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Edge-Plasma Modeling for Liquid Walls and Divertors
T.D. Rognlien, M.E. Rensink, & M. UmanskyLawrence Livermore National Lab
Presented at the ALPS/APEX Meeting
San Diego, CA
April 15-19, 2002
Outline
1. CLIFF design
2. NSTX module
3. CDX-U lithium wall
4. Spheromak design
5. ELM SOL transport
6 3D edge-plasma code development
Average impurity gas flux from wall (m s )-2 -1
Cor
e-ed
ge im
purit
y co
ncen
trat
ion
Temperature Limit Results
ITER slab: Tw = 390 CARIES-RS, uniform Tw: Tw = 450 C
ARIES-RS, noniform Tw: Tw_in=300 C, Tw_out = 480 CARIES-RS, noniform Tw, tilted plate, He incl. = 515 C
Wall temperature limit for flinabe (F) improvesfor full ARIES-RS tokamak geometry
Core-edgeimp. limit
Old ITER-sizedslab
ARIES-RSuniform Tw
ARIES-RSnonuif. Tw;fix Tin=300 C,vary Tout
Tiltedplatewith He
1021
1020
1018
1019
Ver
tical
pos
ition
(m
)
1019
1018
1017
1016
Major radius (m)
Ver
tical
pos
ition
(m
)
DT ion density
Fluorine ion density
Both hydrogenic and impurity densitiespeak near the divertor plates
ARIES-RS for CLIFF design
Helium ion density fairly broadly distributed,and helium gas is localized near outer plate
ARIES-RS for CLIFF design
Helium ion density
1019
1018
1017
1016
Ver
tical
pos
ition
(m
)
1019
1018
1017
1016
Major radius (m)
Ver
tical
pos
ition
(m
)
Helium gas density
Impurity radiation is dominated by fluorineand is strongest near the divertor plate
ARIES-RS for CLIFF design
Poloidal position (m)Top ofmachine
Divertor plate
Fluorine & helium
Hydrogen
80 MW input from core13 MW radiated by Fluorine 3 MW radiated by helium
Pow
er d
ensi
ty lo
st v
ia r
adia
tion
(W/m
)
UEDGE meshes used for NSTX module modeling differ inthe shape of the divertor surface (eqdsk 104312.00250)
R=0.9module
Mesh & module perpendicularto poloidal flux surfaces
Mesh & module conform toexisting divertor surfaces
R=0.9module
Orthogonal plates
Fit to divertors
Particle and energy fluxes to plate depend on detailsof plate orientation
Orthogonal plates
Fit to divertors
Density and temperature on outer plate depend on detailsof plate orientation
400
300
200
100
00 4 8 12
Power into SOL (MW)
Pea
k el
ectr
on te
mpe
ratu
re (
eV)
ncore = 8e19
ncore = 4e19
ncore = 2e19
ncore = 1e19 1/m**3
Power into SOL (MW)0 4 8 12
0
20
40
60
80
Pea
k he
at fl
ux (
MW
/m**
2)
ncore = 8e19
Various core-edge densities used as boundary conditions; n_sep ~ 0.6 ncore
UEDGE simulations of NSTX single null with pumpingmodule 2 cm beyond separatrix on outer plate
Impurity radiation is neglected; module aligned to divertor plate
Peak heat flux on outer plate Peak Te on outer plate
ne ~ 1/Te
0 4 8 120
0.5
1.0
1.5
Power into SOL (MW)
Pea
k io
n de
nsity
, out
er p
late
(10
m
)
20-3
Peak ni on outer divertor plate
ncore = 1e19 1/m**3
ncore = 2e19
ncore = 4e19
ncore = 8e19
0 4 8 120
4
8
12
Power into SOL (MW)
Mod
ule
pum
ping
rat
e (1
0
/s)
21
Module pumping rate
Divertor density usually about twice the separatrixdensity owing to the pumping module (R=0.9)
Divertor density peaks outside of Te maximum
For fixed ncore, divertor density increases by factor of ~3 for no pumping
Major radius (m)
Ver
tical
pos
ition
(m
)
CDX-U meshup/down symmetry assumed
CL
Ion density shows little change untilwall recycling coefficient Rw > 0.5
R = 1w
0.98
0.9
0.6
0
5
4
3
2
1
0
Ion
dens
ity (
10
m
)19
-3
-12 -8 -4 0Distance from wall (cm)
Magneticaxis
wall
0.2
Ion and electron temperatures changeinversely to ion density as Rw is varied
R = 1w
0.98
0.9
0.6
0
200
100
0
Ion
tem
pera
ture
(eV
)
R = 1w
0.98
0.9
0.6
0
0-12 -8 -4 0
Distance from wall (cm)Magneticaxis
wall
Ele
ctro
n te
mpe
ratu
re (
eV)
200
100
Ion and electron temperatures decrease with wall recycling, Rw
The total plasma pressure, n (T + T ), changeslittle as R is varied.
