Introduction to edge plasma modelling

Forschungszentrum Jülich in der Helmholtz-Gemeinschaft

Detlev Reiter

Forschungszentrum Jülich GmbH, Institute for Energy and Climate Research

52425 Jülich, Germany

ICTP-IAEA Joint Workshop on Fusion Plasma Modelling using Atomic Molecular Data, Trieste 23-27 Jan. 2012

Introduction to edge plasma modelling

Forschungszentrum Jülich in der Helmholtz-Gemeinschaft

Introduction to edge plasma modelling

Like in any applied science: Three questions

I.) WHAT : …happens? A &M & plasma-wall interaction processes

II.) HOW : …can we make the application work? ITER

III.) WHY : understanding the edge plasma,

using A&M&S data in edge plasma modelling

Outline of course:

See other lectures

Some unfinished business

www.eirene.de

www.hydkin.de

JET, MARK-I,

density ramp-up

-ohmic

-no imp. injection

-simply: D2-puff

Full detachment is a problem

JET, A. Huber, et al.

Detachment which is too “strong” (particle flux reduced across the whole target) is often associated with zones of high radiation in the X-point region and confined plasma (MARFE)

MARFE formation can drive a transition from H to L-mode (H-mode density limit) or disruption

MARFE physics still not well understood

Limit detachment to regions of highest power flux (where it is needed most).

Maintain remainder of SOL in high recycling (attached)

A few ways to arrange that this happens more readily:

Divertor closure Target orientation Impurity seeding

Courtesy: R. Pitts

Divertor closure

Increased closure significantly improves divertor neutral pressure increased neutral density (nn), promoting earlier detachment

Closing “bypass” leaks important for increasing nn

Divertor closure also promotes helium compression and exhaust – very important for ITER and reactors

JET, R. D. Monk, et al.

Courtesy: R. Pitts

Target orientation

Parallel heat fluxes significantly reduced for vertical cf. horizontal targets

Underlying effect is preferential reflection of recycled deuterium neutrals towards the separatrix

Neutrals into hotter plasma

near separatrix

Increased ionisation near sep.

Higher nt, lower Tt

Higher CX losses

AUG, A. Kallenbach, et al.

Neutrals into cooler, less

dense plasma

Pressure loss q||

ratrix

Courtesy: R. Pitts

Impurity seeding

JET, G. F. Matthews et al.

Unfuelled

(attached)

Strong D2 puff

(weak detachment)

Strong D2 +N2 puff

(stronger detachm.)

Strong impurity seeding also reduces ELM size but

high price can be paid in confinement

ITER divertor designed to achieve partial detachment

ITER Divertor DDD 17, Case 489 (SOLPS4.2 runs by A.

Kukushkin)

Deep V-shaped divertor, vertical, inclined targets

Dome separating inner and outer targets – also helpful for

diagnostics, neutron shielding and reducing neutral reflux to

the core

Inner strike pt.

Outer strike pt.

Courtesy: R. Pitts

Candle, on earth

Convection, driven by buoyancy

(i.e. gravity)

Only Diffusion (no convection)

Candle, under mircogravity

(only small,

dim burn,

at best)

Fresh air

e.g.: parabola flight,

g ≈ 0

Can we hope that magnetic confinement core plasma physics progress

will mitigate plasma-surface problems ?

Divertor exhaust

Apart from power handling, primary function of

divertor is to deal with He from fusion reactions

compress D, T, and He exhaust as much as

possible for efficient pumping (and therefore also

good density control).

To cryopumps

Critical criterion for an ITER burning plasma

is that He is removed fast enough such that:

is satisfied.

is the global helium particle residence

time – a function of tp, the He neutral

density in the divertor and the pumping

speed (conductance) .

Helium

enrichment:

is the ratio of He concentration in the

divertor compared to the main plasma.

, EHep tt

plasma

,Hepte.g. ITER: He prod. rate ~21020s-1

Max. divertor pumping speed

~200 Pa m3s-1 ~ 11023 He atom s-1

Cpump ~ 210-3 = 0.2%

Typical acceptable He conc. in the

core: ~4% He = 0.2/4 = 0.05 is

minimum required. The values of

and required for ITER have

been achieved experimentally

,Hept He

Courtesy: R. Pitts

Opacity in Fusion edge plasmas?

