Forschungszentrum Jülichin der Helmholtz-Gemeinschaft
Detlev
Reiter
Forschungszentrum Jülich GmbH, Institut für Energieforschung-452425 Jülich, Germany
NMCF09, Porquerolles, France, April 20-24, 2009
Computational fusion edge plasma physics
Mankind learning to tend a fire, once again….
100.000 years later….
Fire from processes in atomic shell Fire from processes in atomic nucleus
The Energy source of the sun and the stars in the universe is: Nuclear Fusion
The vision of nuclear fusion research: A miniatur
star in a solid container.
The Sun: T=15 Mill. degrees in the center
p + p d, Reaction time 1/(np
<σv>fus
)=tfus
approx. 109
years
Fusion Reactor: T=100 Mill. degrees
d + t He + n
Much too cold !
Role of Edge Plasma Science
Early days
of magnetic fusion (sometimes still today?):
Hope that a fusion plasma would not be strongly influenced by boundary:
“The edge region takes care of itself”.
Single goal: optimize fusion plasma performance (“advanced scenarios”,…..)
Now:man made fusion plasmas are now powerful enough to be dangerous for the integrity of the container:
The edge region does NOT take care of itself. It requires significant attention!
The ITER lifetime, performance and availability will not only be influenced, it will be controlled
by the edge region
Role of Edge Plasma Science, cont.
Almost...
The layman’s response to the idea:
“A miniature star (100 Mill degrees) in a solid container”:
THIS MUST BE IMPOSSIBLE !
It turned out unfortunately (early 1990th):
THE LAYMAN IS RIGHT !
Physics of hot plasmacore
Atomic/Molecularprocesses,Plasma material interaction
ITER
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
Used air
e.g.: parabola flight,g ≈
0
Can we hope that magnetic confinement core plasma physics progresswill mitigate plasma-surface problems ?
IP
ID
IDID
Magnetic Fusion: how to produce convection ? DIVERTOR
Increase
convection increase plasma surface interaction
JET (Joint European Torus) : Ø
8.5 m, 2.5 m high, 3.4 T, 7 MA, 1 min
Key area for plasma wall interaction
A
U
G
J
E
T
I T E R
Major Radius
TorusAxis
Core:plasma similarity:present experimentsare “wind tunnel experiments”for ITER
Extrapolation: present experiments ⇒ ITER
Extrapolation of core plasma confinement to ITER
ITER referencescenario
div(nv
)+div(nv
)= ionization/recombination/charge exchange
Core
Relative importance of plasma flow forces over chemistry and PWII Plasma Core
(collisional
+turbulent) cross field flow, D, V
Present:(empirical) transport scaling e.g.: from spectroscopy on surfacereleased impurities (interpretation, line shape modelling):
Spectroscopy : nZ*CR Model : nZ* nZTransport Model : nZ D, VEmp. Scaling law :
D
, V tauE
Future:advanced plasma scenario development,“ab
initio core turbulence modelling”
A
U
G
J
E
T
I T E R
Major Radius
TorusAxis
Core:plasma similarity:present experimentsare “wind tunnel experiments”for ITER
Edge:Computational plasma edge modelling
Extrapolation: present experiments ⇒ ITER
Edge/divertor modelling
• interdisciplinary• already
a highly
integrated
field-
plasma
physics- CFD -
rarefied
gas dynamics-
opacity-
plasma
wall interaction-
atomic
physics-
molecular
physics-
.....
FZJ activities in edge plasma simulation:
EIRENE : gas dynamics, radiation, gyro-averaged impuritiesERO : PWI, microscopic: Erosion and re-deposition edge code integration: B2-EIRENE (a.k.a. SOLPS….),
EMC3-EIRENE, EDGE2D-EIRENEOSM-EIRENE
atomic and molecular databases
(with IAEA, Vienna)
fusion, technical, astrofluid-dynamicsaero-dynamics, vacuumlighting, inertial fusion
currently through IAEA
div(nv
)+div(nv
)= ionization/recombination/charge exchange
II: midplain
III: target
Relative importance of plasma flow forces over chemistry and PWIII edge region III divertor
parallel
vs.(turbulent)cross fieldflow
parallel
vs.chemistry and PWIdriven flow
div(nv
)+div(nv
)= ionization/recombination/charge exchange
EDGE plasma challenge:
• No clearly separated timescales, no natural separation into reduced sub-models.Far more challenging than ab initio core plasma transport:There: turbulence and transport time scales are clearly separable.
