Introduction of SOLPS and Modeling of Hydrogen Isotope Inventory in mixed materials

Chaofeng Sang, Dezhen Wang, Xavier Bonnin and PSI&AD group

Dalian University of Technology

School of Physics and Optoelectronic Technology

2011.11.26, HefeiPSI&AD: http:// sites.google.com/site/dlutplasma

Introduction of SOLPS code package ；

Hydrogen isotope inventory ；

Recent work

Outline

Introduction of SOLPS code package ；

Hydrogen isotope inventory ；

Recent work

Outline

Introduction of SOLPS

B2, Braams' multi-species, 2D, fluid plasma code

Eirene , Reiter's Monte-Carlo neutrals code

Carre , grid generator

DG, Kukushkin's pre-processor

b2plot, Coster's post-processor

SOLPS (Scrape-off Layer Plasma simulator) is code package which can simulate the 2D SOL plasma. The package mainly includes ：

The main version of SOLPS code is SOLPS4.X ， SOLPS5.X; the difference of these two series of version is that, 4.x use b2 and 5.x use b2.5; X is depended by the different version of EIRENE (EIRENE96, EIRENE99, and latest version). SOLPS6.0 is in developing.

System and compiler requirements for SOLPS:

IBM AIX well supported

SUN : SUN’s compiler suite, Fujitsu;

SGI: has been used in the past;

Linux: (main)

Fujitsu’s PC compiler main one in use at Garching;

Linux.pfg90 compiler; (ITM-gateway, JET)

Intel compiler; gfortran compiler, g77

Introduction of SOLPS

Simulation domain of SOLPS ：

Region for single-null geometries

Introduction of SOLPS

Region for double-null geometries

Introduction of SOLPS

The function of each code of SOLPS ：

B2, a multi-fluid plasma code (2D), which can simulate different particles

(H/D/T/He/C/W/Be) in the SOL. The type of the particle can be defined.

Eirene , a 3D Monte Carlo kinetic code, which can trace the movement of

neutral particles.

DG, a graphical tool used for developing and modifying plasma devices

and plasma grids (define magnetic field, wall materials etc.), as well as

producing input date for some of the other codes (Carre, Triangle, Unip) ；

Carre , to creat grid, （ use the output of DG as input data ）；

b2plot, used for plotting results from simulation runs.

Introduction of SOLPS

Introduction of SOLPS

Long-term SOLPS programming projects Revamp of the meshing workflow (not started, nobody identified) Re-evaluation of sparse-matrix solvers, see Sparse Solvers (in progress, Klingshirn) Examination and possible implementation of also solving density equations summed over homonuclear sequences (not started, nobody identified) Implementation of H/D/T inventories in walls/targets (CS, in progress) Stabilization of 2d wall heat transport model by source linearization and self-consistent treatments of heat fluxes to the walls (including SEE, backscattering, etc...) (not started, XPB) More accurate calculation of electron cooling rates from atomic data (in progress, see issues 1-3 below, DPC + XPB + LDH) Improve the treatment of drifts (in progress, St. Petersburg) Development of SOLPS6 (in progress, Klingshirn) Improvement of b2fstati to create a 'reasonable' non-flat start state (not started, nobody identified)

An example of EAST case ：

SOLPS 5.0 SOLPS 5.1

Introduction of SOLPS

Introduction of SOLPS code package ；

Hydrogen isotope inventory ；

Recent work

Background

Hydrogen Isotopes(HIs) inventory is a key issue for the next fusion device because of safety reasons (T limited to 700 g, ITER).

In the future fusion device, simultaneous use of Be, W and C as the wall material for different parts of plasma facing components (PFCs) will bring in material mixing issues, which compound that of hydrogen isotopes retention.

For large simulation code such SOLPS, a standalone module which can simulate fuel retention is required.