Only for resonance lines: Lyman-series

Trilateral Euregio Cluster

Inst itut für PlasmaphysikAssoziat ion EURATOM-Forschungszentrum Jülich

The Photon mean free path

T108.1n

T104.5mfp

Ly- Doppler Profile (5 eV) 10 cm

50 cm mfp for na=1013

At line centre:

for Lyman lines

Experimental observations

Terry et al, PoP 5,5 (1998) 1759:

Alcator C-Mod:

clear evidence for strong opacity effects

Ratio: Lyman- /Balmer-: proof of opacity

ne: low

ne: high

remains opt. thin

sion l

Lyman- Voigt-Lineshapes mfp

1~ (Photon mean-free-path)-1

April 29th 2002

Escape factors: zero dimensional corrections

to account for radiation trapping

Line escape factors:

for line of sight spectroscopy

(provided also by EIRENE, with zero statistical noise)

Population escape factors:

modify ionisation-recombination balance.

Important for dynamics in detached plasmas

ddrIrr line

),()(1)( 4

ikPik ArA )(

April 29th 2002

Comparison: ADAS vs. EIRENE escape factors

long cylinder case, homogeneous plasma

pure Doppler broadening (kT = 1 eV)

EIRENE population escape factor evaluation

(Optical thickness)

April 29th 2002

Comparison of D atom profiles

before after

April 29th 2002

Lyman- photon density (log scale), after iteration

April 29th 2002

population escape factor

A.S. Kukushkin, 12th PET, Rostov, Russia, 2nd September 2009 (ITER_D_2NJZH5) Page 20

A.Kukushkin, PET 2009 Episode 11: radiation transport

Partial detachment, high nneut Lyman series radiation MFP < 1 cm strong increase of ionisation, change of ionisation/recombination balance

Radiation transport in Eirene: several Ly series, photons like neutrals

SOLPS calculations: no effect on qpk and nHe, although plasma parameters in divertor change strongly

Reason: stronger ionisation in cold region increase of n increase of recombination (Sion n2; Srec n3)

Important for diagnostics, less for performance

don’t trust simple models!

dome, n-n D+He add Lyman trans.

2 4 6 8 10

nHe_sep

[1020m-3]

2 4 6 8 10

[MW/m2]

Why do edge codes take forever to

converge ?

plasma core

target

recycling

Major radius = 2-6 m

(distance to torus center)

A simple model, to illustrate the numerical challenge

Plasma flow

Gas flow

The often hidden challenge: code convergence, iterating on noise ??,…..

Code performance: Plasma Flow alone, B2, serial

B2, without EIRENE

1.00E-11

1.00E-09

1.00E-07

1.00E-05

1.00E-03

1.00E-01

1.00E+01

1.00E+03

1.00E+05

0 500 1000 1500 2000 2500 3000

no. of timesteps

Expected uncritical behavior, errors reduced exponentially to machine

precision.

Numerical Convergence errors (residuals)

during CFD run, vs. timestep Part. Balance (D+)

En. Bal (D+)

En. Bal. (electrons)

Moment. Balance

(Navier Stokes)

convergence behaviour of the coupled

B2-EIRENE codesystem (1)

coupled B2-EIRENE calculation,

recycling coefficient R=0.3

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

0 200 400 600 800 1000

no. of timesteps

ual (1

resee resei resco resmo

B2 with analytic recycling model

(without EIRENE),

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

0 200 400 600 800 1000

no. of timesteps

ual (1

B2, R=0.3 B2-EIRENE, R=0.3

This is what we want (Analytic recycling model=

unrealistically simplified Boltzmann eq.)

And this is what we get (full Boltzmann eq., Monte Carlo)

Numerical Convergence errors (residuals)

during CFD run, vs. timestep

Code performance: serial, B2-EIRENE, ITER test case, Linux PC 3.4 GHz

(typical for all “micro macro models” in computational science)

0 500 1000 1500 2000

no. of timesteps

ual (1

3h 15h 150h =

6.25 days

10s per EIRENE call

100s per

EIRENE call 1000s per

EIRENE call

Convergence limited by statistical Monte Carlo noise.