• Large variation of collisionality
• Large number of physical processes and species
ELECTRON TRANSIT
ISLAND GROWTH CURRENT DIFFUSION
Single frequency and prescribed plasma background
RF Codes wave-heating and current-drive
SEC.10-8 10410210010-210-410-6Ωce
-1
10-10ωLH
-1 τAΩci-1
SAWTOOTH CRASH
TURBULENCE
ENERGY CONFINEMENT
Neglect displacement current, average over gyroangle, (some) with electrons
Gyrokinetics
Codes
turbulent transport
Neglect displacement current, integrate over velocity space, average over surfaces, neglect ion & electron inertiaTransport Codes
discharge time-scale
Typical Time Scales in a next step experiment with B = 10 T, R = 2 m, ne
= 1014
cm-3, T = 10 keV
Neglect displacement current, integrate over velocity space, neglect electron inertia
Extended MHD Codes
device scale stability
Fusion Simulation Project Vol.2, FESAC ISOFS Subcommittee
Final Report, Dec. 2002
core
plasma
ELECTRON TRANSIT
ISLAND GROWTH CURRENT DIFFUSION
SEC.10-8 10410210010-210-410-6Ωce
-1
10-10ωLH
-1 τAΩci-1
SAWTOOTH CRASH
TURBULENCE
ENERGY CONFINEMENT
Typical Time Scales in a next step experiment with B = 10 T, R = 2 m, ne
= 1014
cm-3, T = 10 keV
Neglect displacement current, average over gyroangle, (some) with electrons
Gyrokinetics
Codes
turbulent transport
Neglect displacement current, integrate over velocity space, average over surfaces, neglect ion & electron inertiaCore Transport Codes
discharge time-scale
Atomic & molecular processes
Neutral particle codes, kinetic imp.transport codesplasma chemistry
Ion drift wavesTransients (ELMs)
ITM
Edge turbulence
Parallel dynamics:Ion transit, Ion collisionsParallel sound waveDitto, electrons
2D transport codes
core
plasmaedge plasma Well separated: transport –
turbulence: good !
The EDGE plasma challenge (same for tokamaks
and stellarators) :
• Broad range of space and timescales• no clearly separated timescales, no natural separation into
reduced sub-models.
• large variation of collisionality• multitude of physical processes• near sonic flow • large number of species • three states of matter (at least) involved, strong exchange • complex magnetic fields (2D 3D)
• computational boundary plasma engineering needed now (not in 10
years)
Need for mature edge codes defines work packages for next years.
Generic kinetic (transport) equation
(L. Boltzmann, ~1870)
( ) ( ) ( ) ( ) ( )Ω−Ω=+Ω∇⋅Ω+∂Ω∂ rrrrr
,,,, EfEvESForcesEfvt
Efaσ
( ) ( ) ( ) ( )[ ]∫∫ ΩΩ′⋅Ω′→−Ω′′Ω⋅Ω′→′′Ω′′+∞
π
σσ40
,,,,rrrrrrr
EfEEvEfEEvdEd ss
•for particles travelling in a background (plasma)between collisions•with (ions)
or without (neutrals)
forces (Lorentz)
acting on
them between collisions
),,( tvrf rrBasic dependent quantity: distribution function
Free flight External source Absorption
Collisions, boundary conditions
Altogether, just a balance in phase space
Example: MAST (UK)
Plasma temperature in KCourtesy: S. Lisgo
Characteristics (=Trajectories) of kinetic transport equationhere: MAST, Culham, UK
Here: mainly H, H2
, Cx
Hy
neutrals
MAST: Geometry and exp. plasma data provided by S. Lisgo, UKAEA, 2007
Example: MAST (UK), 3D (filament studies)