Simulation flow chart

PIC-MCC SOLPSWall model

Plasma backgroundPlasma flux to the real wall

Impurity recycling

HIIPs

Components of the wall

Temperature distribution

WALLDYN

Heating

including

WALLDYN: Wall dynamic code, which is being developed by surface science group, IPP ；Compounds ： W, Be, C, WC, W2C, Be2C Be2W , Be12W, Be22W

HIIPC: Hydrogen Isotope Inventory Processes Code

PIC-MCC SOLPSWall model

Plasma backgroundPlasma flux to the real wall

WALLDYN

Heating

Impurity recycling

HIIPs

Components of the wall

Temperature distribution

Heating

Hydrogen Isotope Inventory Processes code.

AMNS databaseInput data, database

Simulation flow chart

Outline

HIIPsHeating

Temperature distribution Metal model Porosity model

HIs retention in the metal

wall.HIs retention in

the porous media（ include carbon materials and co-deposition laye

r ）Based on rate equation

1. Heating model

Equations:

Tk

q

z

tzT

z

tzTTk

zt

tzTC

front

p

|,

,,

baT

Tk

1

The heating conductivity

ba, Constants determined by experiments

z The direction normal to the target surface

The density of the materials

q Incident energy load

pC The specific heat of the materials

The heating model is applied to calculate the temporal evolution of temperature distribution in the bulk target, which can be applied to the HIIPs

Metal/Porous media

Cooling side

Flux (energy, particle)

z direction

Schematic of the simulation domain

Simulation results

For different materials (a)The steady-state temperature distribution inside the wall (z=0 is the heating surface of the wall) at long time,(b) the time-dependent surface temperature.

Due to the difference of the thermal conductivity, different material has different temperature distribution.

For wall thickness (distance of surface to the cool side) L = 1 cm, variation of the steady-state surface temperature with the heating flux.

Larger energy load leads to higher surface temperature

Fixed heating flux 3.0 MW/m2, (a) variation of the steady-state surface temperature with L, (b) minimum time to achieve steady-state temperature for different L values

The thicker the wall is, the higher the surface temperature can achieve.

Higher temperature need more time to get steady state.

Simulation results

2. Metal model ： HIIPs in metal materials

kT

E

aCCC

Da

t

tzC

t

tzCzR

z

tzCD

zt

tzC

Hdtraptts

t

tss

exp12

3

2,

,1

,,

30

0

The solute HIs concentration

The trapped HIs concentration

The HIs implantation profile

The incident particle flux

tzCs ,

tzCt ,

z

0

Recombination process only occurs on the surface of the metal wall:

LsrH CKJ ,02 |2

2

The diffusivity

The backscattering coefficient

The lattice constant

The detrapping energy

RD

a

HdtrapE

Simulation results

HIIs as functions of wall temperature after exposition to a HIs flux for 50 s, (a) the total, solute, and trapped HIs retention; (b) the percentage of solute and trapped HIs.

The total and solute retention HIs decrease as the temperature is increasing ；trapped; the trapped HIs areal density first increases with temperature, and then starts to decrease

Temperature range 450-900K, most of the HIs retention inside the wall in the form of trapped.

Simulation results

After exposition to the HIs flux for 50 s, the depth profiles of HIs retention for different wall temperatures.

HIs can diffuse deeper inside the wall when the wall temperature is higher

Comparing the total His retained, varying with time, using either a fixed wall temperature or the temperature from our heating model. The insert graph is the temperature evolution of the two cases.

When the temperature is calculated by the heating model, the retention amount is very different in the first 10 s (discharge time).

Depth profiles of HIs retained in the wall after 50 s as a function of impinging HIs flux

The larger flux can make HIs diffuse deeper inside the wall and increase the total retention amount. (Because of saturated region near the surface of the wall).

After pre-exposure to HIs for 50 s, and turning off the particle flux, (a) HIs retained as a function of time; (b) HIs retention depth profiles at different times.

Total retention amount decrease with time; the fuel diffuse deeper with time.

Simulation results

3. Porosity model ： HII in porous media

Carbon-based materials and co-deposited materials are porous media ， therefore, we can use this four-region model to simulate HIIP in these materials. The definition of of each region for the porosity model is shown .