In order to reduce error by factor 10, runtime

(or number of processors) has to be increased by factor 100

What is a measure for: Performance ? Convergence ?

Comp. Sci + appl. Math.

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

0 500 1000 1500

no. of timesteps

ual (1

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

0 500 1000 1500

no. of timesteps

ual (1

10s per EIRENE call

100s per

EIRENE call

low recycling high recycling

Convergence in given CPU-time depends

on level of recycling (= vacuum pumping speed)

Total particle content

Recycling coefficient R=0.3

5.2E+20

5.3E+20

5.4E+20

5.5E+20

0 500 1000 1500

no. of timesteps

Total particle content

5.2E+20

6.2E+20

7.2E+20

8.2E+20

0 500 1000 1500

no. of timesteps

Total energy content

1.5E+04

2.0E+04

2.5E+04

3.0E+04

3.5E+04

4.0E+04

4.5E+04

5.0E+04

0 500 1000 1500

no. of timestepsen

electron energy

ion energy

Total energy content

1.5E+04

2.0E+04

2.5E+04

3.0E+04

3.5E+04

4.0E+04

4.5E+04

5.0E+04

0 500 1000 1500

no. of timesteps

electron energy

ion energy

low recycling

recycling

R=0.99

“Is is enough to see one lion to know you are in a desert”

Correlation sampling and convergence of B2-EIRENE

Here: correlation produced by simple manipulation of random

number generator

with correlation sampling

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

0 200 400 600 800 1000

no. of timesteps

ual (1

without correlation sampling

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

0 200 400 600 800 1000

no. of timesteps

ual (1

Without correlation sampling cpu time has to be increased by a factor 100 to reach the

same convergence level !

How much correlation ? Damping of noise, without freezing error from early iterations.

Recent Progress and Challenges

Going from 2D 3D…..

The experimental experience:

to stir a liquid

Creating turbulent (chaotic) flow

can largely increase heat transfer

(avoid local overheating)

The theory:

“passive scalar transport in chaotic force fields”

Not yet understood on a quantitative level

very active modern research field of

•theoretical physics

•large scale numerical computing.

Avoid excessive heat loads by stirring (magnetically) the plasma?

TEXTOR-DED: Dynamic Ergodic Divertor

13th of April 2011

Dynamic Ergodic Divertor (DED) in TEXTOR

flexible tool to study the impact of resonant magnetic perturbations on

transport, stability and structure formation (helical divertor)

C - EmissionIII

m/n=12/4 m/n=6/2

C - EmissionIII

m/n=3/1

C - EmissionIII

16 coils mounted at the HFS:

- covered with graphite tiles

- helical set-up

- resonant on q=3 surface

different operation modes:

DC operation

AC operation [1-10kHz]

slow strike point sweeps

resonant perturbation:

- m/n = 12/4, 6/2, 3/1 base mode

- different penetration depth

- B /B ~ 10% DED q

D.Harting, D.Reiter, JUEL-4173, May 2005

Field line tracing- 3D plasma fluid –neutral gas kinetic modeling

Partially ergodic 3D magnetic field topology

3D edge codes also Monte Carlo for plasma flow fields (EMC3)

TEXTOR-DED B-Field (R-Z) TEXTOR-DED B-Field (r-θ)

“Particle” methods:

also well established in fluid dynamics

• Lagrangian method Eulerian (grid based) method

• Advantages:

• + concentrate “particle” in the interesting region

• + Convective transport essentially without numerical dissipation in arbitrarily complex geometry

• Disadvantages:

• - Non-convective terms (collisions, diffusion)

• Solution: Monte Carlo fluid (random walk model)

• in Fusion: this is the concept of E3D and EMC3-EIRENE codes (IPP Greifswald)

• - looses accuracy in region of interfacial boundaries

EMC3-EIRENE: FZJ: mainly tokamak applications (RMPs)

Example: DIII-D ELM mitigation scenarios

Goal: quantify PSI, when RMPs are applied in ITER

Electron Temperature, DIII-D, with RMPs

(initially developed for stellarator applications

W7AS, W7X, LHD) was advanced to a

more flexible grid structure to allow divertor

tokamak + RMP applications. first self-consistent 3D plasma and neutral gas transport simulations for poloidal divertor tokamak configurations with RMPs.