eiw
i
R = 1w
0.98
0.9
0.6
0400
200
0
Ion
+ el
ectr
on te
mpe
ratu
res
(eV
)
-12 -8 -4 0Distance from wall (cm)
Magneticaxis
wall
T + Tei
0.2
Total plasma pressure, n (T + T ), changeslittle as R is varied.
eiw
i
R = 1w
0
3000
2000
0-12 -8 -4 0
Distance from wall (cm)Magneticaxis
wall
Pla
sma
pres
sure
(N
wt/m
)2
1000
n (T + T )ei i
Thick liquid-walled spheromak magnetic fusion power plant
R. W. Moir, R. H. Bulmer, T. K. Fowler, T. D. Rognlien, M. Z. Youssef
April 8, 2002
Abstract
We assume a spheromak configuration can be made and sustained by a steadygun current, which injects particles, current and magnetic field, i.e., helicityinjection. The equilibrium is calculated with an MHD equilibrium code, where anaverage beta of 10% is found. The toroidal current of 40 MA is sustained by aninjection current of 100 kA (125 MW of gun power). The flux linking the gun is1/1000th that of the flux in the spheromak. The geometry allows a flow of liquid,
either molten salt, (flibe–Li2BeF4 or flinabe–LiNaBeF4) or liquid metal such as
SnLi which protects most of the walls and structures from neutron damage. Thefree surface between the liquid and the burning plasma is heated bybremsstrahlung and optical radiation and neutrons from the plasma. Thetemperature of the free surface of the liquid is calculated and then theevaporation rate is estimated. The impurity concentration in the burning plasmais estimated and limited to a 20% reduction in the fusion power. For a high
radiating edge plasma, the divertor power density of 460 MW/m2 is handled by
high-speed (20 m/s), liquid jets. For low radiating edge plasmas, the divertor-
power density of 1860 MW/m2 is too high to handle for flibe but possibly
acceptable for SnLi with jets of 100 m/s flow speed. Calculations show the
tritium breeding is adequate with enriched 6Li and appropriate design of the
walls not covered by flowing liquid 15% of the total). We have come up with anumber of problem areas needing further study to make the design selfconsistent and workable.
2
Table of contentsTable of contents .............................................................................................................2
Introduction and background ...........................................Error! Bookmark not defined.Configuration-equilibria ..................................................Error! Bookmark not defined.Plasma parameters...........................................................Error! Bookmark not defined.Current Drive Model .......................................................Error! Bookmark not defined.Electrode design ..............................................................Error! Bookmark not defined.Insulator design ...............................................................Error! Bookmark not defined.Power plant considerations ..............................................Error! Bookmark not defined.Liquid wall design...........................................................Error! Bookmark not defined.Divertor design................................................................Error! Bookmark not defined.Edge plasma analysis.......................................................Error! Bookmark not defined.Tritium breeding analysis ................................................Error! Bookmark not defined.Conclusions and discussion .............................................Error! Bookmark not defined.Acknowledgments...........................................................Error! Bookmark not defined.References.......................................................................Error! Bookmark not defined.
Radial position
Den
sity
, ene
rgy
Sep.