(Molecular) Gas Density (1 –
3 E20).
Example: MAST (UK), 3D (filament studies)
(Atomic) Gas Density (1—3E19
Consistent Plasma-Gas-Radiation fields in MAST edge
Tene nD nD29.5×1018 m-3 max 30 eV max 0.6×1018 m-3 max 0.6×1019 m-3 max
Tene nD nD29.5×1018 m-3 max 30 eV max 0.6×1018 m-3 max 0.6×1019 m-3 max
Plasma flow (experiment + OSMModelling)
Gas flow (atomic and molecular)EIRENE
Courtesy: S.Lisgo
et al., MAST Team, EPS 2007
INVERTED Dα
IMAGE
OSM-Eirene
UPPER DIVERTORDα
IMAGE
Courtesy: S.Lisgo
et al., MAST Team, EPS 2007
Spectroscopy OSM transport modelling CR plasma chemistry modellingQuantitative comparison experimental validation of tokamak edge chemistry
EXAMPLE FOR A TYPICAL/REPRESENTATIVE ELM in MASTdivertor
not resolved in this example due to memory limitationsN = 6 for the simulation
Fast Camera, unfiltered
OSM-EIRENE (UKAEA/FZJ) : Towards fully authentic 3D edge interpretation codes:
OSM-EIRENE reconstruction: D-alpha
a new fully general 3D adaptive grid geometry option in EIRENE, using Tetrahedons
Grid refined near ELM filament
EIRENE kinetic transport code (www.eirene.de): gyro averaged ion kinetic up to edge-core interface
MAST: Geometry and exp. plasma data provided by S. Lisgo, UKAEA
Here: Cx
Hy
, C, C+, C2+, …
atomic & molecular neutrals and ions
V&V: ongoing:Cx
Hy
source,CH, C, C++
spectroscopy
MAST: DivertorTEXTOR: Limiter
In the
absense
of the
diffusion
(Fokker Planck) term:
The
trajectory
between
collisions
is
known
exactly
(straight
line)
The
equation
can
then
be
casted
into
an Integral equation(Greens
function
is
known
in closed
form)
ASIDE: The mathematics of EIRENE:
(use
Ψ, (pre-)collision
density
distr., rather
than
f, particle
density
distr.)
samplebirth
pointsamplefree
flight
samplefree
flight
collisionevent
Mean
number
ofsecondariesafter
collision
Discrete
state
space system of linear eqs., YAbYrtrr
+=
Weighted average over phase space cell
initial
distribution
Transition
probability
Construct
Markovian
random
walk from
integral equation
Weighting, to account for:- Branching (multiplication)- Absorption-….
weight
correction, „on the
fly“
What if the Plasma state (host medium) is not known from experiment (e.g.: ITER ??)
Some historical background
1987: NET contract (F. Engelmann, M. Harrison)Consortium KFA Jülich
-
AEA Culham
–
ERM BrusselsEric Hotston, Geoff Maddison, Mike HarrisonMartine Baelmans, Petra Börner, Detlev
Reiter1st
Code release: 1991: EPS-Berlin, D. Reiter et al., PPCF 33
13
(1991)
since around 1995: Multi-side developments, proliferation of versions, …
This talk: The joint “ITER.org
–
FZ Jülich”
version SOLPS4.3
B2-EIRENE (SOLPS-xx):
Continuity
equation
for
ions
and electrons
Momentum
balance
for
ions
and electrons
Energy balances
for
ions
and electrons
( )∂∂t
n n V Si i i ni+ ∇ ⋅ =r r ( )∂
∂tn n V Se e e ne+ ∇ ⋅ =r r
( ) ( ) ( )iiVmiiiiiiiiiiiii SRBVEenZpVVnmVnm
tr
rrrrrtrrrrrr++×++∏⋅∇−∇−=⋅∇+
∂∂
( )−∇ − + × + =r r r r r
p en E V B Re e e e 0
( ) iEeiiiiiiiii
iiiii
iiii SQVREZenqVVV
nmTnV
nmTn
t+−⋅−=⎥
⎦
⎤⎢⎣
⎡+⋅∏+⎟
⎠⎞
⎜⎝⎛ +⋅∇+⎟
⎠⎞
⎜⎝⎛ +
rrrrrtrrrr22
225
223
∂∂
∂∂t
n T n T V q en E V R V Q Se e e e e e e e i ei Ee3
252
⎛⎝⎜
⎞⎠⎟ + ∇ ⋅ +⎛
⎝⎜⎞⎠⎟ = − ⋅ + ⋅ + +
r r r r r r r
Collisionality plasma fluid approximationmulti-ion fluid (α ion species, Tα = Ti, and electrons)multi-species Boltzmann eq. for neutrals (n neutral species)Braginskii, Reviews of Plasma Physics, 1965
Momentum
balance
for
ions
and electrons(Navier
Stokes
„Braginskii“
equations)
( ) ( ) ( )iiVmiiiiiiiiiiiii SRBVEenZpVVnmVnm
tr
rrrrrtrrrrrr++×++∏⋅∇−∇−=⋅∇+
∂∂
⊥+⊥∂−⊥∂−= ⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛
⊥⊥⊥ Vph
Dnh
Dv pn αα
αα
α lnln
In edge codes often used only for αvװ
the flow parallel to B-field
The cross field momentum balance is replaced by diffusion-convection ansatz:
with
ad hoc (anomalous?)
