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


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)


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


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


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


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)


0 V

-100 kV-112 kV

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

[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


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


z

x

Return conductor

Return conductors

Magnetic shield

GridsFilter field magnet Lateral forward

conductor

Line ofsymmetry

Line ofsymmetry

Grids


Plasma Grid(forward conductor)Ferromagnetic

layer


Source wallsSource walls


• 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


z

x

Return conductor

Return conductors

Magnetic shield

GridsFilter field magnet Lateral forward

conductor

Line ofsymmetry

Line ofsymmetry

Grids


Plasma Grid(forward conductor)Ferromagnetic

layer


Bias Plate

Ferromagnetic layer

Plasma Grid

ExtractionGrid

GroundedGrid

Source wallsSource walls


• 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


z

x

Space distribution of Bx along a beamlet

PlasmaGrid

GroundedGrid

Ferromagnetic layer

Referenceconfiguration

Optimizedconfiguration

Plasmasource


z (mm)

Bx (mT)

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 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


• 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


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


Space distribution of Bx along horizontal paths located 20 mm upstream PG

x (mm)

Bx (mT)

y

x


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


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


z (mm)

Bx, By (mT)

PG

EG


Compensation field

Suppression field

Filter fieldBx

By


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


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


Section view of the SPIDER grids and electron dump

Centralbeamletgroup

Lateralbeamletgroup


Comparison of all models: space distribution of Bx along horizontal paths located 20 mm upstream PG

y

x

x (mm)

Bx (mT)


Comparison of all models: space distribution of Bx along a beamlet

y

x

z (mm)

Bx (mT)

Ion deflection compensation


z (mm)

PG

EG


Compensation field

Suppression field

By

Space distribution of Bx along horizontal paths located 20 mm upstream PG

Centralbeamletgroup

Lateralbeamletgroup


Space distribution of Bz along horizontal paths located 20 mm upstream PG

Centralbeamletgroup

Lateralbeamletgroup


Space distribution of Bx along horizontal paths located 10 mm upstream GG

Centralbeamletgroup

Lateralbeamletgroup


Space distribution of Bx along horizontal paths located 50 mm downstream PG

Centralbeamletgroup

Lateralbeamletgroup


Beamlet deflection estimation:

Centralbeamletgroup

Lateralbeamletgroup


Reference @ 1.5 m from GG

Reference @ 0.5 m from GG

Optimized @ 1.5 m from GG

Optimized @ 0.5 m from GG


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


Lack of uniformity in vertical direction into the iron sheet


∆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


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



Magnetic vector potential formulation


Reduced scalar magnetic potential formulation

Documents

Nicolò Marconato Consorzio RFX, Euratom-ENEA Association, and University of Padova, Italy