Porous media is made up of granules and voids, the granules are consist of surface and bulk.

Some experimental data about mixed materials is demanded （ IPP-Garching）

Basic equations

surfbulkbulksurfLHHAvoid

bulksurfsurfbulkHdtrapHTrap

LHHERHHDAvoid

rrV

Srrf

V

S

z

ND

t

N

rrrr

rrrrfz

Dt

2

22

2

21

2

2

2

2

Where

The surface concentration of solute HIs in regions I and III tz,The volume concentration of solute HIs in regions II and IV tzN ,

Inter-regional transport from bulk to surfacesurfbulkr

The surface void fractionvoidf zrrA 01 The area of the surfaceS

The volume of the bulkV

thermal desorption rateHDr

Eley-Rideal processesERHr 2

Langmuir-Hinshelwood processesLHHr 2

Real flux inside the wall

Detail equations

Simulation results

Hydrogen isotope inventory (a) two-region for carbon-based target, (b) four region for carbon and co-deposited layer with the interface at z=0.

HIs diffuse more deeper inside the co-deposited layer than inside the carbon-based wall. There is a suddenly drop of the HIs density at the interface. (The diffusivity is very different)

Simulation results

Higher temperature can increase the diffusivity and make the fuel diffuse deeper.

Four-region case, at different temperatures (700-1200 K), t = 1 s, the depth profiles of HIs retained in (a) surface (region I, III), (b) bulk (region II, IV) .

Hydrogen isotope inventory (a) two-region for carbon-based target, (b) four region for carbon and co-deposited layer with the interface at z=0.

Given a fixed co-deposited growth rate (0.1 μm.s-1), the HIs retained density distribution evolution (a) σI + σI

Htrap and σIII + σIIIHtrap, (b) nII and nIV

After the implanting flux (Γ0) is turned off, the HIs release rate evolution for different wall temperatures (800 ~1300 K).

HIs release rate drops very quickly just after the flux turning off. Higher temperature have a higher release rate.

Simulation results

Conclusions

Heating model ： Calculate the wall temperature which is the input of metal and porosity

modules. We find that the material properties has big influence on the temperature; thicker

wall would increase temperature of the wall surface; and larger energy load can also increase

wall temperature. ；

Metal model: The model is based on the rate equations which can simulate HIs retention

inside the metal materials (W/Be). We investigate the wall temperature effect to the HIIPs, and

the HIIPs during and after the injected flux.

Pososity model ： This model can handle fuel retention inside the porous media (carbon,

co-deposited layer). The wall temperature effect, inject flux, release rate, and retention during

co-deposition are studied.

The HIIPC code is applied to simulate Hydrogen isotope inventory in the mixed materials. The code include three modules: heating ， metal ， porosity module

4. Bubble growth during HIIPs in Tungsten

For metal materials (tungsten) wall, bubble growth is a key issue. It can change material properties, increase HIs retention, and even make blistering occur, which can create metal impurity, and thus reduce the lifetime of the wall. Therefore, it is important to study bubble growth during fuel retention. We improve the metal model to have the capability to handle bubble growth.

Assumptions of the model ：To make the model simple and flexible, we make the following assumptions.

Bubble nucleation has already took place （ small bubbles already exist ）； The pressure in the bubble satisfies the Greenwood mechanical equilibrium condition ；

The bubble shape is spherical with a radius rb

Hydride formation is neglected ；

The effects of helium is not considered ；

There are only hydrogen molecules (no hydrogen atoms) in the bubbles.

Equations

Density of Bubbles

Number of HIs molecules inside Bubble

Absorption rate

Recombination rate

Fugacity in the bubble

Pressure inside bubble ： Greenwood’s equilibrium condition

Shear modulus of tungsten

The temperature should be much lower than the melting temperature of tungsten.

Equations

To get the relationship between pressure and HIs number inside the bubble, the state equation for HIs is required:

In the very high pressure case, we use the fugacity to replace the pressure:

Physical validation ：To make the model physically valid, we should make sure that the bubbles should not be too big and avoid the case when they are touching each other ：

Simulation results

The bubble radius and internal pressure as function of particle number inside bubble.