D⊥
,V⊥
κ⊥
, η⊥,
Future: coupling to turbulence codes ??
ASIDE: eliminating turbulence from edge transport models (ab-initio ad hoc)
Numerical tool for the edge plasma science:B2-EIRENE code package (FZJ-ITER)
B2: a 2D multi species (D+, He+,++, C1+..6+,…) plasma fluid code
EIRENE: a
Monte-Carlo neutral particle, trace ion and radiation transport code.
Plasma flowParameters
Source terms (Particle, Momentum, Energy)
Computational Grid
Self-consistent description of the magnetized plasma, and neutral particles produced due to surface and volume recombination and sputtering
see www.eirene.de
Reiter, D., PPCF 33
13 (1991)Reiter, D., et al., Fusion Science and Technology 47 (2005) 172.
CR codes:HYDKIN
Fusion devices
TEXTOR (R=1.75 m), Jülich, GER
JET (R=2.96 m), Oxford, UK
ITER (R=6.2 m), Cadarache, FRA
joint: EU joint: world-wide
Fusion devices: typical edge transport code runtime
TEXTOR (R=1.75 m), Jülich, GER
JET (R=2.96 m), Oxford, UK
ITER (R=6.2 m), Cadarache, FRA
joint: EU joint: world-wide
1 day
1-2 weeks 3 months
Why become edge transport codes so slow for ITER sized machines?
(for same model, same equations, same grid size)
Because of more important plasma chemistry
(increased non-linearity, non-locality, in sources).
Advection -
diffusion reaction - diffusion
Continuity
equation
for
ions
and electrons
Momentum
balance
for
ions
and electrons
Energy balances
for
ions
and electrons
Fluid
equations
for
charged
particles
( )∂∂t
n n V Si i i ni+ ∇ ⋅ =r r
( ) ( ) ( )iiVmiiiiiiiiiiiii SRBVEenZpVVnmVnm
tr
rrrrrtrrrrrr++×++∏⋅∇−∇−=⋅∇+
∂∂
( )−∇ − + × + =r r r r r
p en E V B Re e e e 0
( ) iEeiiiiiiiii
iiiii
iiii SQVREZenqVVV
nmTnV
nmTn
t+−⋅−=⎥
⎦
⎤⎢⎣
⎡+⋅∏+⎟
⎠⎞
⎜⎝⎛ +⋅∇+⎟
⎠⎞
⎜⎝⎛ +
rrrrrtrrrr22
225
223
∂∂
∂∂t
n T n T V q en E V R V Q Se e e e e e e e i ei Ee3
252
⎛⎝⎜
⎞⎠⎟ + ∇ ⋅ +⎛
⎝⎜⎞⎠⎟ = − ⋅ + ⋅ + +
r r r r r r r
System of PDGL’s
with locally dominating sources:“diffusion-reaction-equations”
rather than pure CFD
Pfus
= 500 MWPheat
= 140 MW
Prad
= 30 MW
110MW
Divertor plates
Injected power (auxiliary heating: 40 MW) Fusion power 500 MW
α-heating + auxiliary heating 140MWLoss: Bremstrahlung+ Synchroton
Radiation 30MW
Power load withoutadditional radiation:
110MW
Wetted area: 2*U*width of strike zone
4.0 m2
(2 *40 * 0.05
)Power load ~ 25
MW/m2
Well above technical limit (10 MW/m2)
The power exhaust problem in fusion (ITER as example)
The problem results from the very small power SOL width (~ 0.5 cm)
•
Magnetic confinement is now effective enough to contain the main fusion flame, but it is too good for the plasma edge (SOL): very narrow heat-footprints on targets.
•
Magnetic Confinement Fusion Reactors must operate at reduced target fluxes and temperatures (“detached regime”).
•
n, T upstream (core) fixed by burn criteria, density limit, etc.
