2. Efremov Research Institute Russia, St. Petersburg, http:// www.niiefa.spb.su, E-mail: filatov@niiefa.spb.su, Sytch@niiefa.spb.su, FAX: (812) 464-4882, Phone: (812) 462-77-82

3. Electromagnetic Analysis of the ITER Facility Vacuum Vessel & Blanket Modules.Vacuum Vessel & Blanket Modules. Shielding Structure of Vacuum Vessel.Shielding Structure of Vacuum Vessel. Thermal Shield of Vacuum Vessel.Thermal Shield of Vacuum Vessel. Divertor Components.Divertor Components. Conducting Case of the Toroidal Field Coils.Conducting Case of the Toroidal Field Coils. Poloidal and Toroidal Field Coils.Poloidal and Toroidal Field Coils. Correction Coils.Correction Coils. Neutral Beam Magnetic Field Reduction System.Neutral Beam Magnetic Field Reduction System. Appl. Math. Dept. of STC “SINTEZ”, Efremov Research Institute, St. Petersburg, RF

4. Vacuum Vessel and Blanket Modules The 3D shell model development.The 3D shell model development. Estimation of electromagnetic loads acting on the Vacuum Vessel and Blanket modules during some operational conditions: 1) Central Disruptions, 2) fast and slow Vertical Displacement Events with Halo currents, 3) Toroidal Field Coil Fast Discharge using the TYPHOON code.Estimation of electromagnetic loads acting on the Vacuum Vessel and Blanket modules during some operational conditions: 1) Central Disruptions, 2) fast and slow Vertical Displacement Events with Halo currents, 3) Toroidal Field Coil Fast Discharge using the TYPHOON code. EM loads transfer to nodal forces for subsequent dynamic structural analysis.EM loads transfer to nodal forces for subsequent dynamic structural analysis. Estimation of magnetic field penetration time and one turn toroidal and poloidal resistivities of Vacuum Vessel.Estimation of magnetic field penetration time and one turn toroidal and poloidal resistivities of Vacuum Vessel. Appl. Math. Dept. of STC “SINTEZ”, Efremov Research Institute, St. Petersburg, RF The figure illustrates surface eddy current density distribution over Vacuum Vessel segment 1/18 part. The profile lines indicate surface current density. The figure shows time variation of total forces acting on the Vacuum Vessel during plasma Central Disruption 27ms.

5. Blanket modules The 3D shell model development.The 3D shell model development. The transient electromagnetic analysis of Blanket modules under different loading conditions: 1) Central Disruptions (CD), 2) fast and slow Vertical Displacement Events (VDE) with Halo currents, 3) Toroidal Field Coil Fast Discharge (TFCFD).The transient electromagnetic analysis of Blanket modules under different loading conditions: 1) Central Disruptions (CD), 2) fast and slow Vertical Displacement Events (VDE) with Halo currents, 3) Toroidal Field Coil Fast Discharge (TFCFD). Time behaviors of the total radial, toroidal and poloidal torque moments acting on the all (17 items) modules.Time behaviors of the total radial, toroidal and poloidal torque moments acting on the all (17 items) modules. Determination of the most loaded construction elements.Determination of the most loaded construction elements. Transfer local EM loads to nodal forces for subsequent dynamic structure analysis.Transfer local EM loads to nodal forces for subsequent dynamic structure analysis. Taking into consideration different options of electrical connections between Blanket modules and Vacuum Vessel.Taking into consideration different options of electrical connections between Blanket modules and Vacuum Vessel. Appl. Math. Dept. of STC “SINTEZ”, Efremov Research Institute, St. Petersburg, RF TYPHOON code Distribution of surface force density normal component over Blanket modules.

6. Vacuum Vessel Shielding Blocks The 3D shell model development.The 3D shell model development. Calculation of the EM loads: eddy current, forces, torque moments acting on VV Shielding Blocks under different loading conditions: Central Disruption, fast upward and downward VDE.Calculation of the EM loads: eddy current, forces, torque moments acting on VV Shielding Blocks under different loading conditions: Central Disruption, fast upward and downward VDE. Estimation of the ponderomotive forces associated with magnetization of the ferromagnetic shielding blocksEstimation of the ponderomotive forces associated with magnetization of the ferromagnetic shielding blocks Consideration of real ferromagnetic properties of material.Consideration of real ferromagnetic properties of material. Estimation of the ferromagnetic blocks influence on the toroidal field ripple and error field.Estimation of the ferromagnetic blocks influence on the toroidal field ripple and error field. 3D shell model of Vacuum Vessel and Outer Shielding block.. Appl. Math. Dept. of STC “SINTEZ”, Efremov Research Institute, St. Petersburg, RF TYPHOON code Outer shielding block. Distribution of eddy current (step of flux lines is 200A).