Simulation results for ITER similar shape plasmas at DIII-D show a strong 3D spatial modulation of plasma parameter, e.g. in T

EMC3-EIRENE code verification (by benchmarks with 2D tokamak edge codes) and validation (TEXTOR, DIII-D, JET, LHD experiments) ongoing

EMC3-EIRENE is currently being used for contractual ITER RMP design studies (jointly by FZJ and IPP, 2010-2012)

= 60 eV T

e,2 = 120 eV

= 200 eV

Towards fully 3D CFD: The EMC3-EIRENE code (IPP Greifswald – FZ-Juelich)

Atomic database, as currently used

Detlev Reiter | Institute of Energy Research – Plasma Physics | Association EURATOM – FZJ No 40

This work: “plasma chemistry modeling

for magnetic fusion devices”

Many, external resources

www hydkin.de

B2-EIRENE

Matlab

www.eirene.de/A+Mdata

www.hydkin.de

www.eirene.de/A&Mdata

www.eirene.de A&M&S Data BCA: TRIM

All data, figs,

and references:

www.eirene.de: online (TRIM) reflection database

Data files with tables of

reflection distributions,

e.g. for particle simulation codes (conditional quantile format)

Backscattering

Dependency of reflection coefficient on incident energy

1 10 100 10000.00

Incident energy [eV]

Monte Carlo simulation (BCA): C on C, in = 60°

At low energies:

BCA not valid

Molecular Dynamic

calculations yield

Plasma-Wall Interaction Processes

Particle reflection coefficient, D --> FE, 30 degree

1 10 100 1000 10000

Eckstein 1983

TRIM-1985

TRIM-2002

SDTrimSP 2007

Sensitivity of reflection coefficient at low Ein (all within BCA, TRIM)

Incident energy,

Uncertain

Quite reliable,

Hidden key parameter:

Surface binding energy ( from MD?)

TRIM.xxx: reflected energy spectra

red: 200.000 TRIM particles,

blue: reconstructed from 10 quantiles

Challenge: what is the minimal dataset that allows

to re-sample the full backscattering (and sputtering) Eout,Θout-distribution ?

www.eirene.de

Surface data

EER inin

);,( q

TRIM-codes family, online database

for fully kinetic reflection velocity space PDFs

Particle reflection coefficient, D --> FE, 30 degree

1 10 100 1000 10000

Eckstein 1983

TRIM-1985

TRIM-2002

SDTrimSP 2007

Storing full 3D pdf of reflected

particles, for given incident

energy (12) and angle (7)

i.e. 84 tables for each

target-projectile combination

Next: similar database for

sputtering.

TRIM database (www.eirene.de)

Goal: replace various scalings (e.g. Yamamura

for incident angle dependence) by full database,

same format as for EIRENE-reflection database

Still not decided:

how to parameterize

a) Surface roughness,

b) Material mixing

Universal sputtering law: Janev, Ralchenko, et al.

for normal incidence yield.

0 degree

80 degree incident angle

Sputter yield database

For normal incidence:

probably ok.

Lost information, due to

raw data processing at too early stage

Detlev Reiter | Institute of Energy and Climate Research – Plasma Physics | Association EURATOM – FZJ No 52

www.eirene.de A&M Data HYDHEL, AMJUEL

All data, figs,

and references:

1986 -…., Polynomial fits

Automated

Interface to

EIRENE

History A&M Data, H and He, in EIRENE (=current status in ITER modelling)

1987 -…. He, He*, He+

Metastable

resolved.

Polyn. Fits

produced,

Elec. Cooling

rates added

H, H* , H+,

H2, H2+

2000 -….

Rad. transfer

Lyman opacity

1983 - 1999

Johnson-Hinnov

CR model for

H,H* H+

www.hydkin.de

Online data base

and data analysis tool-box:

- CR model condensation

- Sensitivity analysis

- Fragmentation pathway analysis

- Reduced models

• Hydrocarbons

• Silanes

• H, H2, H3+,….