•
For ITER: Detached regime: decrease particle flux to target for given upstream conditions: self sustained neutral cushion (reactive plasma) controlled by PWI and A&M processes.
•
Divertor detachment physics involves a rich complexity of plasma chemistry not otherwise encountered in fusion devices .
Plas. Surf. Interact. & Plas.-Chemistry
Pfus ≈
540-600 MW⇒ He flux⇒ PSOL ≈86-120 MW
ns ≈(2-4)·1019
m-3
Sinj ≤
10·1022
s-1
Spump ≤
200 Pa·m-3/s
Zeff ≤1.6CHe ≤6%qpk ≤10 MW/m2
Provide
sufficient
convection
without
accumulating
tritiumand with
sufficiently
long
divertor lifetime
(availability).
Engineering parameter : Spuff ~ (1…13)·1022
s-1
!
?
Numerical tool for the edge plasma science:B2-EIRENE code package (FZJ-ITER)
B2: a 2D multi species (D+, He+,++, C1+..6+,…) plasma fluid code
EIRENE: a
Monte-Carlo neutral particle, trace ion and radiation transport code.
Plasma flowParameters
Source terms (Particle, Momentum, Energy)
Computational Grid
Self-consistent description of the magnetized plasma, and neutral particles produced due to surface and volume recombination and sputtering
see www.eirene.de
Reiter, D., et al., Fusion Science and Technology 47 (2005) 172.
CR codes:HYDKIN
ITER, B2-EIRENE simulation, fully detached, Te
field
hotter than 1 Mill deg.
ITER, B2-EIRENE simulation, detached, ne
field
1021
m-3
1019
-1020
m-3
ITER, B2-EIRENE simulation, detached, nA
field
1015
-1016
m-3
1020
m-3
ITER, B2-EIRENE simulation, detached, nH2
field
1021
m-3
PPFR
: average neutral pressure in Private Flux Region
ITER divertor engineering parameter: target heat flux
vs. divertor gas pressure
1996 (ITER physics basis1999)
2003, neutral -
neutral collisions
….+ molecular kinetics (D2
(v)+D+, MAR) 2005, + photon opacity
Consequences
for
ITER design
(B2-EIRENE): shift
towards
higher
divertor
gas pressure
to maintain
a
given
peak
heat
flux
(Kotov
et al., CPP, July
2006)
ITER design
review 2007-2009:
“Dome“
re-design now
ongoing
Compare: re-entry problems e.g. Space shuttle)
~10 MW/m2, for some minutes
10 MW/m2
stationary: perhaps tolerable, but not trivial
wallplasma
core
target
target
10 m
10 cm
recycling
Major radius
= 2-6 m(distance to torus
center)
Simple Model
B
Plasma flow
Gas flow
ASIDE: 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
resi
dual
(1/s
ec)
reseereseirescoresmo
Expected uncritical behavior, errors reduced exponentially to machineprecision.
Numerical Convergence errors 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
resi
dual
(1/s
ec)
resee resei resco resmo
B2 with analytic recycling model (without EIRENE),
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
resi
dual
(1/s
ec)
resee resei resco resmo
B2, R=0.3 B2-EIRENE, R=0.3
Code performance: serial, B2-EIRENE, ITER test case, Linux PC 3.4 GHz
(typical for all “micro macro models”
in computational science)
0.01
0.1
1
10
100
1000
10000
0 500 1000 1500 2000
no. of timesteps
resi
dual
(1/s
ec)
resee resei resco resmo
3h 15h150h =
6.25 days
10s per EIRENE call100s 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.
convergence behaviour of the coupled B2-EIRENE codesystem (2)
coupled B2-EIRENE calculation,recycling coefficient R=0.99
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
resi
dual
(1/s
ec)
resee resei resco resmo
coupled B2-EIRENE calculation,recycling coefficient R=0.3
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
resi
dual
(1/s
ec)
resee resei resco resmo
10s per EIRENE call
100s per EIRENE call
3 h15 h
low
recycling high recyclingConvergence in given CPU-time level depends on level of recycling (= vacuum pumping speed)
3 h
15 h
convergence behaviour of the coupled B2-EIRENE codesystem (3)
Total particle contentRecycling coefficient R=0.3
5.2E+20
5.3E+20
5.4E+20
5.5E+20
0 500 1000 1500
no. of timesteps
part
icle
con
tent
(#/m
**3)
Total particle contentRecycling coefficient R=0.99
5.2E+20
6.2E+20
7.2E+20
8.2E+20
0 500 1000 1500
no. of timesteps
part
icle
con
tent
(#/c
m**
3)
Total energy contentRecycling coefficient R=0.3
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
ergy
con
tent
electron energy
ion energy
Total energy contentRecycling coefficient R=0.99
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
ener
gy c
onte
nt
electron energy
ion energy
low
recycling
R=0.3
high recycling
R=0.99
“Is is enough to see one lion to know you are in a desert”
Code validation: in the presence of many still remaining free ad hoc parameters ?
