Tokamak 3D Heat Load Investigations Using an Integrated Simulation Framework: HEAT
T. Looby�Nov. 29 2021
This work is supported in part by U.S. Department of Energy Awards: DE-AC05-00OR22725 & DE-AC02- 09CH11466
TABLE OF CONTENTS
HEAT gyro-orbit physics
Goals for the future
The need for 3D PFC integrated modeling
Example HEAT gyro-orbit investigations
H.E.A.T.
Example HEAT investigations
04
06
01
05
02
03
2
The need for 3D PFC integrated modeling
01
3
The tokamak wall is the interface between fusion plasmas and many tokamak systems
4
Interface!
High power tokamaks push the plasma facing components (PFCs) to their engineering limits
5
J. W. Coenen et al., Phys. Scr., vol. T170, p. 014013, Dec. 2017, doi: 10.1088/1402-4896/aa8789.
R. Neu et al., Journal of Nuclear Materials, vol. 511, pp. 567–573, Dec. 2018, doi: 10.1016/j.jnucmat.2018.05.066.
R. A. Pitts et al., Nuclear Materials and Energy, vol. 20, p. 100696, Aug. 2019, doi: 10.1016/j.nme.2019.100696.
A. Q. Kuang et al., Journal of Plasma Physics, vol. 86, no. 5, p. 28, doi: 10.1017/S0022377820001117.
JET (intentional)
ASDEX-U (unintentional)
Tungsten melting examples:
ITER
Extreme heat flux examples:
SPARC
PFC design engineers manage high heat loads via 3D shaping of the PFC surfaces
6
Bevel
Fish-scale
2
1
3
Castellations
Chamfer
HEAT FLUX
ITER
JET ILW
NSTX-U
T. Looby et al., Fusion Science and Technology. In press. 2021
NSTX-U Recovery PFCs employ a castellated graphite design to mitigate heat loads
7
IBDV
CSAS
OBD
IBDH
NSTX-U Lower Divertor
IBDH Tile
Single Castellation
Fish-scale protects toroidally facing leading edges from high angle of incidence heat fluxes
8
Note step between castellations (fish-scale)
Heat Flux
Prototype NSTX-U PFC Front View
ɸ
Side View
3D geometry creates magnetic shadows in toroidal direction (missed with axisymmetric model)
9
Ignoring magnetic shadows loads entire PFC surface
Including magnetic shadows decreases loaded surface area by >55%
toroidal direction
Note: these results for high flux expansion case where angle of incidence ~ 1°
IBDH
Tile
IBDH
Tile
IBDH
Tile
The Heat flux Engineering Analysis Toolkit (H.E.A.T.)
02
10
Each Plasma Facing Component (PFC) interfaces to many systems and physical domains
11
PFC
Cooling System
Mechanical / Fastener System
Coolant
Magnet System
Vacuum System
Plasma Physics, MHD, Turbulence, E&M,
ELMs,
Fast Particle Losses,...
Sheath physics, material transport, recycling, PKA effects,...
Boundary physics, heat flux, gyro orbits, radiated power,
blobs & filaments,...
Material properties / limits, radiation effects, temperature / stresses,...
Example PFC Design and Physics Space (many domains omitted)
Core
SOL
Sheath
Tokamak PFC analysis requires interfacing many complex simulation systems
12
3D MHD EQ (M3D-C1)
2D MHD EQ (EFIT)
Field Line Tracer (MAFOT)
Fast Ion Tracer �(SPIRAL)
Parametric CAD Software (Solidworks)
Design Optimization Algorithms
Finite Volume Solver �(ANSYS)
Boundary Plasma Physics
(SOLPS)
Gettering and Redeposition
CFD Software (openFOAM)
Synthetic Diagnostic Simulator
User Interface
Data Visualization
Grad - Shafranov Solvers (FreeGS)
Neutronics (MCNP)
Machine Learning (tensorflow)
Physics Codes:
Engineering Codes:
Visualization Codes:
Control Algorithms
Control and AI Codes:
+ many more…!
The Heat flux Engineering Analysis Toolkit couples MHD EQ, CAD, physics, visualization, and more
13
CAD
HTML GUI
MHD
HEAT FLUX SIMULATOR
FVM
STP / CAD
(from Engineer)
EFIT (MDS+),
GEQDSK,
M3DC1*,
SIESTA*,
VMEC*
grid
EQ
q(x,y,z,t)
PHYSICS
T(x,y,z,t)
Scalings, Models, �etc.
