1. Development and validation of numerical models for the optimization of magnetic field configurations in fusion devices
Nicolò Marconato
Consorzio RFX, Euratom-ENEA Association, and
University of Padova, Italy
8 October 2009, European Doctorate in Fusion Science and Engineering

2. Two different activities:
Activity plan
Two different activities:
Magnetic analysis for the optimization of the magnetic configuration of the SPIDER device (1st year)
Improvement of the numerical model of the RFX-mod passive structure in the finite element CARIDDI code (2nd & 3rd year)
8 October 2009, European Doctorate in Fusion Science and Engineering

3. First activity outline
Introduction to ITER NBI & SPIDER description
Optimization of SPIDER magnetic configuration
3D verification & Ion deflection compensation
Conclusions & Foreseen activities
8 October 2009, European Doctorate in Fusion Science and Engineering

4. Introduction to ITER NBI
Neutral Beam
Negative Ion Beam
High Voltage Bushing
Calorimeter
Residual Ion Dump
Neutralizer
Negative
Ion Source
ITER main parameter:
Q (Fusion Energy Gain Factor)>10
Ion beam composition: H-, D-
Heating Power by Neutrals: 16.7 MW
Accelerated Ion Power: 40 MW
Ion current: 40 A
Ion current Density: 200 A/m2
Total voltage: 1 MV
H&CD for ITER
Neutral Beam Injectors
Radio Frequency Antennas
8 October 2009, European Doctorate in Fusion Science and Engineering

5. Eb=Eb(a, np) ITER NBI: Eb = 1 MeV
Neutral Beam Heating and Current Drive System: issues
Eb=Eb(a, np)
Physics issue
Neutral Beam Energy needed depends on minor radius a and plasma density np
ITER NBI: Eb = 1 MeV
Physics/Technological
issue
Positive-ion-driven neutral beams lose their efficiencies above 100 keV
Negative-ion-driven neutral beams maintain their efficiency up to energies on the order of 1 MeV
Positive ion technology will not scale favorably into the reactor regime and current research is focused on developing high-energy negative ion sources
Neutralization fraction vs. beam energy for positive and negative ion beams
8 October 2009, European Doctorate in Fusion Science and Engineering

6. inside the vacuum vessel
SPIDER: Source for Production of Ion of Deuterium Extracted from RF plasma
vacuum vessel
electrical bushing
beam source
pumping port
calorimeter
hydraulic bushing
beam tomography
source spectroscopy
beam source
inside the vacuum vessel
Ion Current Density: 200 A/m2
Ion Current: 40 A
Total Voltage: 100 kV
8 October 2009, European Doctorate in Fusion Science and Engineering

7. Reference design[1] - 1 -112 kV -100 kV 0 V
[1] ITER Technical Basis 2002, “Neutral beam heating & current drive (NB H&CD) system”, Detailed Design Document (section 5.3 DDD5.3) (Vienna: IAEA)
8 October 2009, European Doctorate in Fusion Science and Engineering

8. Reference design[1] - 2
Magnetic field necessary for avoiding acceleration of co-extracted electrons and consequent reduction of efficiency and increase of thermal loads.
Two different contributions:
Filter field: horizontal (Bx) across PG, produced by magnets and PG current
Suppression field: vertical (By) across EG, produced by magnets PG
PG current y
magnets z x EG
magnets
[1] ITER Technical Basis 2002, “Neutral beam heating & current drive (NB H&CD) system”, Detailed Design Document (section 5.3 DDD5.3) (Vienna: IAEA)
8 October 2009, European Doctorate in Fusion Science and Engineering

9. Motivation and Definition of Magnetic Problemx
Magnetic field profile of the reference configuration[1] (PG current and filter magnets)
poor uniformity in plasma source
increase of co-extracted electrons
large magnetic field downstream
deflection of negative ions
Possible approaches:
ferromagnetic material:
in Bias Plate
in Plasma Grid
in Grounded Grid
different paths for PG current
bias plate PG EG GG z
8 October 2009, European Doctorate in Fusion Science and Engineering

10. Filter Field optimization: 2D models
Return conductor
Magnetic shield
4 kA PG current
Single return conductor
Permanent magnets
Magnetic shield
Line of
symmetry
Reference
configuration x z
Source walls
Filter field magnet
Grids
Plasma Grid
(forward conductor)
8 October 2009, European Doctorate in Fusion Science and Engineering 10

