4th International Workshop onModels and Data for Plasma-Material Interaction in Fusion Devices

Weighted PIC simulation forvapor shielding at wall undertransient heat loads
K . IB ANO 1 , Y. K IK UCH I 2 , Y. UEDA 1 AND T. TAK IZUK A 1
1 G R A D U AT E S C H O O L O F E N G I N E E R I N G ,O S A K A U N I VE R S I T Y, J A PA N
2 G R A D U AT E S C H O O L O F E N G I N E E R I N G ,U N I VE R S I T Y O F H Y O G O , J A PA N

Date: 18-20 June 2019

Vapor shielding at solid walls
Radiation
coolingParticle motion

IonizationB
re-deposition

PlasmaBCollision

Vapor& Plasmareflection& sputtering

Recycling
Secondary Electron

LiquidSolid

Transient heat loads vaporize surface and “shields” incoming plasma.
Numerous physical phenomena should be considered during“Vapor shielding at walls”.
Sheath is important.  PIC simulation
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Transient events and erosions
Rough Estimation of ELM heat flux at ITER

G. Federici et al., PPCF(2003)

ITER
Divertor Area

2~5 m2

Wped~100 MJ∆WELM/Wped

0.01-0.1

WELM

1-10 MJ

ELM energy density

0.3-2.0 MJ/m2

ELM heat flux (1ms)

0.3-2.0 GW/m2

For > 1.0 MJ/m2
transient loads,
natural mitigation by
ELM
 Partial melting, Evaporation
vapor shielding is(0.1~ 1 ms, 0.1~10 GW/m2)
expected.
Disruption
 Melting, Droplet, Evaporation (Massive)(a few ms, 1~10 GW/m2)
Slow transient Recrystallization (W), Melting(~10s, ~20 MW/m2)

WEIGHTED PIC FOR VAPOR SHIELDING2

Outline
Intro: Vapor shielding, phenomena and importance

PIC simulation for vapor shielding
Weighted PIC, Multi component, Heat transfer for Vapor
Erosion of Be and W walls

Pulse shape dependence

Summary
VAPOR SHIELDING SIMULATION BY WEIGHTED PIC

Overall simulation model
PIC code treats

K. Ibano et al. CPP(2016); K. Ibano et al. NME(2017); K. Ibano et al. NF (2019)• 1 dimensional in space and 3 dimensional in velocity (1d3v)

 Sheath & magnetic pre sheath calculation• Sputtering by particle bombardments based on a semi-empirical model.
• Monte-Carlo collision for ionization & Recombination (OPEN-ADAS based)• Radiation cooling due to line and Recomb&Brems. (OPEN-ADAS based)• Other collision processes (Coulomb, Ion-neutral) are treated by the BC model.

Temperature

Heat transfer

Particle-In-Cell (PIC)
Vapor amount Surface ejected particles The Langevin heat bath
(Be, W and/or electron) (Numerical heating & Fueling)

Heat flux

Depth-Temperature profile-Surface temperature-Melting, ablation-Sputteringz𝑩𝑩x
Boundary atfixed potential

Heated plasma(electron & He, H, D)

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Weighted particle in PIC
vapor

Because of strong variations in ejection flux
as a function of surface temperature, vapor
particles are needed to be analyzed byweighted particles.
Weight= number of actual particle in a super cellion

Conventional PIC

Weighted PIC

electronelectron

ion

vapor

vapor

Electron : Ion : Vapor = 2 : 2 : 1

Electron : Ion : Vapor = 24 : 24 : 1

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A&M simulation by weighted particles
Special attentions were paid for Collision, Ionization,Recombination and Radiation cooling.

Ionization wvapor < welectron
electron

Radiation
ionization

ion

Radiation wvapor > welectron

vapor

mergingenergyvapor

Add “charges” to a randomly
selected electron in the same cell.

electron
Radiation energy (excitation) istaken from electrons in a same cell.

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Simulation of Multi Components Plasma
GIF movie
ELM

In ELM, background (BG)
and ELM plasma should be
separately treated.
 Multi components model.

Vapor

ELM

Distance from surface [m]ELM
BG plasma

TimePlasma temperature and density are solved, and A&M process
are also separately treated for both plasma components.
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Heat transfer and vaporization

Heat flux- Re-meshing as surface
eroded. (moving boundary)- Latent heat was consideredby subtracting energy fromheat flux.
- If temperature exceeds
ablation point (boiling point atA.P. or artificial),corresponding layer wascounted as “ablated.”