Material Properties
New Physics
+
The Heat flux Engineering Analysis Toolkit couples MHD EQ, CAD, physics, visualization, and more
14
CAD from engineer
MHD EQ (time varying) from plasma physicist
Heat flux (time varying) calculated on CAD surface
Temperature (time varying) solved thru CAD volume
HEAT’s sleek HTML5 user interface enables it to be run headless on a Local Area Network (LAN)
15
ip address for your network here
HEAT users follow simple GUI steps to generate heat load predictions
16
+
=
Step 1: user loads MHD Equilibrium, can correct EQDSK formatting errors, or stitch together a sweep
17
Step 2: user loads CAD in STP (ISO 10303-21) format, and HEAT meshes CAD according to user specs
18
Example 5 mm maximum edge length
Step 3: user defines Region of Interest (ROI) and potential Intersection PFCs that could cast shadows
19
Intersects
ROI
Power Flow
Lower NSTX-U divertor view from core
Step 4: HEAT calculates magnetic shadows via the MAFOT magnetic field line tracing code
20
Intersection face
Field line trace
Shadowed point
upstream tile
downstream tile
gap
Shadowed point
Shadowed points identified by checking for intersections with other mesh elements
upstream tile
downstream tile
MAFOT: A. Wingen, et al, “High resolution numerical studies of separatrix splitting,” Nucl. Fusion, p. 9, 2009.
Step 5: HEAT calculates the optical heat flux to each mesh center, creating a heat flux point cloud
21
Example shown for maximum mesh edge length of 2 mm
Step 6: HEAT calculates the gyro-orbit heat loads for ions with finite Larmor radii
22
Helical gyro orbit trace�for T=100 eV
Optical field line trace
Step 7: HEAT calculates temperatures using an internal finite volume solver (openFOAM)
23
HEAT is open source under the MIT license and available to users via an appImage for Linux
24
Github:
https://github.com/plasmapotential/HEAT
Tutorials:
https://heat-flux-engineering-analysis-toolkit-heat.readthedocs.io/en/latest/
Within 9 months of v1 release, HEAT appImage users are popping up all over the fusion community:
Example HEAT Investigations
03
25
HEAT was used to revisit NSTX-U Recovery PFC working group analyses
26
BT = 1T
Ip = 2MA
∠ @ peak = 0.86°
Profile: Gaussian Spreading
λq = 1.903mm (Eich #15)
S = 0.914 mm (Makowski #6)
Max Mesh Edge Length: 3 mm
PSOL = 3.5 MW
Psum = 3.582 MW
IBDH
OBD
IBDV
CSAS
OBD
IBDV
CSAS
IBDH
Using HEATs time varying 3D capabilities enables the determination of PFC operational limits
27
Probe �Locations
IBDH
OBD
R
ɸ
Both PFCs sublimate in this operational scenario. Results for Psol = 7MW, fully attached
T. Looby et al., Fusion Science and Technology. In press. 2021
Using HEATs time varying 3D capabilities enables the determination of PFC operational limits
28
Probe �Locations
IBDH
OBD
R
ɸ
Both PFCs sublimate in this operational scenario. Results for Psol = 7MW, fully attached
T. Looby et al., Fusion Science and Technology. In press. 2021
PFCs constrain tokamak operational scenario!
HEAT couples directly to engineering solvers for time varying temperature and stress predictions
29
Time varying analysis enables maximization of the allowable tokamak operational space
30
T. Looby et al., Fusion Science and Technology. In press. 2021
10Hz strike point sweep frequency enables this magnetic scenario to run for 3.36s before engineering limit is reached
Time varying analysis enables maximization of the allowable tokamak operational space
31
T. Looby et al., Fusion Science and Technology. In press. 2021
10Hz strike point sweep frequency enables this magnetic scenario to run for 3.36s before engineering limit is reached
Time varying plasma extends shot duration.
HEAT can quantify the extension.
