Error Field Correction Research Articles

Correction coil and magnet feeder lessons learned

China has contributed to the manufacturing of the Error Field Correction Coils (CC) and the Magnet Feeders for ITER (International Thermonuclear Experimental Reactor). The manufacturing projects have been carried by ASIPP (Institute of Plasma Physics Chinese Academy of Sciences). In this paper, the lessons learned from these two manufacturing projects will be described with special focus on some key manufacturing processes. These experiences gained from the work carried so far in CC and magnet feeder manufacturing and testing are very valuable not only for the remaining manufacturing tasks of these two projects, but also for similar systems of other Tokamak fusion device.

Error field detection and correction studies towards ITER operation

In magnetic fusion devices, error field (EF) sources, spurious magnetic field perturbations, need to be identified and corrected for safe and stable (disruption-free) tokamak operation. Within Work Package Tokamak Exploitation RT04, a series of studies have been carried out to test the portability of the novel non-disruptive method, designed and tested in DIII-D (Paz-Soldan et al 2022 Nucl. Fusion 62 126007), and to perform an assessment of model-based EF control strategies towards their applicability in ITER. In this paper, the lessons learned, the physical mechanism behind the magnetic island healing, which relies on enhanced viscous torque that acts against the static electro-magnetic torque, and the main control achievements are reported, together with the first design of the asynchronous EF correction current/density controller for ITER.

On the use of error field correction coils in JET

This work describes the usage of Error Field Correction Coil (EFCC) system [Barlow I. et al. 2001 Fusion Eng. Des. 58–59 189], which is a set of 4 coils located external to the vessel of the JET device, with the aim of introducing non-axisymmetric n = 1 magnetic field perturbations in various targeted plasma experiments. Besides being used to characterize and correct the intrinsic error field, the EFCCs system has been exploited to i) probe plasma stability in high-βN regimes through the MHD spectroscopy technique, allowing the identification of resistive-wall mode stable operational scenarios, ii) study radiation asymmetry when testing the shattered pellet injector as the prime candidate for ITER disruption mitigation system, and iii) control edge localized modes, permitting a reduction in heat fluxes and carbon erosion of the divertor target plates.

Studies on EU-DEMO 3D coils requirements and conceptual design for error field correction and plasma control

This work presents the initial studies on the requirements for the design of 3D coils on EU-DEMO. The use of 3D coils in present machines includes two main purposes: the first one is the Error Field Correction (EFC). The EFC aims at minimizing the intrinsic non-axisymmetric fields in the machine. Fulfilling the requirements is evaluated with the minimization of residual error fields, both in vacuum and with plasma response. The second purpose relates to the application of 3D fields to control the plasma. The first of these control functions includes the manipulation of the locked neoclassical tearing modes (NTMs) phase, and their positioning in front of the electron cyclotron antennae, for optimum stabilization. A second function is the application of 3D perturbation of the plasma edge to suppress ELMs. As the fastest required time constant of the applied 3D fields is comparable or longer with respect to that of the vacuum vessel, ex-vessel coils can be considered. Another constraint considered is that the 3D fields applied do not generate 3D power exhaust effects, such as divertor lobes, that jeopardize the protection of the machine divertor/wall. This constriant is met in the finding of this work, in the case considered of the ELMs suppression. The aim of this study is to assess if one set of coils could be designed that fulfills all these purposes/functions. The results show that, by using ITER tolerances for the TF, CS and PF coils, all these functions on EFC (using the overlap criterion assumption, which includes the plasma response), NTM phase control and ELMs suppression can be met with the proposed design of one row of ex vessel coils. An additional activity has started to study if the non-resonant perturbations generated by this set of coils could lead to detrimental effects via neoclassical toroidal viscosity (NTV) torque. Preliminary considerations on the coil technology, are also presented, with no showstopper found in this preliminary phase.