• W, W+, ….W 74+

• N, N2

Basic input for ITER divertor code: A&M data, ( & surface data)

Goal: publicly expose raw data used in any modelling

Next GOAL: BeH, BH, ……

A: constructed from reaction rates for losses and gains of population y

(Maxw. reaction rates are obtained by integration of reaction cross sections, “on the fly”)

Gas puff, chem. sputtering Transport losses

HYDKIN: select a number of species,

and a set of reactions. Then:

NEW: surface reflection database

NEW: added after Juel-Reports and

PoP papers

Choose plasma background

Integration time

Graphical presentation

Printout:

Reflect input as selected

(composition, initial condition,

Influx, transport losses, per species)

Printout:

All individual rates used

Output for interface to EIRENE

Solution, vs. time (distance)

Here: 0 1e-4 s

Species selected for printout and plotting

Online solution of time-dep. (1D) Hydrocarbon breakup,

for any prescribed divertor plasma conditions, up to C3H8

Same, integration time 0 1e-3

Runtime of online code is independent

of chosen time interval for integration

(same for 1e-6 or 1e+6 s integration period),

time dependent solution is given fully explicitly in

terms of A matrix elements (+ initial cond.)

If A matrix is upper triagonal, all eigenvalues

and eigenvectors are explicitly given

Closed form analytic solution for Hydrocarbons: Phys. Scr. T138 (2009) 014014

raw data

HYDKIN

database

toolbox

EIRENE

3D Monte Carlo

kinetic transport

Interface

2004 -- ……(ongoing)

TEXTOR, JET,

ASDEX, DIII-D,

JT-60, LHD, ….. ITER

Spectral (time scale) analysis

fragmentation pathways

Sensitivity analysis

Verify Interface: HYDKIN --- EIRENE

(check for correct transfer of chemisty,

correct integration of cross sections)

Periodic BC Periodic BC

EIRENE: Make one grid cell, homogeneous plasma,

source of CH4 somewhere in box, run Monte Carlo

e.g. point source of CH4 Mostly H from CH4 fragmentation

focus stat. weights on

C containing fragments

1 eV, 1000 Eirene particles (<< 1 sec cpu)

0.0E+00

1.0E+07

2.0E+07

3.0E+07

4.0E+07

5.0E+07

6.0E+07

7.0E+07

0.0E+00 1.0E-04 2.0E-04 3.0E-04 4.0E-04 5.0E-04 6.0E-04 7.0E-04 8.0E-04 9.0E-04 1.0E-03

time (s)

C Hydkin

CH Hydkin

CH_2 Hydkin

CH_3 Hydkin

CH_4 Hydkin

C Eirene

CH Eirene

CH_2 Eirene

CH_3 Eirene

CH_4 Eirene

Choose in HYDKIN and in EIRENE:

same Influx: CH4, density: 5e12 cm-3 , Te=Ti=1 eV, same [0,tmax] time period

Density of CHx vs. time

1 eV, 1000000 Eirene particles (~23 sec cpu)

0.0E+00

1.0E+07

2.0E+07

3.0E+07

4.0E+07

5.0E+07

6.0E+07

7.0E+07

0.0E+00 1.0E-04 2.0E-04 3.0E-04 4.0E-04 5.0E-04 6.0E-04 7.0E-04 8.0E-04 9.0E-04 1.0E-03

time (s)

C Hydkin

CH Hydkin

CH_2 Hydkin

CH_3 Hydkin

CH_4 Hydkin

C Eirene

CH Eirene

CH_2 Eirene

CH_3 Eirene

CH_4 Eirene

Spectral analysis:

Identification of reduced models:

Very complex reaction chains (approx. 500 individual processes)

in fusion plasmas: catabolic sequence dominant, little: anabolism Eigenmode analysis of reaction rate equations very simple:

Define “Stiffness parameter”: λmax/ λmin,, ratio of max. to min. eigenvalues

fast slow

Combustion and flame modelling is mathematically analog

to diffusion-reaction modelling of ITER divertor detachment.