7. Vacuum Vessel Thermal Shield The 3D shell model of Thermal Shield.The 3D shell model of Thermal Shield. Estimations of EM loads from Halo and eddy currents acting on the Thermal Shield for various plasma disruption regimes: CD27ms, CD54ms, fast upward and downward VDE, slow upward, downward VDE with Halo current and Toroidal Field Coil Fast Discharge (TFCFD).Estimations of EM loads from Halo and eddy currents acting on the Thermal Shield for various plasma disruption regimes: CD27ms, CD54ms, fast upward and downward VDE, slow upward, downward VDE with Halo current and Toroidal Field Coil Fast Discharge (TFCFD). Determination of the most dangerous time moment during plasma regimes.Determination of the most dangerous time moment during plasma regimes. Identification of extreme values of EM loads and their location.Identification of extreme values of EM loads and their location. Transfer EM loads to nodal forces for subsequent static structural analysis.Transfer EM loads to nodal forces for subsequent static structural analysis. TYPHOON code Appl. Math. Dept. of STC “SINTEZ”, Efremov Research Institute, St. Petersburg, RF The eddy current distribution over the Vacuum Vessel Thermal Shield is presented in this figure.

8. The estimation of EM-loads on the Divertor Cassette The 3D shell model.The 3D shell model. The calculation of electromagnetic loads acting on the Divertor Cassette under fast and slow downward VDEs with Halo Current.The calculation of electromagnetic loads acting on the Divertor Cassette under fast and slow downward VDEs with Halo Current. Taking into account static magnetic fields from Toroidal and Poloidal Field Coils.Taking into account static magnetic fields from Toroidal and Poloidal Field Coils. Estimation and drawing of total forces and moments time histories for different elements of Divertor Cassette: Cassette Body, Inner and Outer Vertical Targets, Dome and Liners.Estimation and drawing of total forces and moments time histories for different elements of Divertor Cassette: Cassette Body, Inner and Outer Vertical Targets, Dome and Liners. Determination of the most dangerous time moment during plasma regimes.Determination of the most dangerous time moment during plasma regimes. Identification of extreme values of EM loads and their location.Identification of extreme values of EM loads and their location. Carrying out of the EM loads transfer to nodal forces for subsequent structure analysis.Carrying out of the EM loads transfer to nodal forces for subsequent structure analysis. Consideration of different electrical properties of material.Consideration of different electrical properties of material. Appl. Math. Dept. of STC “SINTEZ”, Efremov Research Institute, St. Petersburg, RF TYPHOON code The profile lines of eddy current are shown in this figure. The various colors indicate the surface current density.

9. EM Analysis of Divertor Components. The 3D shell model of Divertor Components: Inner and Outer Vertical Targets, Dome and Liners.The 3D shell model of Divertor Components: Inner and Outer Vertical Targets, Dome and Liners. EM analysis of Divertor Components for fast and slow downward VDE with.EM analysis of Divertor Components for fast and slow downward VDE with. Taking into account the EM loads from eddy and Halo currents.Taking into account the EM loads from eddy and Halo currents. Consideration of static magnetic fields from TF and PF coils.Consideration of static magnetic fields from TF and PF coils. Time behaviors of total forces and moments acting on each Divertor component estimation and drawing.Time behaviors of total forces and moments acting on each Divertor component estimation and drawing. Determination of the most dangerous time moments when EM loads achieve their peaks.Determination of the most dangerous time moments when EM loads achieve their peaks. Searching of the most loaded elements of construction.Searching of the most loaded elements of construction. Performance of EM loads transfer to nodal forces for subsequent structure analysis.Performance of EM loads transfer to nodal forces for subsequent structure analysis. Appl. Math. Dept. of STC “SINTEZ”, Efremov Research Institute, St. Petersburg, RF Distribution of the surface force density over Inner Vertical Target. TYPHOON code Distribution of surface current density over Outer Vertical Target. Distribution of the surface force density over Dome and Liners.

