Nicolò Marconato Consorzio RFX, Euratom-ENEA Association, and University of Padova, Italy
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Transcript of Nicolò Marconato Consorzio RFX, Euratom-ENEA Association, and University of Padova, Italy
Nicolò Marconato
Consorzio RFX, Euratom-ENEA Association, andUniversity of Padova, Italy
Development and validation of numerical models for the optimization of magnetic field configurations in fusion devices
8 October 2009, European Doctorate in Fusion Science and Engineering
Activity plan
8 October 2009, European Doctorate in Fusion Science and Engineering
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
First activity outline
• Introduction to ITER NBI & SPIDER description
• Optimization of SPIDER magnetic configuration
• 3D verification & Ion deflection compensation
• Conclusions & Foreseen activities
Introduction to ITER NBI
ITER main parameter:Q (Fusion Energy Gain Factor)>10
H&CD for ITERNeutral Beam Injectors Radio Frequency Antennas
Ion beam composition: H-, D-
Heating Power by Neutrals: 16.7 MWAccelerated Ion Power: 40 MWIon current: 40 AIon current Density: 200 A/m2
Total voltage: 1 MV
NegativeIon Source
Neutralizer
Residual Ion Dump
Calorimeter
High Voltage BushingNeutral Beam Negative Ion Beam
8 October 2009, European Doctorate in Fusion Science and Engineering
Neutral Beam Heating and Current Drive System: issues
Physics issue Eb=Eb(a, np)Neutral Beam Energy needed depends on minor radius a
and plasma density np
ITER NBI: Eb = 1 MeV
8 October 2009, European Doctorate in Fusion Science and Engineering
Physics/Technological
issue
Neutralization fraction vs. beam energy for positive and negative ion
beams
• 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
SPIDER: Source for Production of Ion of Deuterium Extracted from RF plasma
Ion Current Density: 200 A/m2
Ion Current: 40 A
Total Voltage: 100 kV
calorimeter
beam source
beam source
electrical bushing
pumping port
beam tomography
source spectroscopy
vacuum vessel
inside the vacuum vessel
hydraulic bushing
8 October 2009, European Doctorate in Fusion Science and Engineering
Reference design[1] - 1
[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
0 V
-100 kV-112 kV
Reference design[1] - 2
8 October 2009, European Doctorate in Fusion Science and Engineering
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
[1] ITER Technical Basis 2002, “Neutral beam heating & current drive (NB H&CD) system”, Detailed Design Document (section 5.3 DDD5.3) (Vienna: IAEA)
PG current
magnets
EG
PG
magnets
z x
y
Motivation and Definition of Magnetic Problem
• 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
EGGG
8 October 2009, European Doctorate in Fusion Science and Engineering
x
z
Return conductor
Magnetic shield
GridsFilter field magnet
Line ofsymmetry
Plasma Grid(forward conductor)
Filter Field optimization: 2D models
Source walls
• 4 kA PG current• Single return conductor• Permanent magnets• Magnetic shield
8 October 2009, European Doctorate in Fusion Science and Engineering
z
x
Return conductor
Return conductors
Magnetic shield
GridsFilter field magnet Lateral forward
conductor
Line ofsymmetry
Line ofsymmetry
Grids
Plasma Grid(forward conductor)
Plasma Grid(forward conductor)Ferromagnetic
layer
Filter Field optimization: 2D models
Source wallsSource walls
• 4 kA PG current• Single return conductor• Permanent magnets• Magnetic shield
• 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
8 October 2009, European Doctorate in Fusion Science and Engineering
z
x
Return conductor
Return conductors
Magnetic shield
GridsFilter field magnet Lateral forward
conductor
Line ofsymmetry
Line ofsymmetry
Grids
Plasma Grid(forward conductor)
Plasma Grid(forward conductor)Ferromagnetic
layer
Filter Field optimization: 2D models
Bias Plate
Ferromagnetic layer
Plasma Grid
ExtractionGrid
GroundedGrid
Source wallsSource walls
• 4 kA PG current• Single return conductor• Permanent magnets• Magnetic shield
• 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
8 October 2009, European Doctorate in Fusion Science and Engineering
z
x
Space distribution of Bx along a beamlet
PlasmaGrid
GroundedGrid
Ferromagnetic layer
Referenceconfiguration
Optimizedconfiguration
Plasmasource
8 October 2009, European Doctorate in Fusion Science and Engineering
z (mm)
Bx (mT)
2D model limits
8 October 2009, European Doctorate in Fusion Science and Engineering
However, 2D "infinite slab" models cannot account for the local 3D configuration due to grid holes and edge effects.