Maximum Equilibrium Solution (MES) and Maximum Solute density (MSD) as function of temperature

It is easier for bubbles to grow at lower temperature

MESKey temperature (520 K)

Simulation results

T = 500 K, bubble can grow，Cs, rb, Nb distribution at different time.

T = 600 K, bubble can not grow，Cs, rb, Nb distribution at different time.

Simulation result and conclusions

T = 500 K, the total HIs retained evolution for different bubble densities.

Bubble can grow under 500 k. When the bubble density (Cb) is large enough, the total HIs inventory amount can be increased during bubble growing.

Conclusions

This section of work includes：

Develop a new model which can

handle bubble growth；

We find that the wall temperature

is important during bubble growth. It

is easier for bubbles to grow at

lower temperature

Bubble growth could increase the

total HIs retention amount.

0 10 20 30 40 50 60 70

4.0x1021

6.0x1021

8.0x1021

0 = 1024 atoms.m-2.s-1

Temperature = 500 K

Time (s)

HIs

ret

ain

ed (

ato

ms.

m-2)

without bubble

Cb = 1.0*1012 m-3

Cb = 1.0*1013 m-3

Cb = 5.0*1013 m-3

References

1. R. Schneider, X. Bonnin et.al., Plasma Edge Physics with B2-Eirene, Contrib. Plasma Phys. 46, 3 (2006);

2. SOLPS5.1 Manual;

3. M. Warrier, Macroscopic particle balance model of hydrogen reactive-diffusive transport and inventory in porous media (private communication);

4. C. Sang, X. Bonnin, M. Warrier, A. Rai, R. Schneider, J. Sun, D. Wang , Modeling of Hydrogen reactive-diffusive transport and inventory in porous media with mixed materials deposited layers, EPS2011 38th Conference on Plasma Physics. (2011) ;

5. C. Sang, X. Bonnin, M. Warrier, A. Rai, R. Schneider, J. Sun, D. Wang , Modeling of hydrogen isotope inventory in mixed materials including porous deposited layers in fusion devices (submitted to Nucl. Fusion);

6. C. Sang, X. Bonnin, J. Sun, D. Wang, An improved model to simulate the effect of bubble growth on the hydrogen isotope inventory in tungsten (submitted to J. Nucl. Mater.)

7. C. Sang, D. Wang, X. Bonnin, M. Warrier, A. Rai, R. Schneider and J. Sun, Modeling of hydrogen isotope inventory in mixed materials in fusion devices, 53rd Annual Meeting of the APS Division of Plasma Physics (APS-DPP), November 14-18, 2011 • Salt Lake City, Utah – Poster YP9

Introduction of SOLPS code package ；

Hydrogen isotope inventory ；

Recent work

Recent work

Collaborate with Tore Supra about fuel retention；

Fuel retention in the gaps of the divertor tiles (tungsten）；

Dust Transport Simulation In EAST Device;

Kinetic simulation of divertor plasma detachment

Deuterium retention and release from pores in tungsten

Others

Prepare for 2012 PSI conference

End

Collaborate with Tore Supra

back

Prepare the abstracts for PSI 2012

Long term outgassing of carbon deposits in Tore Supra

S. Panayotis(1), C. Sang(2,3), B. Pégourié(1), X. Bonnin(2),E. Caprin(1), D. Douai(1), J.-C. Hatchressian(1), V. Negrier(1),J.-Y. Pascal(1), S. Vartanian(1), J. Bucalossi(1), P. Monier-Garbet(1)

(1) IRFM/DSM/CEA, CE Cadarache, F-13108 Saint-Paul-lez-Durance(2) LSPM-CNRS, Université Paris 13, Villetaneuse, France (3) School of Physics and Optoelectronic Technology, Dalian University of Technology,

Dalian, China

Simulation of Fuel retention processes in the carbon-lined wall of Tore Supra

Chaofeng Sang1,2, Xavier Bonnin2, B. Pégourié3, Jizhong Sun1 and Dezhen. Wang1

1 School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian, 116024, China. 2 LSPM-CNRS, Université Paris 13, Villetaneuse, France . 3 IRFM/DSM/CEA, CE Cadarache, F-13108 Saint-Paul-lez-Durance, France.

