A simulation technique is described that was applied to optimise the design and ensure the desired field quality of a superconducting solenoid. A three-section solenoid with a lengthwise split winding was chosen as a reference configuration. The design was optimized through MathCAD calculations with the Levenberg-Marquardt minimization. The calculated data enabled adjustment of the coil geometry so as to provide required field homogeneity with respect to manufacture limitations. The optimised design was validated in comparative simulations and measurements on a prototype. The study was performed within the R&D activities on construction of an original electron beam ion source (EBIS). The results of the study were reported in the project documents.

The work is devoted to the development and testing of a computational model of the precision magnetic system of the experimental facility “Beta-decay” for measuring the correlation coefficients of the neutron beta-decay, created at the Scientific Research Center “Kurchatov Institute”. The magnetic field of the system in its various configurations is studied, and the possibility of applying an adapted geometric model to calculations is also investigated. The distributions of magnetic fields and forces arising in the system are calculated. Verification of the model is carried out by comparing the results of calculations performed by several independent software. The results of numerical modeling coincide with the required accuracy for all software packages used, in particular, the estimate of the relative deviation of the force values does not exceed 3 %.

Computational models are described which were built for parametric simulations of permanent magnet (PM) dipoles with a longitudinal field gradient. The dipoles will be used as bending magnets in the synchrotron facility SILA, a new project of the National Research Center “Kurchatov Institute”. The dipoles employ a Sm-Co permanent magnet material and pure iron. The need for high magnetic performance and anticipated interference between neighbouring components is a challenge for design and construction of the magnet system. For this reason the magnet designs must rely on precision 3D simulations. The dipoles are described in detail with parameterized models. Parametric simulations are to be applied at all stages of the project till the commissioning to provide realistic prediction of the magnet behaviour.

The 40 cell lattice of the new Russian synchrotron radiation facility SILA is envisaged to employ permanent magnet (PM) dipoles as bend magnets. Numerical study of the basic concept for short PM dipoles is described. Iterative 3D simulations with a detailed model were used to assess anticipated field distribution and magnetic forces. A scope of critical aspects was investigated to move up to the engineering design including candidate materials, geometry, thermal stability, magnetic interaction, and field tuning. Aggregated results made it possible to optimize the initial concept and get guidance to practical implementation.

An optimized magnetic specification has been searched for a PM quadrupole constructed for the DC-140 cyclotron in JINR, Dubna. The field inhomogeneity should be reduced to come closer to an ideal distribution. The quad parameters should be determined with very high mechanical and magnetic precision in order to reach the specified gradient. Results of the analytic study based on a 2D model gave initial values for the PM blocks dimensions and orientations. To ensure stringent performance criteria, parametrized 2D and 3D models of the quad were built. These models were used to optimize the magnet configuration, analyze its sensitivity to various errors and derive parameter tolerances. Additional adjustment to suitable field quality is foreseen using results of a trajectory analysis and acceptance inspection. The design parameters for the best suited magnet configuration are presented and the performance criteria are defined. However, an electromagnetic analysis of the selected configuration has revealed that the relative field error adopted previously as the optimization criterion gives low accuracy estimate. Alternative estimations are proposed utilizing the field gradient error as the basic criterion to satisfy the constraint on the field inhomogeneity.

On ITER, plasma start-up will be performed in limiter configuration on the inboard equatorial beryllium first wall panels (FWP). In contrast to most present tokamaks, however, this ramp-up phase will be comparatively long (∼10 s) and the use of actively cooled components means that power flux management is key if FWP lifetime is not to be compromised. Shaping of the FWPs is mandatory to ensure that leading edges do not appear between neighbouring units. For the ITER inboard panels, this has been optimized to account for the discovery in recent years on current devices of narrow scrape-off layer power flux channels for inner wall limited plasmas. However, the shaping results in power densities which are particularly sensitive to the overall ‘longwave’ (LW) alignment of the central column FWP ring with the structure of the toroidal magnetic field (TF), placing tight constraints on the target alignment. This target is currently based on a pure n = 1 LW alignment, but simulations of TF coil (TFC) locking upon energization show that, depending on the initial configuration of the gaps between the TFC inner legs, the field structure can be more complex. Although the TFC manufacture and machine assembly strategy is to make every effort possible to approach the ideal TF structure, an NMR sensor-based TF mapping diagnostic will be implemented to measure the field structure during the first plasma and engineering operation phase. An analytic framework has been developed and verified against numerical simulations to assess the capability for measurements from a set of discrete sensors located on the vacuum vessel inner column to be used to reconstruct the field structure at the FWP locations, a further ∼60 cm radially inward. In parallel with the alignment optimization and TF mapping strategies, modified ramp-up scenarios are also being designed which may be used to reduce inner wall limiter power fluxes if this proves to be necessary during operation.