11. Filter Field optimization: 2D models
Return conductor
3 kA PG current
2 x 1.5 kA lateral conductors
Soft iron sheet behind GG
Subdivided current return path
No permanent magnets
No magnetic shield
Magnetic shield
4 kA PG current
Single return conductor
Permanent magnets
Magnetic shield
Line of
symmetry
Reference
configuration x
Optimized configuration
Return conductors z
Line of
symmetry
Source walls
Source walls
Filter field magnet
Lateral forward
conductor
Grids
Grids
Plasma Grid
(forward conductor)
Plasma Grid
(forward conductor)
Ferromagnetic
layer
8 October 2009, European Doctorate in Fusion Science and Engineering 11

12. Filter Field optimization: 2D models
Return conductor
3 kA PG current
2 x 1.5 kA lateral conductors
Soft iron sheet behind GG
Subdivided current return path
No permanent magnets
No magnetic shield
Magnetic shield
4 kA PG current
Single return conductor
Permanent magnets
Magnetic shield
Line of
symmetry
Reference
configuration x
Optimized configuration
Return conductors z
Line of
symmetry
Source walls
Source walls
Filter field magnet
Lateral forward
conductor
Grids
Grids
Plasma Grid
(forward conductor)
Plasma Grid
(forward conductor)
Ferromagnetic
layer
Bias Plate
Plasma Grid
Extraction
Grid
Grounded
Grid
Ferromagnetic layer
8 October 2009, European Doctorate in Fusion Science and Engineering 12

13. Space distribution of Bx along a beamlet
Bx (mT)
Optimized
configuration
Reference
configuration
Grounded
Grid
Ferromagnetic layer
Plasma
Grid
Plasma
source
z (mm)
8 October 2009, European Doctorate in Fusion Science and Engineering

14. 2D model limits View of the SPIDER filter field source assembly
However, 2D "infinite slab" models cannot account for the local 3D configuration due to grid holes and edge effects.
An assessment of the
validity and limits of the proposed solutions in real 3D geometry was advisable for:
accurate Ion trajectory calculation
detailed thermal loads prediction
View of the SPIDER filter field source assembly
8 October 2009, European Doctorate in Fusion Science and Engineering

15. 3D model: issues very high number of elements (nodes)
Complex geometry, presenting large dimensions (whole grids) and details of little dimensions (single beamlet)
very high number of elements (nodes)
large amount of memory used
high computational time
Particular attention to the mathematical formulation used because of the presence of both electric currents and ferromagnetic materials in the same domain:
magnetic vector potential formulation is good in presence of electric currents, but can give errors in the regions with different permeability
magnetic scalar potential formulation is good in the regions with different permeability, but cannot be used with complex current density distributions
8 October 2009, European Doctorate in Fusion Science and Engineering

16. Simplified global 3D model
Lateral forward
conductor
Return
conductors
Plasma
grid
Cu Conductors
Equivalent Cu for holes
Ferromagnetic material
Equivalent ferromagnetic material for holes
Ferromagnetic sheet
Water manifold
An hybrid formulation has been used:
magnetic vector potential formulation in the inner volume of the domain where are the conductors
magnetic scalar potential formulation in the outer volume of the domain which includes the ferromagnetic sheet and the rest of the air
the link surface is located midway between the PG and the iron sheet
8 October 2009, European Doctorate in Fusion Science and Engineering

17. Space distribution of Bx along horizontal paths located 20 mm upstream PG
Bx (mT) y
Central
beamlet
group
Lateral
beamlet
group x
x (mm)
8 October 2009, European Doctorate in Fusion Science and Engineering

18. Space distribution of Bx along vertical paths located 20 mm upstream PG
Bx (mT) y x
Bottom
beamlet
groups
Upper
beamlet
groups
y (mm)
8 October 2009, European Doctorate in Fusion Science and Engineering

19. Detailed 3D model (full horizontal slice) including grid apertures
Represents a horizontal “slice” of the entire accelerator assembly, with 3 arrays of the actual 4 (groups) x 5 (beamlet per group) apertures.
Includes the Suppression magnets in the EG and magnets and ferromagnetic layer on the GG.
Total number of DOFs is > 106.
Only the information on the vertical lack of uniformity is lost!
Return bars
Plasma grid
Water
manifold
Side bars
3 x 4 x 5 = 60 apertures
Extraction grid magnets
(Suppression field)
Ferromagnetic layer on GG
Grounded grid magnets for Ion deflection compensation
8 October 2009, European Doctorate in Fusion Science and Engineering

20. Ferromagnetic layer on GG
Detailed 3D model (full horizontal slice): Bx and By along 4 beamlet
Bx, By (mT)
Suppression field By EG
Compensation field Bx
Filter field
Ferromagnetic layer on GG PG
z (mm)
8 October 2009, European Doctorate in Fusion Science and Engineering

