Liquid Metal and Stellarator Research at Columbia University...Electron Cyclotron Resonance Ion...
Transcript of Liquid Metal and Stellarator Research at Columbia University...Electron Cyclotron Resonance Ion...
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
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•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
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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!
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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!
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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?
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!
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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
without a solenoid?Do they have non-fusion applications?
• 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.
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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
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IIL/IPF = 3.68 IIL/IPF = 3.18
Initial agreement between measured and predicted flux surfaces was poor
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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
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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
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IL coil displacements were optimized to fit experimental data for IIL/IPF = 3.68
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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.
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Tilted coils need less current to achieve same transform. Also, have lower effective ripple than equivalent tokamak.
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Fieldline tracing suggests generation of rotational transform and compact aspect ratio
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Aspect ratioA≈8
Sharp boundaries correspond to island chains exiting LCFS
6 tilted TF coils were interlinked
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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).
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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
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!
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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
without a solenoid?Do they have non-fusion applications?
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
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r = 2.3 cm r = 3.3 cm r = 5.7 cm
Images from glow discharges were inverted. Peak of emissivity moves with source.
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Reconstructed images agree with experiment
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Reconstructed images agree with experiment and emissivity peaks at edge of microwave plasmas, as expected
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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!
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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?
• 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
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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
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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!
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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?
• 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
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• VMEC equilibrium calculations• Effects expected on equilibrium and stability
(mostly ballooning and Alfvén Eigenmodes).
b =0, 1.4%, 3.7%.Fixed Bz, fixed boundary.
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100 kW of overdense heating could lead to b≈10%
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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!
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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?
• CNT plasmas are started by electron gun and/or microwaves• Synergies when using electron gun and microwaves
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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
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
3.5
beamsurface
No beam50 eV beam100 eV beam200 eV beam200 eV, no ECRH
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
3.5
beamsurface
No beam50 eV beam100 eV beam200 eV beam200 eV, no ECRH
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
3.5
beamsurface
No beam50 eV beam100 eV beam200 eV beam200 eV, no ECRH
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
3.5
beamsurface
No beam50 eV beam100 eV beam200 eV beam200 eV, no ECRH
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
3.5
beamsurface
No beam50 eV beam100 eV beam200 eV beam200 eV, no ECRH
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• 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
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!
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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?
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
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Two ion extraction methods numerically demonstrated: 2) magnetic deflector/divertor
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Inboard extraction seems more efficient.Due to “meniscus”?
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!
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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…
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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
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Outline
• Passive stabilization (B only)
• Active stabilization (jxB)
• Feedback stabilization
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• CNC-machined from single block
• Duct of constant area but variable shape
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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
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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).
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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
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Velocity fluctuations are damped by effective viscous drag ∝ 𝐵2
Outline
• Passive stabilization (B only)
• Active stabilization (jxB)
• Feedback stabilization
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jxB acts as effective gravity, stabilizing
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I=120 AB=0 T
I=120 AB≈0.2 T
I=120 AB≈0.4 T
Broader coverage of substrate?
Outline
• Passive stabilization (B only)
• Active stabilization (jxB)
• Feedback stabilization
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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
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Current Terminals
Current Terminals
PlasticPot
Electrodes
VoltageTerminals
123
456
789
101112
Measurements of LM thickness were extended to a matrix of pin-electrodes
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Kirchhoff + generalized Ohm ÆÆmxn equations to extract height in each electrode
• Where • Can be rearranged as 𝐈 = 𝐀𝐡 and inverted: 𝐡 = 𝐀−1𝐈
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~10 ms time-resolution and ±0.5 mm precision were achieved
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“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
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Summary on Liquid Metals
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• 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