch antenna was designed for simplicity and high first-pass absorption

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10 kW magnetron

twist-flex waveguide rotatable

taper

launch antenna

External waveguide system designed to allow arbitrary linear polarization of the electric field

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magnetron head

twist-flex taper

ECRH setup outside vessel

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Waveguide launcher

IL coils

ECRH setup in-vessel

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First microwave plasmas made with the new ECRH system

5x overdense plasmas

• FX-B mode conversion from LFS? SX-B from HFS?• Improved impedance matching expected to lead to 10 kW

coupled to plasmas Æ higher Te

35




36



• CNT has low BÆ low magnetic pressure• Small volume Æ high heating power density• Overdense heating Æ high n and high T

Calculations suggest high b equilibria to exist in CNT

37

• VMEC equilibrium calculations• Effects expected on equilibrium and stability

(mostly ballooning and Alfvén Eigenmodes).

b =0, 1.4%, 3.7%.Fixed Bz, fixed boundary.

100 kW of overdense heating could lead to b≈10%

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• CNT plasmas are started by electron gun and/or microwaves• Synergies when using electron gun and microwaves

41

Pure-electron plasmas� Neutral pressure kept to ~10-9 Torr� Electrons emitted at axis would fill flux surfaces3

Partially neutral and quasineutral plasmas� Higher background

pressures lead to greater ion concentrations4

� At ~10-5 Torr, plasma is essentially quasineutral

[3] J. P. Kremer et al., Phys. Rev. Lett. 97, 2006[4] X. Sarasola and T. S. Pedersen, Plasma Phys. Control. Fusion 54, 2012

Non-neutral plasmas in CNT were created with a thermionic emitter

Probe displacement (cm)0 10 20 30

Elec

tron

dens

ity (1

016 m

-3)

0

0.5

1

1.5

2

2.5

3

3.5No beam50 eV beam100 eV beam200 eV beam200 eV, no ECRH


Elec

tron

dens

ity (1

016 m

-3)

0

0.5

1

1.5

2

2.5

3

3.5

beamsurface

No beam50 eV beam100 eV beam200 eV beam200 eV, no ECRH


Elec

tron

dens

ity (1

016 m

-3)

0

0.5

1

1.5

2

2.5

3

3.5

beamsurface



Elec

tron

dens

ity (1

016 m

-3)

0

0.5

1

1.5

2

2.5

3

3.5

beamsurface



Elec

tron

dens

ity (1

016 m

-3)

0

0.5

1

1.5

2

2.5

3

3.5

beamsurface



Elec

tron

dens

ity (1

016 m

-3)

0

0.5

1

1.5

2

2.5

3

3.5

beamsurface


42

• Reduced min Pneutr for microwave breakdown• N2: 6.5 × 10-6 Torr

⟶ ~2 × 10-6 Torr• Higher Te attainable (up to

~20 eV at lowest Pneutr )• Increased ne

Synergies are observed when thermoelectrons and microwaves are used at the same time

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NSTX-U uses multiple pre-ionization sources prior to Ohmic heating:� 28 GHz ECRH� Thermoelectrons� coaxial helicity injection

Possible application to tokamak start-up




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Electron Cyclotron Resonance Ion Sources generate high-charge ions for accelerators• Hot electrons (10keV), cold ions (eV)• Trend to higher fECRH, improved

confinement, reduced electron tails• State of the art: 28GHz (1T at center,

3T at mirrors). Plans for 50GHz • Open questions: stochastic heating,

two-frequency phenomena

III Gen.

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D-T Fusion Ignition!

Toroidal ECRIS will improve confinement and make better use of the field

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• Bumpy torus + tor. hexapole

• l=3 classical stellarator• TF “Mono-coil” inspired by MST

Two ion extraction methods numerically demonstrated: 1) ExB

Dielectric used to simulate Debye shielding of

capacitor’s fringing field

47

Two ion extraction methods numerically demonstrated: 2) magnetic deflector/divertor

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Inboard extraction seems more efficient.Due to “meniscus”?




49

But they should not touch the plasma nor expose the solid wall. Can we stabilize/control them?

Liquid metal walls1. Reduce impurities and recycling

[≪ 1mm thickness, 1mm/s to 1cm/s]

“Thick” walls2. Remove heat

[~1m, 1mm/s (turbulent) to 1m/s (laminar)]3. Attenuate neutrons

[~1m, 1mm/s (turbulent) to 1m/s (laminar)]4. Increase survivability to disruption5. If rotating, they stabilize the plasma Æ higher plasma b

[~1cm, >10m/s]

Here: [1-10 mm, 10-60 cm/s]

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Liquid walls will tend to be uneven

• Instabilities – Rayleigh-Taylor

• 1-100 cm, 13-130 ms– Kelvin-Helmholtz

• >1 cm, ≫ 3 ms

• Turbulence • Non-uniform forces

– Non-axisymmetric “error” fields– Inhomogeneous temperature Æ inhomogeneous…

• …resistance Æ current Æ TEMHD• …viscosity Æ shear-flow, convection• …density Æ convection