210 μs160 μs110 μs60 μs

260 μs310 μs460 μsInsulation
boundary

1D heat transfer calculation

W wall under 10 GW/m2(pulse starts at 100 μs, ends at 300 μs)

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Dissipation: Radiation power
Particle-In-Cell (PIC)
Surface ejected particles(Be, W and/or electron)z

Heated plasma(electron & He, H, D)

𝑩𝑩

x

Plasma-vapor interactions arecalculated to determine theshielding effects of vapor (andBe0sputtered particles).
Main contributions are
W0
Radiation (for electron)
Ion-neutral collisions (for ion)
Generalized collisional radiation
Be is good radiator in styles of neutral and ion.
model is used.
VAPOR SHIELDING SIMULATION BY WEIGHTED PIC

Dissipation: Ion-Neutral Collisions
C. H. Liu et al. J. Phys. B: At. Mol. Opt. Phys. 43(2010)144006

At first, we assumed collisions are negligible for higher energy ions.
However, collisions between hydrogen ions and Al/Be neutrals may playmajor role. Ion stopping via collision needs to be considered.
A TA binary collision like model was integrated in the code.
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10Outline
Intro: Vapor shielding, phenomena and importance

PIC simulation for vapor shielding
Weighted PIC, Multi component, Heat transfer for Vapor
Erosion of Be and W walls

Pulse shape dependenceSummary
VAPOR SHIELDING SIMULATION BY WEIGHTED PIC

Simulated profiles during ELM
at Beginning of ELM

Be vapor starts

Sheath disappear

Te ～ Ti
TiTeninepotential

At the beginning of ELM, more electrons reach to wall than ions,then sheath potential is developing.
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Simulated profiles during ELM
at Beginning of ELM
Te ～ Ti
Ti

Be vapor starts

Sheath disappear

Te ＜ TiTeni

nepotential

Further ELM particles are arriving. At the same time, Tsurf increases.
The vapor cools down electrons. The sheath potential drops.
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Simulated profiles during ELM
at Beginning of ELM
Te ～ TiTi

Be vapor starts
Te ＜ Ti

Sheath disappear
Te～ TiTeni

Te ≪ Tinepotential

The vapor clouds well developed. Ti also decreases, and ne～ni.
The sheath potential disappears.  different heat transmission.
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Heat flux during an ELM pulse
Pulse duration

ELM~1 keV, 5×1019m-3~3GW/m20.2ms pulse
2T magnetic field(~6o incident angle)
the Be wall component

Total Heat Flux
-without Be cooling-with Be radiation cooling-with Be rad+collisiondissipation
Time evolution of incoming heat flux during ELM (assuming square pulse).
Radiation cooling dissipates electron energies.
Ion-neutral collisions scatters ions.
Heat flux of both electrons and ions are decreased by vapor.
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Estimated erosion amounts
ELM

Be~1 keV, 3~20 GW/m2
0.2ms pulse
magnetic field(~6o incident angle)

W
Self-sputtering is considered
only in vapor shielding cases.
Erosion due to sputtering, vaporization, ablation are considered.
Reduced erosions are predicted for the cases with vapor shielding.
For >10 GW/m2 cases, W erosion is larger than Be due to lesseffective shielding.
～1µm of Be layer on W will effectively shield a 10 GW/m2 pulse.
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Estimation of W tile lifetime
G. Federici et al., PPCF(2003)

W with shieldW wo shield

10 mm thick W tile life time
analyzed by G. Federici.
(1.0 ms triangular pulse)
5 MW/m 2 are 10 MW/m2 areinter-ELM heat flux values.

Direct comparison is not accurate due to the pulse length and shape difference.
Longer pulse shows less erosion.
Even with the severe condition assumed in this PIXY calculation, the 10 mmthick W wall survives 107 ELMs if the energy density is < 1MJ/m2.
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Outline
Intro: Vapor shielding, phenomena and importance

PIC simulation for vapor shielding
Weighted PIC, Multi component, Heat transfer for Vapor
Erosion of Be and W walls

Pulse shape dependence

Summary
VAPOR SHIELDING SIMULATION BY WEIGHTED PIC

Pulse shape dependence
T. Eich et al 2011 J. Nucl. Mat. 415 S865-S859

J.H. Yu et al 2015 Nucl. Fusion 55 093027

Most of heat flux tests are taken by square shape waves,
but actual ELM pulse is triangular.
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Pulse shape: Laser loads
Negative ramp