Unfortunately: reduced models („intrinsic low dimensional manifolds, ILDM“)

only applicable at very low plasma temperatures

Full reaction

kinetics required

importance of CX-DR over DE-DI channels: put one CxHy into plasma. How many e,p pairs are neutralized?

p+CxHy H + CxHy+, CxHy

DE, DI CX, DR

Molecular Data analysis (www.HYDKIN.de):

ITM , IAEA

CH4 C2H6 C3H8

DE RKJ 2009 JR 2004 JR 2004

DE+ RKJ 2009 JR 2004 JR 2004

I-DI RKJ 2009 RKJ 2009

## JR 2004 ##

DI+ RKJ 2009 JR 2004 # JR 2004 #

CX-PR JR 2002 JR 2004 JR 2004

R-DR JR 2002 RKJ 2009 RKJ 2009

R. K. Janev and D. Reiter, Phys. Plasmas 9,

4071 (2002);

R. K. Janev and D. Reiter, Phys. Plasmas 11,

780 (2004)

D. Reiter, B. Küppers, R. K. Janev, Hydrocarbon

collision database: revisions, upgrades and

extensions, Atomic and Plasma-Material

Interaction Data for Fusion, Vol 16, International

Atomic Energy Agency (IAEA), Vienna, (2010)

# new experiments planned in 2010, Univ. Louvian la Neuve, P. Defrance et al.

# # Revision planned in 2010, Univ. Innsbruck, T. Märk et al

DE: Dissociative excitation of neutral molecules

DE+: Dissociative excitation of molecular ions

I-DI: Ionisation and Dissociative Ionisation of neutral molecules

DI+: Dissociative Ionisation of molecular ions

CX-PR: Charge exchange and particle re-arrangement

R-DR: Recombination, Dissociative Recombination

Upgrade disabled:

published exp. Data

inconsistent

Upgrade ongoing:

Mainly: more low T

reactions:

Particle exchange

2010: more (DR) channels for Geroe Band emission added

New class of processes in thermal region

May 2011

previous database

New class of

processes (2011),

thermal region,

data from Astrophysics

Old: cx

How sensitive is a result to particular process

reaction rates (or transport losses) ?

Define sensitivity Z of density nj wrt. reaction rate Rk

as logarithmic derivative:

Z = d (ln nj) / d (ln Rk)

For n species in the system, and m different processes active,

there are n x m such sensitivity functions.

Fortunately: the system of DGL for these Z has the same form as

that for the densities n, and can also be solved in closed form

using the known eigenvalues and eigenvectors.

If this option is activated, HYKIN prints and plots the s (input)

largest (at t=tmax) such sensitivity functions

Phys. Scr. T138 (2009) 014014

HYDKIN.de: online sensitivity analysis

Analytic solution for sensitivity,

online

Zjk(t)=d(ln[nj])/d(ln<ratek>)

Identify, print and plot the most

sensitive parameters:

If <ratek> changes by x %

Then nj changes by x * Zjk %

Breakup of CH4 @ 40 eV

(143 parameters)

At 40 eV (TEXTOR)

Only DE, I, DI processes are relevant,

(nearly) no dependence on transport at all

D.Reiter et al., Phys. Scr. T138 (2009) 014014

HYDKIN.de: online sensitivity analysis D.Reiter et al., Phys. Scr. T138 (2009) 014014

Identify, print and plot the most

sensitive parameters:

If <ratek> changes by x %

Then nj changes by x * Zjk %

Breakup of CH4 @ 2 eV

(143 parameters)

At 2 eV (detached divertor, PSI-2)

Only CX, DR processes are relevant,

strong dependence on transport details

Analytic solution for sensitivity,

online

Zjk(t)=d(ln[nj])/d(ln<ratek>)

Conclusions/Outlook

Similar to previous steps: progress to ITER is based mainly on experimental and empirical extrapolation

guided by theory and aided by modelling

Present goal:

include all of edge physics that we are sure must be operative (opacity, A&M physics, surface processes, drifts…, even while our capability to confirm these directly remains limited.

Codes = bookkeeping tools

Present upgrading:

- low temperature plasma chemistry

- consistent wall models

- drifts and electrical currents in the edge

- 2D 3D

- coupling to first principle edge turbulence codes

- code integration: Core- ETB – Edge (ELM modelling)

Introduction to edge plasma modelling

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