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

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.

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

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  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)>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. Neutral Beam Heating and Current Drive System: issues Eb=Eb(a, np) Neutral Beam Energy needed depends on minor radiusaand plasma densitynp Physics issue 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 Ion Current Density: 200 A/m2 Ion Current: 40 A Total Voltage: 100 kV pumping port calorimeter hydraulic bushing beam tomography source spectroscopy beam source inside the vacuum vessel 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 Problem x • 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

  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 > 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 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 Support structure Saddle coils Copper shell Vacuum vessel 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 @ 1.5 m from GG Central beamlet group Lateral beamlet group 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

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

  37. Neutral Beam Heating and Current Drive System (2) • Positive-ion-driven neutral beams lose their efficiencies above 100 keV Technological issue • 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

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