Symmetric triangle

Positive ramp

Thermal conductivity of W
Surface luminescence of W under
different shape laser pulses

The surface reaches higher temperaturewhen the peak heat flux comes later.
 Slow thermal diffusion during a heat flux pulse.
 Lower thermal conductivity at higher temperature.
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Pulse shape dependence on
ELM simulation~1 keV, 5×1019m-3, ~3GW/m2
0.2ms pulse, 2T magnetic field (~6o incident angle)
the W wall component

Symmetric triangle

Negative ramp

Again, ion heat flux is dissipated by ion-neutral collisions.
Three pulse shapes (Symmetric triangle, negative ramp, and rectangular)
were analyzed.
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Erosion vs Energy density
All energy is the samewaveform shapes
Symmetric triangle Negative ramp Half width square

1.0 ms

1.0 ms

0.5 msWithin same energy flux, shorter time width pulses show higher erosion.
(due to higher peak heat flux value)
Within triangle pulses, negative ramp pulses show smaller erosion thansymmetric triangle.
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Vapor shielding rate
Vapor shielding rate =(𝛿𝛿shield − 𝛿𝛿no shield )/𝛿𝛿no shield 𝛿𝛿:erosion thickness

The negative ramp shows the leasterosion again in this comparison.
The erosion amounts shows similartrends.
 Longer pulse time is better.

Some erosions are needed for vapor shielding. However, for pulses causing
higher erosions, vapor shielding becomes less effective (the incoming pulse
energy is higher than the dissipatable energy).
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Vapor shielding rate
Vapor shielding rate =(𝛿𝛿shield − 𝛿𝛿no shield )/𝛿𝛿no shield 𝛿𝛿:erosion thickness

The negative ramp shows the leasterosion again in this comparison.
The erosion amounts shows similar
trends.
 Longer pulse time is better.

Vapor shielding effects are apparent (>0.5)
when erosion thickness exceeds 10-7m (Triangle) and 10-6m (Rectangular)
Vapor shielding can be more effective to the triangle than the rectangular.
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Summary and Conclusion
1-d PIC (Two components) and heat transfer models were
coupled to simulate vapor shielding phenomena at a solid surface.
Weighted PIC was applied in order to treat the temperaturedependent vapor flux.
Erosion amounts were estimated for 3~10 GW/m2 squarepulse, 0.2 ms ELM loads. Reduced erosions were estimatedfor Be and W walls.
Less erosions are observed for triangular pulse shapes.
Lower vapor shielding thresholds (in terms of erosionthickness) are observed for triangular pulse shapes.

Thank you for your attention.
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Sputtering
T+  BeBe+  Be

Sputtering yields are calculated from an empirical model. Yields
are determined by the energy and the angle of incidence.
The code reads table data of sputtering yields.
VAPOR SHIELDING SIMULATION BY WEIGHTED PIC

Erosion vs Energy flux
All energy is the same
waveform shapes
Positive ramp Symmetric triangle Negative ramp

Half amp square

Half width square

Within same energy flux, shorter width pulses show higher erosion.
(due to higher peak heat flux value)
Within triangle pulses, negative ramp pulses show smaller erosion thansymmetric triangle.
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Erosion vs Heat flux factor

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Erosion vs Peak Heat flux

The negative ramp shows the leasterosion again in this comparison.
The erosion amounts shows similar
trends.
 Longer pulse time is better.

Within same energy flux, shorter width pulses show higher erosion.
(due to higher peak heat flux value)
Within triangle pulses, negative ramp pulses show smaller erosion thansymmetric triangle.
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Heat transfer and vaporization
160 μs110 μs60 μs

260 μs310 μs460 μsInsulation
boundary

Heat flux

210 μsW wall under 10 GW/m2(pulse starts at 100 μs,ends at 300 μs)

1D heat transfer calculation- Multi layer. (e.g. Al/W, Be/W)- Re-meshing as surface eroded. (moving boundary)- Latent heat was considered by subtracting energy from heat flux.
- If temperature exceeds ablation point (boiling point at A.P. orartificial), corresponding layer was counted as “ablated.”
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Temporal change of potential near wall
Wall is 0V (grounded)

Electron reaches first

Radiation cooling onlyTiTe

ELM reaches steady-state
Sheath disappearsniElectron sheathnepotential

In case of “radiation cooling only”, only electrons are cooled.
Electron sheath (negative potential) is formed
due to the Te << Ti and ne > ni condition.
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