21. First activity conclusions & planned actions
The filter field uniformity has been improved with a more flexible solution (no permanent magnets)
The vertical ion deflection has been reduced and a possible solution for the ion deflection has been proposed, with benefits in terms of co-extracted electrons
Magnetic field map useful for more realistic 3D particle trajectory code benchmarking
Due to large model size, some convergence difficulties and numerical "noise" encountered and improvements of mesh efficiency are in progress
Optimization of the compensation magnet is in progress
8 October 2009, European Doctorate in Fusion Science and Engineering

22. Improvement of the numerical model of the RFX-mod passive
structure in the finite element CARIDDI code
CARIDDI code:
FEM code suitably developed for eddy current evaluation
based on an integral formulation of a 2 component electric vector potential
only the conducting structures have to be modelled
coupled with the MARS-F code in the self-consistent CarMa code for the plasma response calculation
Support structure
Saddle coils
Copper shell
Vacuum vessel
My tasks:
Model integration of non-axisymmetric passive structure discontinuities (i.e. holes, extensions, etc.) in order to assess their effect on the magnetic configuration and to improve the model of the saddle coil controller
Test of possible modifications on the passive structures (i.e. different copper shell thickness, etc.) of RFX-mod to improve the confinement performances
8 October 2009, European Doctorate in Fusion Science and Engineering

23. Spare slides

24. Section view of the SPIDER grids and electron dump
8 October 2009, European Doctorate in Fusion Science and Engineering

25. Comparison of all models: space distribution of Bx along horizontal paths located 20 mm upstream PG
Bx (mT) y x
Central
beamlet
group
Lateral
beamlet
group
x (mm)
8 October 2009, European Doctorate in Fusion Science and Engineering

26. Comparison of all models: space distribution of Bx along a beamlet
Bx (mT) y x
z (mm)
8 October 2009, European Doctorate in Fusion Science and Engineering

27. Ferromagnetic layer on GG
Ion deflection compensation
Suppression field
Compensation field By EG
Ferromagnetic layer on GG PG
z (mm)
8 October 2009, European Doctorate in Fusion Science and Engineering

28. Space distribution of Bx along horizontal paths located 20 mm upstream PG
Central
beamlet
group
Lateral
beamlet
group
8 October 2009, European Doctorate in Fusion Science and Engineering

29. Space distribution of Bz along horizontal paths located 20 mm upstream PG
Central
beamlet
group
Lateral
beamlet
group
8 October 2009, European Doctorate in Fusion Science and Engineering

30. Space distribution of Bx along horizontal paths located 10 mm upstream GG
Central
beamlet
group
Lateral
beamlet
group
8 October 2009, European Doctorate in Fusion Science and Engineering

31. Space distribution of Bx along horizontal paths located 50 mm downstream PG
Central
beamlet
group
Lateral
beamlet
group
8 October 2009, European Doctorate in Fusion Science and Engineering

32. Beamlet deflection estimation:
1.5 m from GG
Central
beamlet
group
Lateral
beamlet
group
0.5 m from GG
1.5 m from GG
0.5 m from GG
8 October 2009, European Doctorate in Fusion Science and Engineering

33. Space distribution of Bx along vertical paths located 3 mm downstream PG
Bx (mT)
Bx (mT) y x
Bottom
beamlet
groups
Upper
beamlet
groups
y (mm)
y (mm)
8 October 2009, European Doctorate in Fusion Science and Engineering

34. Detailed 3D model (full horizontal slice): current density distribution
8 October 2009, European Doctorate in Fusion Science and Engineering

35. Lack of uniformity in vertical direction into the iron sheet
∆B ≈ 30–40%
8 October 2009, European Doctorate in Fusion Science and Engineering

36. Physical issue Eb=Eb(a)
Neutral Beam Heating and Current Drive System (1)
Physical issue
Eb=Eb(a)
Neutral Beam Energy
Neutral Beam Flux penetrating and absorbed into the plasma
Decay length
Energy dependence in implicit form
A different value for parallel injection
Energy needed for Neutral Beam Heating depends on minor radius a and plasma density np
ITER NBI: Eb = 1 MeV
8 October 2009, European Doctorate in Fusion Science and Engineering

37. Technological issue Neutral Beam Heating and Current Drive System (2)
Positive-ion-driven neutral beams lose their efficiencies above 100 keV
Negative-ion-driven neutral beams maintain their efficiency up to energies on the order of 1 MeV
Positive ion technology will not scale favorably into the reactor regime and current research is focused on developing high-energy negative ion sources
Neutralization fraction vs. beam energy for positive and negative ion beams
8 October 2009, European Doctorate in Fusion Science and Engineering

38. Magnetic vector potential formulation
8 October 2009, European Doctorate in Fusion Science and Engineering

39. Reduced scalar magnetic potential formulation
8 October 2009, European Doctorate in Fusion Science and Engineering