10. Calculational Model of Toroidal Field Coils Case. 3D thin conducting shell model 3D thin conducting shell model. Appl. Math. Dept. of STC “SINTEZ”, Efremov Research Institute, St. Petersburg, RF TYPHOON code

11. Toroidal Field Coil Case The 3D shell model development.The 3D shell model development. Numerical simulation of eddy current behavior and a calculation of the heat deposition observed in the magnet cold structures.Numerical simulation of eddy current behavior and a calculation of the heat deposition observed in the magnet cold structures. Transient EM analysis of AC losses in Toroidal Field Coil (TFC) case under different loading conditions: fast and slow VDEs, poloidal coil fast discharges and the plasma reference scenario (0- 1800sec).Transient EM analysis of AC losses in Toroidal Field Coil (TFC) case under different loading conditions: fast and slow VDEs, poloidal coil fast discharges and the plasma reference scenario (0- 1800sec). Time evolution of total energy dissipated in TFC case calculation and drawing.Time evolution of total energy dissipated in TFC case calculation and drawing. Determination of the TFC case parts, where AC loss density is the highest.Determination of the TFC case parts, where AC loss density is the highest. Appl. Math. Dept. of STC “SINTEZ”, Efremov Research Institute, St. Petersburg, RF TYPHOON code Distribution of AC loss surface density. Evolution of total energy dissipated in TFC case during plasma reference scenario (0-1800sec).

12. Calculational model of Poloidal and Toroidal Field Coils and Plasma The 3D solid model development.The 3D solid model development. Calculations of the magnetic fields and forces for normal and abnormal conditions.Calculations of the magnetic fields and forces for normal and abnormal conditions. Safety analysis.Safety analysis. Calculation of three harmonic modes. Preliminary estimation of expected spectrum of Error Field due to coils deviations and misalignments.Calculation of three harmonic modes. Preliminary estimation of expected spectrum of Error Field due to coils deviations and misalignments. The statistical analysis of total Error Field for 246 degrees of freedom of poloidal and toroidal magnet system on the basis of Monte-Carlo method.The statistical analysis of total Error Field for 246 degrees of freedom of poloidal and toroidal magnet system on the basis of Monte-Carlo method. Calculation of correction coils currents required to suppress error fields below the specified limit.Calculation of correction coils currents required to suppress error fields below the specified limit. Appl. Math. Dept. of STC “SINTEZ”, Efremov Research Institute, St. Petersburg, RF KLONDIKE code The 3D solid model of Plasma, Poloidal and Toroidal Field Coils.

13. Toroidal Field Ripple. The ripple loss of fast alpha particles in configurations with negative central shear in TOKAMAK without ferromagnetic inserts is large.The ripple loss of fast alpha particles in configurations with negative central shear in TOKAMAK without ferromagnetic inserts is large. Ferromagnetic inserts are going to be used in ITER to reduce the value of Toroidal Field (TF) ripple.Ferromagnetic inserts are going to be used in ITER to reduce the value of Toroidal Field (TF) ripple. The 3D solid model of Poloidal and Toroidal Field coils and ferromagnetic inserts.The 3D solid model of Poloidal and Toroidal Field coils and ferromagnetic inserts. Estimation of ferromagnetic inserts influence on TF ripple.Estimation of ferromagnetic inserts influence on TF ripple. Taking into account real unlinear properties of ferromagnetic materials.Taking into account real unlinear properties of ferromagnetic materials. Estimation of residual magnetic fieldsEstimation of residual magnetic fields Optimization of ferromagnetic inserts.Optimization of ferromagnetic inserts. TF ripple  (%) with ferromagnetic inserts with different filling factor for regions. Ferromagnetic insert and TF coil. 1/36 of facility. KLONDIKE code Appl. Math. Dept. of STC “SINTEZ”, Efremov Research Institute, St. Petersburg, RF

14. Correction Coils (CC). Estimation of CC capability to reduce error fields.Estimation of CC capability to reduce error fields. Estimation of CC capability to stabilize the Resistive Wall Mode (RWM). The RWM are know to grow on time scale characteristic of the magnetic field penetration through a conducting wall. So the screening effect of the Vacuum Vessel (VV) should be taking into account for oscillating current in CC.Estimation of CC capability to stabilize the Resistive Wall Mode (RWM). The RWM are know to grow on time scale characteristic of the magnetic field penetration through a conducting wall. So the screening effect of the Vacuum Vessel (VV) should be taking into account for oscillating current in CC. The 3D shell model of VV development.The 3D shell model of VV development. Calculation of steady amplitudes of normal and tangential (to VV surface) components of magnetic field for different CC current frequencies.Calculation of steady amplitudes of normal and tangential (to VV surface) components of magnetic field for different CC current frequencies. Estimation of characteristic time constant for transient process.Estimation of characteristic time constant for transient process. Determination of CC inductance.Determination of CC inductance. Calculation model. 1/4 part of facility. Top view. Appl. Math. Dept. of STC “SINTEZ”, Efremov Research Institute, St. Petersburg, RF TYPHOON code Distribution of eddy current over Vacuum Vessel shells generated by CC current.