Locked mode detection during error field identification studies

At the beginning of a machine operation, an assessment of the intrinsic error fields, spurious magnetic field perturbations which can affect plasma dynamics, is often carried out by executing the compass scan method [Scoville J.T. et al. Nucl. Fusion 43 250 (2003)]. This method relies on the application of 3D magnetic fields with various phases, induced by EF correction coils, to trigger a locked mode. The instant of locked mode onset allows the identification of the amplitude and phase of the intrinsic error field, from which the empirical correction currents for its minimization can be deduced. The presence of a locked mode needs to be carefully monitored during this study because of the potential disruptive mode behavior, especially in devices which can tolerate a maximum number of disruptions, as in SPARC and in ITER. A novel method, the so-called non-disruptive compass scan method [Paz-Soldan C. et al., Nuclear Fusion 54 (2014) 073013], avoids the disruption risk, as the name recalls, via magnetic island healing, i.e. stabilizing the locked mode. The magnetic island healing is achieved by switching off the error field correction coil current during the execution of the compass scan and asynchronously by increasing the plasma density. The crucial point of this new method is the detection of the locked mode to initiate the EFCC-density control actions. In this work, the locked mode detector adopted during non-disruptive compass scan test at JET is presented, together with brand-new locked mode metrics, which take into account the actual poloidal deformation due to a locked mode and a class of MHD instabilities, named Beta Alfvén Eigenmodes, that appear in the Mirnov signal in concomitance to the locked mode. The use of multiple metrics for locked mode detection during the execution of the non-disruptive compass scan increases the fidelity of the real-time control system to pinpoint the event, compensating possible magnetic probe failure, and initiate the control sequences to heal the magnetic island.

Mutual Induction Caused by IVCC Currents on Quench Detection Circuits of the KSTAR TF Coils

The Quench Detection System (QDS) for the Toroidal Field (TF) coils and the Poloidal Field (PF) coils made of Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn or NbTi cable-in-conduit conductors is using Wheatstone bridges to compensate induced voltages, which are generated by electrical currents of the superconducting coils and a plasma, on the quench detection circuits of the Korea Superconducting Tokamak Advanced Research (KSTAR) device. On the other hand, the KSTAR device is equipped with In-Vessel Control Coils (IVCCs), which consist of 16 segmented windings made of normal conductors, for fast plasma position control, field error correction, and resistive wall mode stabilization. Electrical currents of the middle Field Error correction Coil (FEC) in a part of the IVCCs have strong mutual induction on the quench detection circuits of the TF coils due to the paths of the FEC's conductors, and the middle FEC currents, which had unusually long and very steep ramps, raised an emergency protection sequence of the TF coils in a KSTAR plasma experiment. Quench detection circuits only using traditional Wheatstone bridges are insufficient to cancel out such a mutual induction; whereas, the mutual induction can be numerically compensated in a theoretically straightforward calculation.

Manufacturing of pedestal supporting error field correction coil in JT-60SA

Eighteen error field correction coils (EFCCs) consisting of copper conductor and epoxy resin are installed in the vacuum vessel of JT-60SA in order to correct magnetic fields caused by manufacturing and installation errors of superconducting coils. Pedestals consisting of plate and spring bars for supporting the EFCCs were designed to withstand electromagnetic force during plasma operations and allow relative displacement between the EFCC at 40 °C and the vacuum vessel at 200 °C during baking operations. Feasibility of fixing the ends of the spring bars to the plates with plug welding and clearance of 50 μm was investigated using mechanical load test and trial manufacturing. Design for manufacturing was decided based on the results. Structural integrity of the design was confirmed through structural analysis with finite element method (FEM). Manufacturing of the pedestals has successfully completed.

A novel scheme for error field correction in permanent magnet stellarators

Stellarators offer a promising path towards fusion reactors, but their design and construction are complicated by stringent tolerance requirements on highly complex 3D coils. A potential way to simplify the engineering requirements for stellarators is to use simple planar toroidal field coils along with permanent magnet arrays to generate shaping fields. In order to ensure sufficient field accuracy while minimizing engineering complexity and system cost, new techniques are required to correct the field produced by the permanent magnet arrays to within requirements set by plasma physics. This work describes a novel correction method developed for this purpose. This analysis is applied to the design of a quasi-axisymmetric stellarator that employs a combination of permanent magnets and planar toroidal field coils to generate its magnetic field. Analysis techniques and initial results using the method for error correction on a proposed permanent magnet stellarator are shown, and it is demonstrated that the method successfully meets the design requirements of the project.