An assessment of thevalidity 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
3D model: issues
8 October 2009, European Doctorate in Fusion Science and Engineering
• Complex geometry, presenting large dimensions (whole grids) and details of little dimensions (single beamlet)
large amount of memory used
• 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
very high number of elements (nodes)
magnetic scalar potential formulation is good in the regions with different permeability, but cannot be used with complex current density distributions
high computational time
Simplified global 3D model
Cu Conductors
Equivalent Cu for holes
Ferromagnetic material
Equivalent ferromagnetic material for holes
Water manifold
Lateral forwardconductor
Returnconductors Plasma
grid
Ferromagnetic sheet
8 October 2009, European Doctorate in Fusion Science and Engineering
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
Centralbeamletgroup
Lateralbeamletgroup
8 October 2009, European Doctorate in Fusion Science and Engineering
Space distribution of Bx along horizontal paths located 20 mm upstream PG
x (mm)
Bx (mT)
y
x
8 October 2009, European Doctorate in Fusion Science and Engineering
Bottom
beamlet
groups
Upper
beamlet
groups
y
x
y (mm)
Bx (mT)
Space distribution of Bx along vertical paths located 20 mm upstream PG
Detailed 3D model (full horizontal slice) including grid apertures
8 October 2009, European Doctorate in Fusion Science and Engineering
Return bars
Side bars
Plasma grid
Watermanifold
Ferromagnetic layer on GG
Extraction grid magnets(Suppression field)
Grounded grid magnets for Ion deflection compensation
3 x 4 x 5 = 60 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!
Detailed 3D model (full horizontal slice): Bx and By along 4 beamlet
8 October 2009, European Doctorate in Fusion Science and Engineering
z (mm)
Bx, By (mT)
PG
EG
Ferromagnetic layer on GG
Compensation field
Suppression field
Filter fieldBx
By
8 October 2009, European Doctorate in Fusion Science and Engineering
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
Improvement of the numerical model of the RFX-mod passive
structure in the finite element CARIDDI code
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
Vacuum vessel
Copper shell
Support structureSaddle
coils
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
Spare slides
8 October 2009, European Doctorate in Fusion Science and Engineering
Section view of the SPIDER grids and electron dump
Centralbeamletgroup
Lateralbeamletgroup
8 October 2009, European Doctorate in Fusion Science and Engineering
Comparison of all models: space distribution of Bx along horizontal paths located 20 mm upstream PG
y
x
x (mm)
Bx (mT)
8 October 2009, European Doctorate in Fusion Science and Engineering
Comparison of all models: space distribution of Bx along a beamlet
y
x
z (mm)
Bx (mT)
Ion deflection compensation
8 October 2009, European Doctorate in Fusion Science and Engineering
z (mm)
PG
EG
Ferromagnetic layer on GG
Compensation field
Suppression field
By
Space distribution of Bx along horizontal paths located 20 mm upstream PG
Centralbeamletgroup
Lateralbeamletgroup
8 October 2009, European Doctorate in Fusion Science and Engineering
Space distribution of Bz along horizontal paths located 20 mm upstream PG
Centralbeamletgroup
Lateralbeamletgroup
8 October 2009, European Doctorate in Fusion Science and Engineering
Space distribution of Bx along horizontal paths located 10 mm upstream GG
Centralbeamletgroup
Lateralbeamletgroup
8 October 2009, European Doctorate in Fusion Science and Engineering
Space distribution of Bx along horizontal paths located 50 mm downstream PG
Centralbeamletgroup
Lateralbeamletgroup
8 October 2009, European Doctorate in Fusion Science and Engineering
Beamlet deflection estimation:
Centralbeamletgroup
Lateralbeamletgroup
8 October 2009, European Doctorate in Fusion Science and Engineering
Reference @ 1.5 m from GG
Reference @ 0.5 m from GG
Optimized @ 1.5 m from GG
Optimized @ 0.5 m from GG
8 October 2009, European Doctorate in Fusion Science and Engineering
Bottom
beamlet
groups
Upper
beamlet
groups
y
x
y (mm)
Bx (mT)
Space distribution of Bx along vertical paths located 3 mm downstream PG
y (mm)
Bx (mT)
Detailed 3D model (full horizontal slice): current density distribution
8 October 2009, European Doctorate in Fusion Science and Engineering
Lack of uniformity in vertical direction into the iron sheet
8 October 2009, European Doctorate in Fusion Science and Engineering
∆B ≈ 30–40%
Neutral Beam Heating and Current Drive System (1)
Physical issue Eb=Eb(a)
/0 xbb ex
icpn
1
Neutral Beam Energy
Neutral Beam Flux penetrating and absorbed into the plasma
Decay length
icpb n
Ea
5.1
2
3 Energy dependence in implicit form
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
A different value for parallel injection
Neutral Beam Heating and Current Drive System (2)
Technological issue
Neutralization fraction vs. beam energy for positive and negative ion beams
Positive ion technology will not scale favorably into the reactor regime and current research is focused on developing high-energy negative ion sources
• 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
8 October 2009, European Doctorate in Fusion Science and Engineering
8 October 2009, European Doctorate in Fusion Science and Engineering
Magnetic vector potential formulation
8 October 2009, European Doctorate in Fusion Science and Engineering
Reduced scalar magnetic potential formulation