Fuel retention in the gaps of the divertor tiles

PIC-GAP 2D HIIPC2DHIs flux and energy

Fuel retention amount in the gap can be modeled

Prepare the abstract for PSI 2012

Simulation of Fuel retention in the gap of the deivertor tiles

Chaofeng Sang1,2, Jizhong Sun1, Xavier Bonnin2 , Dezhen. Wang1 , Houyang Guo 3

1 School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian, 116024, China.

2 LSPM CNRS, Université Paris 13, 99 avenue J.-B. Clément, Villetaneuse, 93430, France.

3 Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031, China

We set tungsten as the tile material, and improve the HIIPC to 2D, the plasma flux and energy is handled by PIC-GAP 2D

back

Prepare the abstract for PSI 2012

Dust in the fusion device

Dust Transport Simulation In EAST Device

Zhuang Liu1, Chaofeng Sang1, Jizhong Sun1, Dezhen Wang1

Houyang Guo2, and Sizheng Zhu2 1 School of Physics and Optoelectronic Technology, Dalian University of Technology2 Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031, China

The transport of dust particles in East device is studied using computer simulations with the dust transport code, DUST code. Recent developments in modeling with the DUST code are reported.

DUST code includes five sections. They are charging, force, ablation, transport and dust & wall interaction section, respectively. Taking into account EAST configuration and different parameters, DUST can simulate the transport process of dusts in EAST device.

back

Dust transport simulation in EAST contains five processes：

1. Charging

2. Forces

di e z th see

Z

dQI I I I I

dt Ions, electrons, impurity, thermionic, SEE Ions, electrons, impurity, thermionic, SEE

Dust Transport Simulation In EAST DeviceDust Transport Simulation In EAST Device

22 2

, 2

0

2{ [1 2( )] ( )}

2 4d i i th i u d i

id i

R Z en v Z Z euI e u erf u

u R T

22

0

8exp( )

4e d

e d ee d e

T Z eI e R n

m R T

i E BF F F F G ����������������������������������������������������������������������

Ion drag , E , B, gravityIon drag , E , B, gravity

i iab iscF F F ������������������������������������������

ion absorption, ion Coulomb scatteringion absorption, ion Coulomb scattering

2 ( , / ),i diab d i i iab i e

i d

V vF R n T u T T

V v

������������������������������������������

����������������������������

2 ( , / )i disc d i i isc i e

i d

V vF R n T u T T

V v

������������������������������������������

����������������������������

Force due to absorption of ionsForce due to absorption of ions

Force due to Coulomb scattering of ionsForce due to Coulomb scattering of ions

IonsIons

electronselectrons

3. Energy Balance and Ablation

Dust Transport Simulation In EAST DeviceDust Transport Simulation In EAST Device

22 4 2 2

2

1( , / ) { (2 1 2 ) [4 4 1 2(1 2 ) ] ( )}

2u

iab i e i iu T T u u e u u u erf uu

2

2

( ) 2 exp( ) /( , / ) 4 ln

2isc i e i

erf u u uu T T

u

2

,0 0

( , / )4 4

i d i ei i e d eq

d i i

Z Z e Z e Tu T T

R T T

, , /d eq d eq d eZ R T

/d h cdH dt P P

0

dT

d d pdH M c dT

Total heating / cooling powerTotal heating / cooling power

dust enthalpy, dust mass, dust specific heat dust enthalpy, dust mass, dust specific heat

2 2 2, , , ,

, ,

1[3 12 4 2 (1 2 )] ( )}i z i z i z i z

i z i z

Zu u u erf u

u

2 2 2, , , ,

,

1 2{ [5 2( )]exp( )