PM4Stell: A prototype permanent magnet stellarator structure

Permanent magnets provide a possible solution to simplify complicated stellarator coils. A prototype permanent magnet stellarator structure, PM4Stell, has been funded to demonstrate the technical feasibility of using permanent magnets to create the shaping field of a stellarator. Permanent magnets in uniform cubes with three polarization directions will be carefully placed to generate the required magnetic field for a National Compact Stellarator eXperiment-like equilibrium together with planar toroidal field coils. Discrete magnets will be glued together and inserted into a “post-office-box-like” supporting structure. Electromagnetic and structural analyses have been done to validate the design. Error field correction magnets will be used to shim possible error fields. The design efforts of the prototype permanent magnet stellarator structure are discussed.

Investigating the n = 1 and n = 2 error fields in W7-X using the newly accelerated FIELDLINES code

No fusion device can be created without some uncertainty; there is always a slight deviation from the geometric specification. These deviations can add up create a deviation of the magnetic field. This deviation is known as the (magnetic) error field. Correcting these error fields is desired as they cause asymmetries in the divertor loads and can thus cause damage to the device if they grow too large. These error fields can be defined by their toroidal (n) and poloidal number (m). The correction of the n = 1 and n = 2 fields in Wendelstein 7-X (W7-X) is investigated in this work. This investigation focuses on field line diffusion to the divertor, a proxy for divertor heat flux. Such work leverages the 25× speedup obtained through the implementation of a new particle-wall collision model. The n = 1 and n = 2 error fields of the as-built coils model of W7-X are corrected by scanning phase and amplitude of the trim and control coils. Reductions in the divertor load asymmetry by factors of four are demonstrated using error field correction. It is found that the as-built coils model has a significantly lower error field than found in experiments (Bozhenkov et al 2018 Nucl. Fusion 59 026004).

Structural design of pedestal for error field correction coil in JT-60SA

Eighteen error field correction coils (EFCCs) consisting of copper conductor and epoxy resin are installed in the vacuum vessel of JT-60SA in order to correct magnetic fields caused by manufacturing and installation errors of superconducting coils. The EFCCs are supported by pedestals made of stainless steel 316 L, and the pedestal has spring bars made of NCF625. The pedestals need to withstand electromagnetic force induced by EFCC current and magnetic field during plasma operations. They also need to allow relative displacement between the EFCC and the vacuum vessel during baking operations caused by the temperature difference between the vacuum vessel of 200 °C and EFCC of 40 °C. Diameter of the spring bars and connection structure for fixing the spring bars were designed through FEM analysis.

Quasisymmetric Optimization of Nonaxisymmetry in Tokamaks.

Predictive 3D optimization reveals a novel approach to modify a nonaxisymmetric magnetic perturbation to be entirely harmless for tokamaks, by essentially restoring quasisymmetry in perturbed particle orbits as much as possible. Such a quasisymmetric magnetic perturbation (QSMP) has been designed and successfully tested in the KSTAR and DIII-D tokamaks, demonstrating no performance degradation despite the large overall amplitudes of nonaxisymmetric fields and strong response otherwise expected in the tested plasmas. The results indicate that a quasisymmetric optimization is a robust path of error field correction across the resonant and nonresonant field spectrum in a tokamak, leveraging the prevailing concept of quasisymmetry for general 3D plasma confinement systems such as stellarators. The optimization becomes, in fact, a simple eigenvalue problem to the so-called torque response matrices if a perturbed equilibrium is calculated consistent with nonaxisymmetric neoclassical transport.

Modeling plasma toroidal flow profile control via NTV torque with n = 2 3D fields in MAST-U

Toroidal modeling utilizing the MARS-Q code (Liu et al 2013 Phys. Plasmas 20 042503) shows that large (compared to electromagnetic torque) neoclassical toroidal viscous (NTV) torque can be achieved in the plasma core region in reference MAST(-U) L-mode plasmas, by applying the n = 2 (n is the toroidal mode number) 3D fields generated by the magnetic coils used for controlling the edge localized mode and/or by the error field correction coils. Large NTV torque, occurring at relatively slow plasma flow, in combination with strong variation of the torque amplitude versus the coil phasing of the 3D coils, offers a tool to control the plasma toroidal rotation profile in spherical tokamaks. To effectively employ the toroidal NTV torque, the potentially fast initial flow needs to first be damped by 3D fields. MARS-Q quasi-linear initial value simulations demonstrate that this is achievable in MAST-U, within the designed 3D coil current capability for the device.

