slide 1 12-15 nov 2006, efda pwi meeting, ljubljanai.s. landman, fz-karlsruhe modelling on wall...

12-15 Nov 2006, EFDA PWI meeting, Ljubljana I.S. Landman, FZ-Karlsruhe Slide 1

Modelling on Wall Surfaces and Tokamak Plasma

Consequences of ITER Transient Events

1 Forschungszentrum Karlsruhe (FZK), Germany2 Troitsk Institute for Innovation and Fusion Research (TRINITI), Russia

Contents

• Surface melting of W divertor armour and Be main chamber wall

• Brittle destruction of Carbon Fibre Composites (CFC) and cracking of W

• Contamination of the SOL and core plasma after ELMs

Forschungszentrum Karlsruhein der Helmholtz-Gemeinschaft

FUSION-PL

FZK – EURATOM FUSION ASSOCIATION

I. Landman1, B. Bazylev1, S. Pestchanyi1

with contributions from

A. Zhitluckhin2, V. Podkovyrov2 N. Klimov2 and V. Safronov2


Introductory comments:• Available tokamaks cannot provide required transient loads Q up to 15 MJ/m2

• Therefore we develop own codes to apply to ITER predictions

-- behavior of candidate materials for fusion (Be, C, W) -- tolerable sizes of off-normal events (ELMs and disruptions)

• For validation, “tokamak simulators” – pulsed plasma guns are engaged ( up to 0.5 ms)

The objectives of our EFDA tasks running in 2006:

TW3-TPP/ MATDAM (finished Jun), TW5-TPP/ ITERTRAN, TW5-TPP/ BEDAM• Modelling support for plasma gun experiments with ITER divertor materials of EU

trademark (TRINITI facilities QSPA-T and MK-200UG)

• Modelling of damage to ITER divertor and main chamber after transients

• Modelling of tokamak plasma contamination following ITER ELMs

• The codes MEMOS, PHEMOBRID, PEGASUS, FOREV and TOKES are engaged


MEMOS calculates melt motion at heated metallic surfaces (Be, W) accounting formelting, resolidification and evaporation.Melt motion is due to 1) p, 2) surface tension, 3) JB force

It was validated against electron beam- and plasma gun experiments (e-beams: JUDITH, plasma guns: QSPA-Kh50 (Kharkov), QSPA-T, MK-200UG)

The code MEMOS: earlier validations

Qmelt works wellMEMOS validations by plasma guns

MEMOS validations by e-beam at 5 MJ/m2 on the depth of resolidification crater


Simulation of W-brushe with MEMOS

Validation by QSPA-T

The 2D profile of W-brushes is implemented

Main conclusion: the depth of W melting and resolidification profile are rather similar to that of bulk W target.

However, melt velocity in W-brushes is less by a factor 0.3 - 0.5

Validation by QSPA-T is carried out

Relevance of QSPA to ITER:

Q ~ 0.5 – 1.5 MJ/m2 and = 0.5 ms as in ITER

QSPA: plasma velocity V is 105m/s, in ITER ~ 106

Pressure at the target: p ~ nEi

Density n follows from Q=EinV p 1/Ei

Ei is ion kinetic energy, in QSPA 100 eV only

Thus in ITER the pressure should be much lower.

(Particular figures significantly depend on the size of transient event)

ITER transients Kind of damage

Disruption

(10 MJ/m2, 3 ms)

ELM

(3 MJ/m2 0.5 ms)

W vaporization loss

1 m 0.1 m

W melt roughness 5-10 m 1 m

Single ELMs and disruptions

Therefore, the QSPA experiments should result in much more pronounced melt motion

Therefore the MEMOS was engaged for ITER predictions


MEMOS (in 2006): simulation of Be melting under radiation impact

Bulk temperature at 0.5 ms.Radiation load duration 0.5 msFull resolidification after 1.1 ms

Radiation heat load distribution over Be target surface

Melt depth vs. heat load duration (T0 = 300 K)

Evaporation depth vs. heat load duration

Melting and evaporation thresholds vs. heat load duration

Resolidification profileon Be target surfaceunder plasma action

Validation by radiation load experiments is required


PHEMOBRID validation against the QSPA

PHEMOBRID calculates evaporation and BD of CFCbased on BD threshold 10 kJ/g (as GOL-3 results)

The recent QSPA experiments (ELM relevant loads with 0.5 ms):• Mass losses appear at the impact energy density W0 > 1.4 MJ/m2• The rate of CFC erosion exceeds 1 μm/shot (evaporation at T0 = 500 C)

Numerical simulations:

• The heat flux at the surface was calculated as W(t) = W0exp(-h(t)/h0), h(t) calculated thickness of evaporated material, h0 = 1.5 μm (vapour shield).

