Nicol

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
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)gt10
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

• HCD for ITER
• Neutral Beam Injectors
• Radio Frequency Antennas

8 October 2009, European Doctorate in Fusion
Science and Engineering
5
Neutral Beam Heating and Current Drive System
issues
EbEb(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
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 design1 - 1
-112 kV
-100 kV
0 V
1 ITER Technical Basis 2002, Neutral beam
heating current drive (NB HCD) system,
Detailed Design Document (section 5.3 DDD5.3)
(Vienna IAEA)
8 October 2009, European Doctorate in Fusion
Science and Engineering
8
Reference design1 - 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 HCD) 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 Problem
x

• Magnetic field profile of the reference
  configuration1 (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
11
Filter Field optimization 2D models

• 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

Return conductor
Magnetic shield

• 4 kA PG current
• Single return conductor
• Permanent magnets
• Magnetic shield

Line of symmetry
Reference configuration
x
Optimized configuration
Return conductors
Line of symmetry
z
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
12
Filter Field optimization 2D models

• 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

Return conductor
Magnetic shield

• 4 kA PG current
• Single return conductor
• Permanent magnets
• Magnetic shield

Line of symmetry
Reference configuration
x
Optimized configuration
Return conductors
Line of symmetry
z
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
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
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

View of the SPIDER filter field source assembly

• detailed thermal loads prediction

8 October 2009, European Doctorate in Fusion
Science and Engineering
15
3D model issues

• 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 gt 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
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
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
Reference _at_ 1.5 m from GG
Central beamlet group
Lateral beamlet group
Reference _at_ 0.5 m from GG
Optimized _at_ 1.5 m from GG
Optimized _at_ 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 3040
8 October 2009, European Doctorate in Fusion
Science and Engineering
36
Neutral Beam Heating and Current Drive System (1)

• Physical issue

EbEb(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
Neutral Beam Heating and Current Drive System (2)

• 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
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