15. Neutral Beam Magnetic Field Reduction System The stray magnetic field from the TOKAMAK magnet system inside Neutral Beam Injectors during the injector operation should be very low to avoid deflection of the ion beam.The stray magnetic field from the TOKAMAK magnet system inside Neutral Beam Injectors during the injector operation should be very low to avoid deflection of the ion beam. Development of 3D solid unlinear models for reduction of the magnetic field to the acceptable level.Development of 3D solid unlinear models for reduction of the magnetic field to the acceptable level. Optimization of active coils and passive ferromagnetic shield.Optimization of active coils and passive ferromagnetic shield. 3D magnetic analysis of Error Field due to Neutral Beam Injector Magnetic Field Reduction System (MFRS).3D magnetic analysis of Error Field due to Neutral Beam Injector Magnetic Field Reduction System (MFRS). KLONDIKE code Neutral Beam InjectorDiagnostic Neutral Beam Injector Appl. Math. Dept. of STC “SINTEZ”, Efremov Research Institute, St. Petersburg, RF

16. Introduction For the Electromagnetic analysis estimation the two codes have been used:For the Electromagnetic analysis estimation the two codes have been used: 1.The TYPHOON code is designed for an advanced 3D simulation of transient electromagnetic processes using thin conducting shell. 2.The KLONDIKE code is intended for a 3D field simulation for current and permanent magnet systems. Appl. Math. Dept. of STC “SINTEZ”, Efremov Research Institute, St. Petersburg, RF

17. KLONDIKE Numerical Simulation of 3D Fields for Current and Permanent Magnet Systems KLONDIKE KLONDIKEThe KLONDIKE package is intended for a 3D field simulation for current and permanent magnet systems. The package is based on FORTRAN and C++ and is available as the object module library on PCs and more powerful computers. An effective numerical algorithms uses analytical solution of surface integrals, that provide prompt and mathematically exact definition for magnetic field strength vector H at any point of observation. KLONDIKE is easy to use and requires no preliminary skills to apply. In fact, users need only to input coordinates, current density and magnetization vector for model polyhedron elements. KLONDIKEKLONDIKE includes five groups of modules: – module defining and displaying the geometry of a currents system (an advanced coil editor implements Graphical User Interface); – main module calculating the field produced by a set of standard elements; – modules calculating surface integrals and the magnetic field strength vector for a current inside an arbitrary volume bounded with planar faces; – modules calculating the magnetic field strength vector for ring conductors of arbitrary cross-section; – subroutine library of standard elements with on-the-fly updating for main types of magnet systems. The package contains the modules for calculations of ponderomotive loads on different elements of a magnetic system (including ferromagnetic ). KOMPOT-M is compatible with thermo-hydraulic and structural analysis codes. KLONDIKE was succesfully applied to the electromagnetic shielding design of an MRI tomograph (the Efremov Research Institute of Electrophysical Apparatus, St.-Petersburg, Russia); magnetic field reconstruction of PHENIX Detector (Brookhaven National Laboratory, USA); design hexapole of an ECR-source (the Efremov Research Institute of Electrophysical Apparatus, St.- Petersburg, Russia); design of Poloidal and Toroidal Fields Systems for the ITER Project (International Test Engineering Reactor).

18. TYPHOON DESCRIPTION TYPHOON TYPHOONThe TYPHOON code is designed for an advanced 3D simulation of transient electromagnetic processes using thin conducting shell. The code allows users to take into account the symmetry of the construction and to reduce significantly the problem dimension. TYPHOON consists of integrated shell, mesh generator, geometry analyzer (preprocessor), system generator, system solver, postprocessor and result viewer. FEATURES Very fast and effective system generator based on specific analytical results and suitable integrating method  Modelling with a set of arbitrary connected thin conducting shells located in a 3D space  Compatibility with: – VINCENTA, COND codes for thermo-hydraulic calculations of superconducting systems, – ANSYS, FEA, COSMOS/M codes for mechanical calculations, – KOMPOT code for 3D non-linear magnetostatic field calculations. TYPHOONHigh performance of the code was proved with the standard test problems presented at Test Elecromagnetic Analysis Method (TEAM) Workshops. TYPHOON was intensively verified during the International Thermonuclear Experimental Reactor Engineering Design Activity. It was applied to the design of the ITER facility, the TEXTOR tokamak (in KFA/IPP, Julich, Germany), and the MRI tomograph (in Efremov Inst., St.Petersburg, Russia)