– Modes in plasma

[Narula 2006]

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LM becomes uneven under effect of time-varying non-uniform field, fast flow and solid wall roughness

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Link: https://www.youtube.com/watch?v=oXp4JsFWqt0

For Lithium and 𝐵 = 5 T,𝑗 = 0.1 A/cm2 suffices to defy gravity

Could be induced by modes in plasma

Liquid walls will need to be stabilized

Otherwise, they could1. “bulge” and interact with plasma

– Contaminate it– Cool it– Act as limiter– Disrupt it

2. “deplete” and expose substrate to heat and neutrons, and plasma to less benign plasma-facing material– Increased sputtering, erosion, recycling, Tritium retention…

55

Of forces considered, only jxB are rapidly, locally adjustableTo sustain the flow:• Gravity• Electromagnetic forces• Magnetic propulsion (𝛻𝐵𝑇)• Thermoelectric drive (𝛻𝑇)

For adhesion to substrate:• Capillary forces• Electromagnetic forces• Centrifugal

56[Abdou, 2001]

Outline

• Passive stabilization (B only)

• Active stabilization (jxB)

• Feedback stabilization

57

Outline




58

• CNC-machined from single block

• Duct of constant area but variable shape

59

Permanent magnets

Ferromagnetic core

PLA plastic, 3D printed

SN

N

N

N

S

S

S

“Frozen-in” field from rotating permanent magnets propels liquid metal

Slots for Fe laminations

Strong B is stabilizing, even in absence of j

60

𝐵 = 0 T 𝐵 = 0.4 T

𝐵

𝑢 ≈ 0.2 [𝑚/𝑠]

Navier-Stokes and generalized Ohm’s law𝜕𝐯𝜕𝑡 + 𝐯 ∙ 𝛻 𝐯 = −1𝜌𝛻𝑝 + 𝜈𝛻2𝐯 + 𝑔 + 1

𝜌 (𝐣 × 𝐁)𝐣 = 𝜎 𝐄 + 𝐯 × 𝐁

Contain a stabilizing term 𝜎𝜌 (𝐯 × 𝐁) × 𝐁 of order 𝜎𝑈𝐵2 𝜌

that dominates over convective term 𝐯 ∙ 𝛻 𝐯 (ratio=44 in our exp)

and over viscous term 𝜈𝛻2𝐯 (𝐻𝑎 = 𝐵𝐿 𝜎 𝜇 = 7 ∙ 104).

61

Strong B is stabilizing

Simplified Navier-Stokes𝜕𝐯𝜕𝑡 = −1𝜌 𝛻𝑝

pump,thermoel. drive,

magn. propulsion…

+ 𝑔gravity

+ 𝜎𝜌 (𝐯 × 𝐁) × 𝐁

effectiveviscous drag

𝛿𝑣⊥Ohm𝛿𝑗⊥ = 𝜎𝐵𝛿𝑣⊥

Lorentz 𝛿𝐹⊥ = −𝜎𝐵2𝛿𝑣⊥/𝑛

Incompressibility 𝛻 ∙ 𝐯 = 0 → 𝛿𝑣∥ also small

62

Velocity fluctuations are damped by effective viscous drag ∝ 𝐵2

Outline




63

jxB acts as effective gravity, stabilizing

64

I=120 AB=0 T

I=120 AB≈0.2 T

I=120 AB≈0.4 T

Broader coverage of substrate?

Outline




65

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+ −𝑉

𝛿𝛿

Similar to feedback control of plasma instabilities by coil arrays

Feedback control by array of electrodes will enforce uniform thickness under more challenging circumstances

Measurements of LM thickness were extended to a matrix of pin-electrodes

67

Current Terminals

Current Terminals

PlasticPot

Electrodes

VoltageTerminals

123

456

789

101112

Measurements of LM thickness were extended to a matrix of pin-electrodes

68

Kirchhoff + generalized Ohm ÆÆmxn equations to extract height in each electrode

• Where • Can be rearranged as 𝐈 = 𝐀𝐡 and inverted: 𝐡 = 𝐀−1𝐈

69

~10 ms time-resolution and ±0.5 mm precision were achieved

70

“Shaker” &Fast camera images Æ

Waves are non-linear, due to shallow liquid and large lat. oscillation

±0.5 mm noise Æ

Summary on Stellarators at Columbia

• CNT– Inversion of

• Error fields• Images

– Overdense plasma heating– High b

• CIRCUS– Rotational transform generation

• TARALLO– Plasma-based source of ions for accelerators

71

Summary on Liquid Metals

72

• Liquid metal walls need to be stabilized• Was stabilized

– Passively, by strong B• Effective viscosity

– Actively, by applied jxB• Effective gravity

• Will be stabilized– By jxB optimized in real-time, in feedback with

measurements of LM thickness• Sensors and actuators

liquid metal and stellarator research at columbia...

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