HEAT is currently being validated against experimental data from ST40
32
Real IR Camera
HEAT Prediction
ST40 Inner Wall Limiter
HEAT gyro-orbit physics
04
33
Refresh your memory on the region of interest: �the IBDH tile and castellations
34
IBDV
CSAS
OBD
IBDH
NSTX-U Lower Divertor
IBDH Tile
Single Castellation
A new ion gyro orbits module calculates the helical trajectories of ions with finite Larmor radii
35
CAD mesh triangles
helical gyro orbit trace
magnetic field line trace
optical strike location
gyro-orbit strike locations
view
ɸ
ɸ
Gyro orbit trajectories determined via forces and equations of motion
36
From Newton’s Law / Lorentz Force, neglecting electric fields:
Solving yields the equations of motion:
Equations of motion contain 3 unknown variables that must be sampled to simulate trajectories
37
Gyro phase angle
Total Speed
Velocity phase angle
Gyro phase angle, is the initial angle of the particle with respect to magnetic field, sampled uniformly
38
Example Field Line + Helical Trace:
𝛼 = 0
𝛼 = 3𝝅/2
NgP = 5
Total speed is sampled from Maxwellian such that energy integrals of bins are equal (v is bin center)
39
NvS = 3
Velocity phase angle defines the energy sharing between v⟂ and v||, sampled uniformly
40
NvP = 4
*Note that here (ex,ey,ez) represent a coordinate system local to the magnetic field line
GyroSourcePlane is used to launch macro-particles
41
Mesh triangle, j, on gyro source plane
Mesh triangle, i, on ROI PFC
Gyro orbit module maps power from j to i using the helical trajectories of ions as the mapping function
Each macro-particle carries a fraction of the pseudo-optical power
42
Power for macro-particle (j,k,l,m)
Pseudo-optical power at mesh element j
Fraction of PSOL that ions carry
Fraction of this gyro phase angle, k
Fraction of this velocity phase angle, l
Fraction of this velocity slice, m
j
j is launch element of macroparticles
i
(NgP, NvP, NvS) = (k,l,m): defines macro-particle
Sum of all macro-particle powers that land on a mesh element, i, is the gyro-orbit power
43
j
i
Where:
Convergence tests were performed to ensure that gyro-orbit algorithm is robust
44
variables are (NgP, NvP, NvS)
Increasing number of macro-particles causes 3D heat flux profiles to converge to ‘ground truth’
45
Here, (5,5,5) is ‘ground truth’
Example HEAT gyro-orbit investigations
05
46
Research for ITER has been performed that does 1-2 Dimensional gyro orbit calculations
Komm
Gunn
J. Gunn et al “Surface heat loads on the ITER divertor vertical targets,” Nuclear Fusion, 2017
M. Komm et al “Particle-in-cell simulations of the plasma interaction with poloidal gaps in the ITER divertor outer vertical target,” Nuclear Fusion, 2017
For comparison to existing research, a test case was created in HEAT
48
HEAT calculates gyro-orbit and optical heat loads on test case CAD then defines 1D chords
49
Comparing against previous 1D research is useful for HEAT benchmarking
50
HEAT
HEAT
Komm
Gunn
J. Gunn et al “Surface heat loads on the ITER divertor vertical targets,” Nuclear Fusion, 2017
M. Komm et al “Particle-in-cell simulations of the plasma interaction with poloidal gaps in the ITER divertor outer vertical target,” Nuclear Fusion, 2017
T. Looby et al, “3D Ion Gyro-orbit Heat Load Simulations Using Engineering CAD Geometry for NSTX-U” Nuclear Fusion, Pending Submission. 2021
Comparing against previous 1D research is useful for HEAT benchmarking
51
HEAT
HEAT
Komm
Gunn
J. Gunn et al “Surface heat loads on the ITER divertor vertical targets,” Nuclear Fusion, 2017
M. Komm et al “Particle-in-cell simulations of the plasma interaction with poloidal gaps in the ITER divertor outer vertical target,” Nuclear Fusion, 2017
T. Looby et al, “3D Ion Gyro-orbit Heat Load Simulations Using Engineering CAD Geometry for NSTX-U” Nuclear Fusion, Pending Submission. 2021
HEAT can reproduce existing research