4h d i z Ti z i z i zi z

ZP R n v u u

/ 0d ee T

2 2 2, , ,

, ,

1[3 12 4 2 (1 2 )]i z i z i z

i z i z

Zu u u

u

2,2 2 2

, , , ,, ,

3 21 2{ [(5 2 )exp( )

8i z

h d i z Ti z i z i zpi z i z

u ZP R n v u u

u

/ 0d ee T

Dust Transport Simulation In EAST DeviceDust Transport Simulation In EAST Device

2,2 2

, ,, ,

3 2(5 2 )exp( )i z

i z i zmi z i z

u Zu u

u

2 4 44 ( )c radiation d d d wP P R T T emissivity, Stefan–Boltzmann constant, wall temperatureemissivity, Stefan–Boltzmann constant, wall temperature

Integrating the Planck function multiplied by the emissivity over wavelengthIntegrating the Planck function multiplied by the emissivity over wavelength

4 42

0 0

216 Im( ) ( )

1.3 ( ) ( )d d w

c dd w

R T TP R G

T T

4. Transport

5. Interaction with wall

d

d d

dVM F

dt

����������������������������

back

Detachment

Simulation of the divertor plasma detachment using kinetic method

Tengfei Tang, Chaofeng Sang, Dezhen Wang and Jizhong Sun

School of Physics and Optoelectronic Technology, Dalian University of Technology

Prepare the abstract for PSI 2012

Detached divertor is an attractive mode of operation for the tokamak reactor conditions with substantial reduction in the peak heat fluxes on the divertor targets which is created by gas injection near the targets. In this work we develop Particle In Cell Monte Carlo (PIC-MCC) code to simulate divertor plasma detachment. The charge-exchange, ionization, elastic, Coulomb and recombination collisions are included in our model.

Previous results: without recombination.Ar gas, by C. SangHydrogen gas, by T. Tang

Code including recombination is under development (by T. Tang)

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Retention in Tungsten

Deuterium retention and release from pores in tungsten

Shengguang Liu, Jizhong Sun and Dezhen Wang

School of Physics and Optoelectronic Technology, Dalian University of Technology

Prepare the abstract for PSI 2012

Pores in the tungsten sample after irradiation were observed directly by SEM. However, the physical mechanism of H isotope trapping and migration in W is not completely understood yet. These pores gives rise to great complexity to understand the H transport behaviour in W. Therefore, a model to simulate deuterium retention and release from pores in tungsten is urgent required.

Pores

Cross-section of irradiated area of the sample, irradiated up to maximal fluence of 5×1018 D+/cm2

Model and resultsModel

H 原子

2

2(1 ) ( )

c cD r F x

t x

3

2 12[ exp( )]

3bEY Da Y

uW uYt a kT

2 2

1 1( (0, ) )dn

V A K c t K S pdt

C: solute H Concentration

Y: Trapping H concentration

n: H concentration inside pores

P: pressure

H density in pore H density near pores H density on tungsten surface

back

SOLPS + HIIPC to simulate total fuel retention amount in fusion device ；

Continue developing HIIPC ；

ERO simulation work (for roughness wall),

The effect of plasma disruption to the plasma facing wall,

Runaway electrons

The interaction between plasma and wall in a strong oblique magnetic field

Others

backEnd

SOLPS+HIIPC to simulate HIIPs in fusion device

backJET

ITER

Recent work

αloc

αnom αloc

projectile sputtered & reflected

re-dep

ositio

n

Local angle of incidence αloc differs from nominal angle of incidence αnom

Reflected and sputtered particles can be re-deposited locally in holes.

Roughness description:Y = sinX

Sputtering: Dependent on energy and local angle

Reflection: TRIM database (dependent on angle and local angle)MD database (dependent on energy only)

Surface modification:Erosion, deposition, re-deposition

Modeling of surface roughness effects on erosion and re-deposition

Shuyu Dai and Zhanfu Yao

ERO code

The end

Thank you!