• Plasma impact was assumed under 30 deg

CFC target layout Evaporation rate of CFC NB31 vs. absorbed energy


PEGASUS simulation for CFC with inclined fibres versus MK-200UG testsIt calculates BD of CFC and cracking on W surface

The last idea was to incline the PAN fibres under 45 deg to the pitch fibres

In PEGASUS simulations, BD erosion rate under ELM-like loads has decreased by ~5 times

Experiments at MK-200UG to proof this qualitative prediction are performed

The experiments have not confirmed the modelling results:

CFC erosion rate does not depend on orientation of CFC sample

PEGASUS: standard (a) and inclined (b) CFC fibres

a) b)

It seems that the CFC surface was so damaged that the CFC properties became isotropic, and at the large temperature the pitch- and PAN fibres acquire equal thermoconductivities.

PEGASUS: BD damage to improved CFC structure

(The PEGASUS is an abbreviation of “Particle Ensemble for Grain Aggregate Simulation ”)


PEGASUS modelling of cracks on W target surface

• A model of W surface cracking is developed by S. Pestchanyi to explain experimental crack patterns with crack depth scales of 500 and 50 µm

• A thermostress that appears in the thin resolidified layer after fast cooling causes the cracks through the bulk

Typical W parameters:

Young’s modulus E 3102 GPaThe Poisson ratio 0.3 (shear modulus/E)Tensile strength T < 1 GPaThermal expansion coeff. 10-5 K-1

Melt layer thickness h ~ 10 mTypical thermostress c ~TmeltE ~ 10 GPa

At c >> T cracking should occur

W cross-section with the cracks:QSPA results versus PEGASUS simulation.Q = 0.9 MJ/m2, = 0.5 ms


PEGASUS simulation of cracks on W target

PEGASUS simulation of cracks on W surface

W surface (QSPA, 100 shots of 0.9 MJ/m2, 0.5 ms. Primary cracks depth ~500 µmSecondary meshes sizes and depth ~102 µm

Typical thermostress F applied to the cracks on W surface (hmelt << L)

A formula for crack depth(F relates with ET )

Cracking scenario:

W surface is fast heated, higher than Tmelt.

Thus pre-surface bulk gets stressed, but in melt c = 0 even just after resolidification

The surface temperature decreases and after c exceeded T, large cracks appear, which decreases c.

Further cooling increases thermostress, and again c exceeded T cracks of small size


Main features of FOREV:

• Magnetic toroidal geometry of ITER and JET

• SOL multi-fluid plasma description (D+, T+, He+2, C+ to C+6)

• Radiation transport in toroidal geometry for C

ELM scenario as calculated by FOREV:

1. Due to a short large increase of cross-diffusion coefficient Ddiff in the pedestal and the SOL, the pedestal plasma fills the SOL.

2. SOL DT-He plasma hits in both divertor surfaces.

3. At the targets, heat flux and plasma pressure cause evaporation, with account of heat transport into carbon material

4. Eroded material propagates back into the SOL.

Comments on the simulations:

• Experimental DT plasma flux was reproduced approximating Ddiff by suitable dependencies from existing tokamaks.

• The calculations had been performed at WELM = 3.5 to 12 MJ.

ITER layoutin FOREV

RMHD code FOREV: applications for ELM simulations

targets maximum heat fluxes and behaviour of Ddiff during an ELM


FOREV modelling for heat flux and plasma pressure at ITER divertor surfaces

In this example ELM size isQ = 0.8 MJ/m2, = 0.5 ms

Distributions of impacting DT heat flux and pressure over inner divertor surface.

Those load profiles at different times are used by MEMOS, PHEMOBRID and PEGASUS.

along separatrix, 1.1 ms

SOL contamination as calculated by FOREV

• The vaporization threshold is obtained at WELM = 4.0 MJ (Q = 0.4 MJ/m2).

• During 0.5 ms a significant carbon plasma density in SOL can occur, up to 1021 m-1.

• Carbon ions occupy SOL for a few ms, with their temperature dropping down to 1-2 eV (due to radiative cooling)

• Further ELM consequences are simulated with the code TOKES using the FOREV data on carbon influx into the pedestal


Newly available features: wall and neutrals

• Heat transport in the wall, surface evaporation

• Underground triangle meshes

• Propagation of neutrals (atoms, photons and neutrons) in the vessel volume as random (Monte-Carlo) beams

• Ionization of atoms by plasma (immediately to Post’s Z)

• The magnetic surfaces are chains of segments through the triangle meshes, which provides optimal plasma-neutral coupling

• Vessel surface of arbitrary poloidal cross-section

• The algorthm of TOKES allows magnetic islands

The TOKES is still under development

(ITER preliminary layout)

Features of TOKES on plasma

• The Grad-Shafranov equation

• Pfirsch-Schlüter transport

• Multi-fluid plasma, (from D to C, and W ions)

• D- and T-beams heat and feed, radiation cools (by Post)

• D+T He + n fusion reaction

• Coil currents feedback upon plasma shape

ITER layout in TOKES

a

b

w


Contamination of ITER core by carbon after ELMs using the FOREV data

Whole ITER discharge of 400 s was simulated

Carbon ions of FOREV were injected into plasma edge

Power losses have been calculated: radiation losses and fusion power decrease

Q from 0.8 to 1.4 MJ/m2. Magnetic field was fixed.