Enhanced diffusion
Den
sity
, ene
rgy Localized
enhanced convection
Sep.
Den
sity
, ene
rgy Added SOL
density, eng.
Sep.
Pedestal Sol
ELM ejection can be modeled various ways
Or 3D turbulence model
Poloidal distribution may also be important
Poloidal distance
Den
sity
, ene
rgy
Midplane Divertor
E p
Midplane density and Te profiles broadeninto SOL with diffusive ELM modelDIII-D case with s.s. power to edge of 4 MW, ExB on,recycling R=0.99
t = 50 µs
100 µs
150 µs
300
200
0
Te
(eV
)
-2 -1 0 1 2 3Distance from separatrix (cm)
0Separatrix
Den
sity
(10
m
)
19-3
Core SOL
100
1
2
3 D, χ = 10 m /s2
Midplane density and Te profiles shift toSOL with convective ELM modelDIII-D case with s.s. power to edge of 4 MW, ExB on,recycling R=0.99
10 µs20 µs
30 µs
400
200
0-2 -1 0 1 2 3
Te
(eV
)
Distance from separatrix (cm)
t = 0
0
1
2
3
Separatrix
Den
sity
(10
m
)
19-3
v_conv = 300 m/s
Core SOL
Ejection phase for convective model
Change in density peaks near the outermidplane during ejection
Flux surface 0.8 cm outsideseparatrix at outer midplane
Poloidal distance (m)
t = 0 µs
t = 30 µs
X-pt1 2 3 4 5
Ion
dens
ity (
10
m
)19
-3
0
1
2
Outermidplane
0 1 2 3 4 5Poloidal distance (m)
Innerdivertor
Outerdivertor
0
200
400
Ele
ctro
stat
ic p
oten
tial (
V)
t = 0 µs
t = 10 µs
t = 20 µs
t = 30 µs
X-ptX-pt
Ejection phase for convective model
SOL potential rises rapidly as hotterelectrons are ejected from core
Flux surface 0.2 cm outsideseparatrix at outer midplane
Ejection phase for convective model
Radial ExB velocity can exceed 200 m/sduring the ejection phase
Poloidal distance (m)
0
200
Rad
ial E
xB v
eloc
ity (
m/s
)
t = 10 µs
t = 20 µs
t = 30 µs
X-pt
Flux surface 0.2 cm outsideseparatrix at outer midplane
5.2 5.4 5.6 5.8
-200
100
-100
Expanded viewnear X-point
Outer divertor plate heat-flux similar withand without ExB terms
DIII-D case using localized convection ELM ejection modelSteady-state power is 4 MW into SOL, recycling R=0.99
0
20
40
0
20
40
60
-2 0 2 4 6 8
Distance from separatrix (cm)
with ExB
without ExB
10 µs
50 µs
200 µs
10 µs
50 µs
200 µs
Hea
t flu
x (M
W/m
)
2H
eat f
lux
(MW
/m
)2
3 ms
3 ms
Summary
- Convective or diffusive ejection model lead to similar SOL response
- Energy per pulse is important for whether or not inner plate receives significant ELM power
- ExB drifts are strong during the ELM pulse in the divertor leg
- when starting from same post-ejection state, heat flux profiles are quite similar; larger effect
on density
- comparing ejection phase, ExB case has substantially lower plate density, and longer time-scale for heat
flux deposition
- So far, the modeled ELM size has been small; we expect ExB to be stronger for large ELMs and will study these
Summary
Analysis of wall evaporation for flinabe in ARIES (CLiFF)shows surface outlet temperature limits
- 480 C for an orthogonal plate- 510 C for a tilted plate
Parameter scans for divertor-plasma conditions in NSTXshow substantial heat loads & provide input to WBC
Initial full-plasma transport simulations for CDX-U showimpact of transition from low to high recycling edge
Characterization of edge-plasmas during ELMs hasbegun
3D transport simulations with BORIS code will allownon-axisymetric edge assessment for liquid modules
Complete a detailed report for the integration of liquidwall system in a spheromak power-plant