Error field correction strategies in preparation to MAST-U operation

Abstract In magnetic fusion devices, unwanted non-axisymmetric magnetic field perturbations, known as error fields (EF), can have detrimental effects on plasma stability and confinement. Such EFs may originate from several sources, such as axi-symmetric coil misalignments, coil feeds, 3D structures in the wall surrounding the plasma, presence of ferromagnetic materials near the plasma surface, blanket materials in future devices. To minimize their impact on plasma performance and on the available operational space, it is important to identify the EF sources and develop EF control strategies. MAST Upgrade (MAST-U) is a spherical tokamak which will operate in the near future after a series of enhancements from the previous MAST experiment (Morris A.W. et al., MAST accomplishments and upgrade for fusion next-steps. IEEE Transactions on Plasma Science, April 2014). To deliver a machine with EF amplitude low enough to allow a high quality experimental programme, systematic analysis of the intrinsic EF sources has been carried out for poloidal field (P) and divertor (D) coils. To deliver a machine with EF amplitude low enough to allow a high quality experimental programme, systematic analysis of the intrinsic EF sources has been carried out for poloidal field (P) and divertor (D) coils, whose magnetic field measurements were available when writing this paper. Such measurements reveal that P and D coils are 3D deformed and thus are responsible for intrinsic EFs, with mainly n = 1 and n = 2 toroidal mode numbers. In preparation to MAST-U operation, both passive and active EF control strategies have been adopted for n = 1 and n = 2 EFs compensation. Passive EF control consisted of installing finely each D and P coil within MAST-U device so as to minimize the intrinsic n = 1 EF amplitude. The optimal coil alignment has been determined based on magnetic field measurements and the corresponding 3D electro-magnetic modelling, and envisaged coil shift and tilt of 3.2 mm and 0.7 mrad, respectively, in the case of P coil named P4. Conversely, active control will be use during MAST-U operation to reduce the n = 2 EF which is associated mainly with P4 and P5, as well (Kirk A. et al. 2014 Plasma Phys. Control. Fusion 56, 104003). Since these coils have been re-used from the MAST device, studies attempting n = 2 EF control, based on MAST plasmas, have been modelled utilizing the MARS-F code (Liu Y.Q. et al. 2000 Phys. Plasmas 7, 3681) to interpret experimental results in MAST and to give hints for future n = 2 EF control studies in MAST-U. A model-based control set for n = 2 EF control has been identified which would allow for the minimization of rotation braking, of the resonant magnetic field at th=agand of the plasma displacement in MAST-U, simultaneously.

Estimation of magnetic error field with alleviating fabrication tolerance of large superconducting magnets on JA DEMO reactor

Abstract Generally, DEMO requires larger toroidal field (TF) coils than ITER, resulting in one of the major difficulties, the tolerance in TF coil fabrication. This paper presents the possible solutions based on the design study on Japan’s DEMO (JA DEMO). It was confirmed that, in the case of adopting a mitigated tolerance by a factor of 2.5–5 compared with that of ITER, the resulting error field of TF coils is correctable to an acceptable level in terms of locked mode avoidance. In addition, the design of the error field correction coil (EFCC) on JA DEMO was investigated.

Commissioning of the Wendelstein 7-X in Vessel Control Coils

The magnet system of the stellarator fusion device Wendelstein 7-X (W7-X) is composed of three different groups of coil systems. The main magnetic field is created by a superconducting magnet system that is accompanied by two sets of normal conducting coil groups, the trim coils positioned outside of the cryostat and the control coils (CCs) inside the plasma vessel. The CC system consists of ten 3-D shaped coils, power supplies, cooling systems, high current feeds, and an autonomous remote control system. The coils are situated behind the baffle plates of the ten divertor units. The magnetic field created by the CC system allows for the correction of error fields to influence the islands at the plasma boundary and for the sweeping of the separatrix, e.g., the point of the largest power position across the divertor. At the end of 2015, the installation of the CC system was completed and the integral commissioning took place in parallel with the ongoing completion of W7-X. For the first time, the CCs and their power supply were operated in conjunction with all auxiliary systems like the power distribution system, the high current feeds, the interspace vacuum system, the cooling system, and the safety control system. This article describes the results obtained and experiences gained during the integral commissioning of the CC system, including the baking process in preparation for the first experimental campaign of W7-X.