Refresh your memory on the region of interest: �the IBDH tile and castellations
52
IBDV
CSAS
OBD
IBDH
NSTX-U Lower Divertor
IBDH Tile
Single Castellation
Gyro-orbit heat flux differs from the optical heat flux in shadows and on edges and corners
53
Shadow
No Shadow
Hot Corners
Cool Corners
ɸ
ɸ
Optical
Gyro-obit
T Looby et al, “3D Ion Gyro-orbit Heat Load Simulations Using Engineering CAD Geometry for NSTX-U” Nuclear Fusion, Pending Submission. 2021
Plotting along toroidal and poloidal chord can yield insight into heat loading footprints
54
ɸ
Spol
Stor
1.0mm
Gyro-orbit heat flux can access regions designed to be protected by castellation fish-scales
55
Stor>0
Stor>0
ɸ
Top Surface
Gyro-orbit heat flux loads both poloidally facing edges, favoring side that aligns with gyro helicity
56
Spol>0
ɸ
Spol>0
Top Surface
HEAT temperature analysis can be applied to determine PFC thermal state
57
Optical
Optical
Optical
Gyro
Gyro
Gyro
Temperature difference between gyro-orbit and optical heat loads is small
58
Peak PFC Temperature [K]
These results for PSOL, Outer = 4.9 MW
2.21s
2.37s
2631K
2720K
Optical
Gyro-orbit
Shadow filling effect enhanced with increasing plasma temperature
59
Optical Approximation
Gyro Approximation� @ Ti = 10 eV
Results for Psol = 4.9MW with 27 (3,3,3) macroparticles
Gyro Approximation �@ Ti = 100 eV
Ti is temperature used to define Maxwellian speed distribution
Shadow filling effect enhanced with increasing plasma temperature
60
Optical Approximation
Gyro Approximation� @ Ti = 10 eV
Results for Psol = 4.9MW with 27 (3,3,3) macroparticles
Gyro Approximation �@ Ti = 100 eV
Ti is temperature used to define Maxwellian speed distribution
Gyro-orbits enhance PFC performance!
Goals For the Future
06
61
Integrated design, analysis, diagnostic, and ML loops
62
HEAT
New physics models
Diagnostics
Machine Control System
HEAT prediction database
Reduced Model AI Algorithms
CAD Generation
AI Optimization Algorithms
Run Experiment
Exper. Research
Engineering Design
Control
HEAT Framework
Inverse prediction
Conclusions
63
Publication and conference list
64
Questions
NSTX-U graphite PFCs are thermally limited at 1600°C
66
8 MW/m2 heat flux applied to SGLR6510 surface for 5s pushes material past sublimation limit
NSTX-U graphite has a engineering limit of ~ 1600°C
NSTX-U Recovery PFC working group understood this limit, but lacked the tools to check physics scenarios against PFC sublimation
PFC temperature can constrain physics scenarios!
PFC performance can be degraded by changes in interfaced systems designed separately
67
Intended Design
As Built
PFC shifted +z by ½ inch!
Z
R
Peak edge HF ~246 MW/m2
Manufacturing error in NSTX-U vacuum vessel results in OutBoard Divertor PFC getting shifted 0.5 inches into the plasma. Exposes leading edge!
Calculation only possible with 3D heat flux predictions interfaced to CAD
HEAT software architecture flow chart
68
dashGUI.py
GUIclass.py
MHDClass.py
CADClass.py
pfcClass.py
heatfluxClass.py
openFOAMclass.py
toolsClass.py
GEQDSK
STP file
PFC file
HEAT Input File
Web browser
User Interface
HEAT Core Modules
Input Files
Yellow / dashed boxes are shared memory between all classes
gyroClass.py
Blue / dotted boxes are user input files
Linux terminal
terminalUI.py
(under dev.)
Existing integrated PFC frameworks exist, but are limited in scope and not open source
69
Runner up: SMITER
L. Kos et al., Fusion Engineering and Design, 2019
HEAT employs state-of-the-art ray-triangle intersection algorithms and acceleration structures
70
These w/ MPI parallel code, enable 1 million mesh faces to be checked in ~5 minutes on 6 CPUs for 10° trace
Möller-Trumbore ray-triangle intersection xfm to barycentric coordinates:
Möller, Tomas; Trumbore, Ben (1997). "Fast, Minimum Storage Ray-Triangle Intersection". Journal of Graphics Tools. 2: 21–28.