Aim: The study was focused on measurement of the lifting force of a hybrid EMS (HEMS) prototype. The measured data were used to verify numerical models. Materials and Methods: Measurements were performed on a certified test bench at a large air gap (13 mm, 17 mm). The measured data were compared with results of numerical experiments. Results: A comparison of measured and simulated parameters have proved reliability of numerical models. Conclusions: A prototype of HEMS for maglev transport has been built and bench tested at JSC NIIEFA. The results obtained will be used to establish measurement, prototyping, and inspection procedures for series production.

Aim: The aim of the study is a comparative representation of a hybrid EM suspension (HEMS) for maglev transport and a pure EM configuration. Methods: Several designs have been numerically investigated and compared to conventional EMS. The numerical model has been validated with magnetic measurements on the experimental set-up. Results: The HEMS implies a combination of electromagnets (EM) and permanent magnets (PM) in a common magnetic circuit. The magnets synergy of HEMS has been demonstrated that leads to sufficient reduction in energy consumption and weight as compared to a conventional EMS. Conclusions: A desired performance of HEMS has been achieved. Efficiency of the design solutions has been verified numerically and experimentally.

Aim: To test the levitation performance of a hybrid EMS prototype. Materials and Methods: a levitation test setup with a 18 mm thick steel rail was constructed on a basis of the certified test bench 1958U-10-1 for measurement in the range up to 100 kN. The attractive force was investigated by varying the air gap size and coil current. Measured data were compared with parametric simulations. Results: Experimental and numerical results agreed with the accuracy required for practical application. Conclusions: A prototype of hybrid EMS (HEMS) for maglev transport has been designed, built, and tested at JSC NIIEFA. The HEMS concept has an advantage of reduced power loss and low stray field. The bench testing has proved good levitation performance and low power consumption of the proposed design. The measured data were used to check design solutions and verify 3D numerical models of the magnets. The comparison demonstrated a good match between measurements and simulations.

The design and specification choices are described for a PM quadrupole used to enable beam transport in a cyclotron. First an analytic study with a simplified 2D model is performed to give initial values for magnet configuration and performance. Characteristics of PM blocks and cylinders are analysed. Then a 3D parametrized model is used to solve the direct magnetostatic problem and accurately define quad specifications. Simulations are carried out with KOMPOT electromagnetic code utilizing the differential formulation. The regulariza- tion method is applied to solve the inverse problem. Magnetic characteristics, dimensions and shapes of the PM units and iron parts are determined in order to reach the specified field gradient. Possible correction of the resulting the ideal specification is discussed with respect to additional constraints put by practical implementation. Candidate PM materials are proposed. Simulated field maps are presented. The method described may serve as a basis for virtual prototyping and be integrated into end-to-end design and construction of magnet systems.

A hybrid suspension system is proposed for maglev transport that utilizes electromagnets (EM) in combination with permanent magnets (PM). Several design schemes are compared searching for optimum performance. Sufficient reduction of power consumption and stray field is achieved on the hybrid configuration as compared to conventional EM suspension systems.

One of the most crucial issues in the design of the ITER machine is the electromagnetic (EM) loads associated with eddy currents induced in the conducting structures during plasma disruptions. The ITER database contains tens of calculation scenarios for possible plasma disruption events. The duration of these scenarios is usually limited by the end of the plasma current quench when the toroidal plasma current decreases to zero. For further EM analysis, the currents in the poloidal field coils are conventionally assumed constant after the end of the current quench. Such approach is not good for estimation of electromagnetic loads acting on the tokamak components located outside vacuum vessel. A possible way to solve this problem is to employ pre-determined coil current variations over the entire period of observation including time interval after the current quench. This paper describes an approach to such electromagnetic calculations and comparative results for selected cases with/out an extended current-time specification.