Generalized framework for PIV-based pressure gradient error field determination and correction

A framework leveraging the governing equations of incompressible flow for the reconstruction and correction of pressure gradient estimation errors from experimental data is extended to incorporate non-zero errors on domain boundaries and Lagrangian pseudo-tracking methods for material acceleration estimation. A second-order system derived from the first-order divergence-curl system governing the pressure gradient error field facilitates handling a variety of error boundary conditions, and the solution can be split into independent Poisson equations, making it straightforward to implement. For known boundary errors, a precise determination of the pressure gradient field is possible, up to the limitations of the numerical method. In practice, the error equations cannot be solved exactly; however, a number of terms may be computed exactly and approximations may be applied on the remaining terms. For the selected test case of a cylinder wake flow in turbulent shedding regime, the analysis of simulated three-dimensional, three-component velocity measurements demonstrates that the errors in pressure estimates can be reduced by up to 50% using a basic finite difference implementation.

Error field impact on mode locking and divertor heat flux in NSTX-U

During the 2016 NSTX-U experimental campaign, locked modes in the plasma edge presented clear evidence of the presence of error fields. Extensive metrology and plasma response modeling with IPEC and M3D-C1 have been conducted to understand the various sources of error fields in NSTX-U as built in 2016, and to determine which of these sources have the greatest effect on the plasma. In particular, modeling finds that the error field from misalignment of the toroidal field (TF) coils may have a significant effect on the plasma. The response to the TF error field is shown to depend on the presence of a q = 1 surface, in qualitative agreement with experimental observations. It is found that certain characteristics of the TF error field present new challenges for error field correction. Specifically, the error field spectrum differs significantly from that of coils on the low-field side (such as the NSTX-U error field correction coils), and does not resonate strongly with the dominant kink mode, thus potentially requiring a multi-mode correction. Furthermore, to mitigate heat fluxes using poloidal flux expansion, the pitch angle at the divertor plates must be small (∼). It is shown that uncorrected error fields may result in potentially significant local perturbation to the pitch angle. Estimates for coil alignment tolerances in NSTX-U are derived based on consideration of both heat flux and core resonant fields independently.

Edge localized mode suppression and plasma response using mixed toroidal harmonic resonant magnetic perturbations in DIII-D

Edge localized mode (ELM) suppression has been achieved in the DIII-D tokamak using mixed toroidal and 3 harmonic resonant magnetic perturbations (RMPs). Here is the toroidal mode number. It is observed that mixed toroidal harmonic RMPs lower the threshold current for ELM suppression compared to the single case. The decreased threshold suggests that mixed toroidal harmonic RMPs offer a better path to ELM control. The error field effect is studied by superimposing error field correction upon the phase scan, which shows that it is possible to suppress the ELM and correct the error field simultaneously. The plasma response measured by magnetic sensors shows the harmonic plays a key role in ELM suppression using mixed toroidal harmonic RMPs. A nonlinear jump in the plasma response is observed during the bifurcation from mitigation to suppression of ELMs, similar to the results reported in Nazikian et al (2015 Phys. Rev. Lett. 114 5). Magneto-hydrodynamic simulations using toroidal rotation find good agreement with the ELM mitigated phase when the input rotation profile is high and induces strong screening of the RMP. Simulations with zero-crossing rotation find strong penetration of the RMP and reproduce the mode structure of ELM suppression on both the low and high field side. This suggests that edge components may penetrate during the transition from ELM mitigation to suppression.

Effects of the applied magnetic fields with various toroidal phase differences on the neoclassical toroidal viscosity in JT-60SA

The integrated framework consisting of TOPICS, VMEC and FORTEC-3D, has been applied to provide an estimate of the neoclassical toroidal viscosity (NTV) produced by the applied magnetic perturbations (MPs). Six picture-frame error field correction coils in each row in JT-60SA realize the various patterns of the applied magnetic field spectrum. The NTV is investigated for various toroidal phase differences. As long as the same coil current is applied, the n = 3 MPs generate the same NTV, regardless of even or odd parity, or energizing the middle coils or not. The n = 1 MPs give rise to larger NTV than the n = 3 ones. The NTV invoked by the n = 1 resonant MPs is virtually equivalent to that by the n = 1 nonresonant MPs with five-fold coil current.