Dimensionality reduction acceleration structure to filter potential intersects:
Acceleration structures increase speed by more than 10X for some cases (more with 𝜓 filter)
71
Result while holding intersects fixed
# of Intersects: 68094
Result while holding ROI fixed
# of ROIs: 22628
Intersection trace length, error %, and simulation time, must all be balanced based on user objective
72
HEAT has been ported to 5 tokamaks: NSTX-U, DIII-D, ST40, STEP, SPARC*
73
*SPARC not shown for IP reasons
NSTX-U Rec.
STEP/DEMO
DIII-D �negD
ST40 2.2
HEAT has a parametric CAD program built into the CAD python module. Can be used for design.
74
FreeCAD is an open source parametric CAD modeler. https://www.freecadweb.org/
HEAT’s python wrapper uses FreeCAD for:
HEAT uses openFOAM for Finite Volume Methods (FVM) and Computational Fluid Dynamics (CFD)
75
openFOAM is an open source package for:
https://www.openfoam.com/releases/openfoam-v1712/
HEAT uses openFOAM to:
ParaView is under the hood of HEAT’s powerful visualization algorithms
76
Global water surface temp by LANL
openFOAM “motorbike” tutorial by NVIDIA
Images from ParaVIEW website gallery
ParaVIEW is an open source package (originally from LANL) for:
HEAT uses ParaView to:
SImulation objective determines the validity of ignoring electric fields. Work for ITER confirms
77
M. Komm et al 2017 Nucl. Fusion 57 126047
Gyro orbit trajectories determined via equations of motion
78
Integrating equations of motion yields helical trajectories:
Using the following relationships:
Highly non-axisymmetric ST40 divertor heat loads are being simulated with HEAT
79
TE EQ009
150 ms discharge
HEAT is being used to simulate divertor heat loads for the DIII-D negD discharges
80
Outer Divertor qpeak ~ 10.2 MW/m2
Inner Divertor qpeak ~ 5.15 MW/m2
HEAT is being used to simulate divertor heat loads for the DIII-D negD discharges
81
R
Outboard side of new PFC gets loaded with a peak of ~ 4.5 MW/m2 on corner
UTK DIII-D DiMES head RFEA is being designed using HEAT optical + gyro orbit simulations
82
Peak for DiMES head is around 127 MW/m2 on edge, but remember this is a mesh (flat triangular faces)
Peak for RFEA holder is around 380 MW/m2
DiMES Head
RFEA Insert
Slit for grid access
UTK DIII-D DiMES head RFEA is being designed using HEAT optical + gyro orbit simulations
83
EU-DEMO / STEP teams are using HEAT to predict HEAT loads
84
Psum, wall ~ 2.75 MW
Psum, divertor ~ 44.17 MW
λq = 50mm; S = 0.1mm; Max Mesh Edge Length = 20mm
qpeak = 1.80 MW/m2
qpeak = 2.02 MW/m2
Inner Divertor
HEAT has been compared to SMARDDA output for EU-DEMO
85
SMARDDA
HEAT
Many other projects have utilized HEAT in some capacity over the past year
86
HEAT can predict heat loads for limited discharges
87
Profile Type: Limiter
λq, near= 3mm
% Power Near: 90%
λq, far = 1mm
% Power Far: 10%
PSOL = 2 MW
Psum = 1.928 MW
Max Mesh Edge Length: 2 mm
SImulation objective determines the validity of ignoring electric fields. Work for ITER confirms
88
M. Komm et al 2017 Nucl. Fusion 57 126047
NSTX-U presents a unique opportunity to study ion gyro orbit heat fluxes for ITER full field ELMs
89
ITER ELM Scenario*:
Magnetic Field ~ 8 T
Ion Temperature ~ 5 keV
Effective Mass ~ 2.5 AMU
Gyro Radius ~ 1.5 mm
NSTX-U Scenario to ~Match:
Magnetic Field ~ 1 T
Ion Temperature ~ 100 eV
Effective Mass ~ 2.0 AMU
Gyro Radius ~ 1.6 mm
*ELM parameters taken from J. P. Gunn, Nuclear Materials and Energy, p. 9, 2017.
NSTX-U has castellated graphite PFCs that can be used to experimentally validate gyro orbit physics models for the ITER tungsten monoblocks!
Primary goals for HEAT (and Tom)
90