One by One identification of controlling physics, implementation,code verification, even if direct experimental validation remainsdifficult.
A lesson learned, from C-Mod modelling, 2000-2006…..
Current hypothesis: in the “detached state”
is the divertor dynamics
and chemistry is controlled by “Collisionality”(inv. Knudsen number)
Estimate “Collisionality”: ne
R-ne
-Divertor Plasma density (×1020 m-3)-R-
Major Radius (m)
Alcator
C-Mod (MIT)10 times smaller than ITERsimilar shapehigher density
Factor
11away Factor
6 away
Dγ
(from D, D2
, D+,D2+):
Profile matched, but high by factor 2Calibration? Atomic Data? Plasma reconstruction?
Results very sensitive eg. to Te
profile
Critical for particle throughput (convection):
Neutral Plenum Pressure
Exp: 25 mTorrCalc 2D (2000) 3 mTorrCalc 2D (2003) 27 mTorr(better A&M data,better Plasma data,better codes)
Very good match: code -
experimentBut:Is there further edge physics that we are sure must be operative?
Additional leakage pathways:
2D 3D
Ionization by electron impact on neutral gas
Radiation transfer: opacity of Ly-lines(though completely elementary, has long remained unnoticed in edge modelling)
hν+H(1) H*, H*+e H+ 2e (additional path for ionization in dense, low Te
divertors)
H-ionization viaopacity effects
JET 10 %C-Mod 30 %ITER 90 %
Neutral Pressure
Exp: 25 mTorrCalc 2D (2000) 3 mTorrCalc 2D (2003) 27 mTorr(better A&M data,better plasma databetter codes)
Ly-opacity: 17 mTorr3D: 11 mTorr
However
Model validation in the presence of many free parameters:
include ALL edge physics that we are sure must be operative even while our capability to confirm these directly remains limited
High Intensity Discharge Lamps
CDM-75 WShop-LightingMaterial:PCA
D2-36 WAutomotive
Material:Quartz
B2B2--EIRENEEIRENE
4 m
m4 m
FIDAPFIDAP--EIRENEEIRENE
Radiation
transfer
module: verification
and validation
using
HID lamps
ITERITER
Computational Science Workflow “Waterfall Model” (1960-th…)
(the dream of code development managers)
1)
Requirement (e.g.: integrated fusion code for ITER)
2) Planning and design
3) Code (Programming)
4) Test
5) Run
Computational Science and Engineering is moving from “few effects”
codes developed by small teams (1-3 scientists) to “many effect codes”
codes developed by larger teams (10-20 or more).
The process is:•Very complex•Risky•Takes Long
The reality in large scale code development projects
Conclusions/Outlook
Similar to previous steps: progress to ITER is based mainly on experimental and empirical extrapolation
guided by theory and aided by modellingPresent 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)
• One and a half decade ago we lacked a credible solution to the divertor
problem.
3 questions
(as of any
applied
science)What
happens? How
can
we
make
the
application
work?Why
? (understanding
the
„What“)
We
now
have
enough
understanding
of „WHAT“
happens.(JET, Tore-Supra, D-IIID, ASDEX, LHD, W7AS,…..)to proceed with the „HOW“
(to build
ITER,…)Very
little
on the
„WHY“
question
still (maturity
of the
field).
Compare to similar situationafter first flights ofWright brothers
• With the discovery of the cold,detached, radiating divertor
inthe 1990s, we now have (themakings of) a divertor
solutionfor high power magneticconfinement devices.
sufficient
for
the
electricity
supply
for
a family
for
one
year
75 mg Deuterium
225 mg Lithium
can
be
found
in
2 litres
water
and
250 g rock
energy
content:
48 000 Millionen Joule
corrresponds
to
1 000 litres
oil
Fuel for Fusion
cheap
and accessible
worldwide
... a new
primary
energy
source