Some aspects of electromagnetic (EM) simulation of the central divertor cassettes (CDC) in the ITER tokamak are described. The study is focused on EM loads anticipated on the plasma-facing units (PFU) of CDC. The paper is devoted to the EM simulations of the most dangerous scenarios associated with high mechanical stresses: fast downward vertical displacement events of Categories II and III with 36-ms linear current quench (FD VDE-II and FD VDE-III with 36-ms LCQ). The selected events have been analyzed using the original TORNADO code intended for simulation of transient EM processes in 3D solids using the finite element representation. Results of computations include evolutions of EM loads on PFUs in the form of integral EM forces and moments, their peak values and relevant time points.

The paper is devoted to the development of the models of magnetic shielding system for the ITER neutral beam injectors. As the reactor operation is quasistationary, the magnetic field reduction system of the injectors combines a passive magnetic shield and a set of active correction coils. Due to the strict restrictions on the field inside the injectors, precision computations are required during the design stage. A special attention has been paid to possible gaps between steel panels of the passive magnetic shields due to manufacturing and assembly inaccuracies. A set of models with different levels of detail has been built for the convergence study. It was shown that the mesh needs to have tens of millions finite elements to provide the required computational accuracy.

The stray poloidal magnetic field produced in ITER outside the tokamak is significantly higher than in any present machines. This magnetic field magnetizes the steel rebar reinforcing the building concrete structures enclosing the tokamak. As a result, reinforced structures of the ITER building may produce a substantial magnetic field with the axisymmetric component (toroidal mode number n = 0) affecting the plasma initiation and non-axisymmetric components ("error fields" with n = 1; 2) deteriorating plasma performance. This paper presents an upgraded Magnetic Model of the ITER Tokamak Complex, MMTC-2.2, for assessment of the stray field associated with the reinforced structures. This magnetic model MMTC-2.2 takes into account the CATIA models of the Tokamak Complex Buildings and volumetric fractions of steel for the rebar in the building structures as they were in the design in 2016.

The paper assesses the n = 1 "overlap" error fields produced by localized steel objects (the object size is much less than the distance from the object to the plasma) placed at different levels of the ITER Tokamak building. The value of the error field proportionally depends on the mass of steel object. This paper studies the effect of the shape of steel objects on error field. For evaluations, three shapes of steel objects are considered allowing analytical calculation of their magnetization: a steel ball and a thin steel cylinder oriented either perpendicularly or parallel to the external magnetic field. The paper demonstrates a strong effect on the error field of the object shape and orientation.

Numerical verification is presented for modelling the magnetic effect of concrete structures reinforced with steel rebar. The model is based on the filling factor concept and takes into account magnetic anisotropy associated with the rebar pattern. Test problems are solved that prove applicability of the model in case of nonlinear properties of the reinforcement steel. A nonuniform field distribution is studied for a reinforced structure with an internal field source. Accuracy of simulated field maps with high gradients near ends of modelled structures has been assessed. The model has been verified in comparative computations with the use of other models. As an example, the proposed approach has been applied to a simplified magnetic model of the ITER tokamak complex. Then fields perturbations associated with the tokamak building structures have been evaluated for the gas breakdown at plasma initiation.

Electromagnetic suspension (EMS) system for magnetically levitated vehicles can utilize different types of magnets, such as room temperature electromagnets, superconducting magnets as well as permanent magnets. In the course of the study the trichotomy has been applied to the electromagnetic suspension system. The EMS configuration considered in this paper has been treated as a combination of these three types of magnets modelled individually. Results of computations were compared to measurements on a working prototype that provided stable levitation of a platform weighing above 190 kg. A good agreement between the simulated and measured parameters enabled verification of the computational models for separate magnets, selection of efficient control algorithms for a combined EMS system, validation of numerical procedures for payload scaling for practical maglev applications. The combined EMS under study has demonstrated improved power consumption as compared to the conventional EMS. Optimal control algorithms for a combined EMS should factor in various criteria, including rapidity, stability, power consumption, weight, reliability, etc. Different types of magnets can be integrated into a single module to reach the desired performance. Hence, the optimum solution for the EMS design and relevant control algorithms should be searched within a common procedure using detailed computational models.

A measurement-based numerical reconstruction technique is proposed to control winding geometry of the poloidal coils manufactured for ITER. A detailed coil model is parameterized in terms of the magnetic characteristics. Deviations from the specified coil shape are evaluated in a comparison of reconstructed "ideal" field and data of magnetic measurements. The technique has been validated in the course of quality inspection of the dummy double pancake similar to the pancakes of the ITER PF1 coil. Experimental results are presented.