Main result:

Tolerable ELM size 1 MJ/m2 for ELM frequency ~1Hz

Carbon impurity propagationinto the core after ELM

Benchmark scenario:


Conclusions and further objectives

MEMOS• Validations for W under plasma impact and Be under e-beams are done

• Validation for Be under radiation load experiments is required (experimental activity on Be using plasma guns is assumed in Kurchatov’s and TRINITI)

PEGASUS and PHEMOBRID• In the modelling the CFC erosion develops mainly due to cracking of PAN fibres

• At the validation of PHEMOBRID the account for vapor shield became necessary

• PEGASUS should be validated extrapolating pitch fibre thermoconductivity down to PAN fibre’s at ~ 4103 K

• PEGASUS modelling on W cracking seems successful. Further development is needed (cracking below the melting threshold: implementation of plasticity).

FOREV and TOKES• The tolerable 1 MJ/m2 obtained is at the minimum of expected ITER ELM sizes.

• In FOREV, Be and W plasma species should be implemented

• In TOKES, at first the radiation transport and the ionization modelling should be improved (now Post’s data are used)


Additional informations

Main results from MK-200UG and QSPA-T at large Q

CFC NB31 and NS31 were exposed to 200 shots 15 MJ/m2

Both CFC behaved similarly (regime with vapour shield)

Maximum erosion rate is proportional to pulse duration

PAN fibres max. erosion rate is of 20 m/ms

Pitch fibres max. erosion rate is of 3 m/ms (evaporation)

Graphite particles of sizes of 1 to 102 m are collected

• Start of vaporization: Qmin=0.3 MJ/m2 for 0.05 ms (MK-200UG) (Qmin: at 0.5 ms would be Qmin = 1 MJ/m2)

Matrix Tow

Direction to axis || to axis

radial axial

10-2k [W/m/K] 2 - 5 0.4 - 0.8 0.5 10 - 20

106 [1/K] 1 ~30 ~10 1

10-2E [GPa] 3 – 7 0.3-0.80.1-0.2

4-8

CFC properties (T < 2103 K)W melt damage after single ELM:

Melting threshold 1.0 MJ/m2 ( = 0.3 ms)

Vaporization threshold: 2.5 MJ/m2

Melt velocity less than 0.5 m/s

Maximum crater depths ~ 0.5 m

Vaporization thickness ~ 0.1 m


Additional informations (continued)

Damage to the dome gapsand the divertor cassette gaps

• the melting of copper at the W-Cu adjoins is significant

• protective tungsten aprons of the gaps may be necessary

PEGASUS features:• 3106 cells of 1 m represent 3D

material structure• Thermal- and mechanical bonds

between the grains• Anisotropic (for CFC) heat transport

through grain boundaries• Stress due to anisotropy and (c)

temperature gradients• Cracking of the bonds above

elasticity threshold (T)


Transient energy fluxes expected at the ITER divertor target

ITER Event Repetition Duration Target load Impact energy

Disruption seldom 1 .. 10 ms 10..30 MJ/m2 up to 10 keV

Type I ELMs 1-10 Hz 0.3..0.6 ms 0.5..4 MJ/m2 1..3 keV

Normal tokamak operation 500 s 10 MJ/ m2/s 1..3 keV

Main parameters of plasma guns

Facility MK-200UG QSPA

Pulse duration [ ms ] 0.05 0.2-0.5

Target load [ MJ/m2 ] 0.3 - 15 0.6 - 30

Load spot size [ cm ] 6 – 7 4-5

Magnetic field [ T ] 2 0.5

Impact energy [ keV ]

1.5 (ions) 0.2 (ions)

Plasma gun QSPA

Plasma gun MK200UG schematically


FZK codes for consequences of ITER off-normal events

Material surface modelling

MEMOS-1.5D (fluid dynamics)• Melt motion at heated metallic surface• (W and Be targets)

PEGASUS-3D (thermomechanics)• Brittle destruction of graphite and CFC• Cracking on W surface

PHEMOBRID-3D (BD threshold model)• Brittle destruction of graphite and CFC

Plasma modelling

FOREV-2D (radiation MHD)• Pulse transient loads at targets• Plasma shield (disruptions, Type I ELMs)• SOL contamination (C, W, Be)

TOKES-2D (equilibrium MHD)• Confined plasma equilibrium• Core contamination (by C so far)• Core plasma wall coupling effects

slide 1 12-15 nov 2006, efda pwi meeting, ljubljanai.s. landman, fz-karlsruhe modelling on wall...

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depth of w

fzkarlsruhe simulation

fzkarlsruhe memos

bd of cfc

iter elms

w accounting