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The data in this repository correspond to the figures of the paper "Impact of error fields and error field correction on heat fluxes in SPARC". They are created by simulations run with the M3D-C1 code, the MAFOT code and python postprocessing tools.
Using a single toroidal array of coils to reduce the m,n = 2,1 resonant error field (EF) produced by the misalignment of the axisymmetric coils in SPARC can result in the enhancement of the local divertor heat fluxes. Managing high divertor heat fluxes (q ∥ $\simeq$ 10 GW m -2 ) poses a challenge for compact tokamak devices such as SPARC. The presence of non-axisymmetric magnetic field perturbations adds complexity to the problem by generating intricate 3D edge magnetic topologies that alter the heat flux distributions on the target plates. The aim of this work is to investigate the impact of the EF correction (EFC) on the heat fluxes at the divertor plates in SPARC. The MHD code M3DC1 has been used to simulate the 3D magnetic perturbations generated by the shift and tilt of several axisymmetric coils within specified tolerances, as well as from the array of EFC coils located at the midplane. Using a heuristic model that extends the concept of an axisymmetric heat flux layer to 3D plasmas, the resultant heat flux distributions is derived from magnetic footprints calculated with the MAFOT code. The results show that the EFC could either decrease or further enhance the local heat flux when used to correct the m,n = 2,1 resonant EF to enhance the core plasma performance.
The upgrade of the EBIS, called ExtendedEBIS, is now in progress in Brookhaven National Laboratory. Two 5T-superconducting solenoids have been placed in series with 200 mm distance from each other for higher trap capacity and production of polarized 3He ions. Since the two superconducting solenoids are used, the field error is expected to be larger. In this research, the field error is estimated based on simulation. It was found that the magnetic field line can be 17 mm off from the center axis at the entrance of the collector, and this offset can be adjusted by three types of correction coils. Additionally, mismatch of the spin direction of polarized 3He due to the misalignment was estimated to be small.
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. Moreover, to mitigate heat fluxes using poloidal flux expansion, the pitch angle at the divertor plates must be small (~1°). 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.
Uncorrected static error fields in axisymmetric fusion devices are one of few remaining serious obstacles for advancing the present tokamak-based approach to practical reactors. The disruption due to magnetohydrodynamic tearing mode locking is one of them. Recently, a hypothesis has been proposed that there may exist a self-healing stabilized regime in which the static resonant error field is effectively shielded by forcing the mode slowly to rotate inductively by the applied non-axisymmetric field, that has been developed based on non-linear, resistive, reduced MHD simulation with cylindrical single helicity model. Proof-of-principle experiments in the DIII-D device showed that the magnetic mode structure on the plasma surface is qualitatively consistent with the simulation prediction. However, radial mode profiles revealed qualitatively different behavior. This finding led to a revised hypothesis that in actual non-circular toroidal devices, a tearing layer in forced rotation induces the shielding-out process at other rational surfaces when we take into account of multi-resonant Fourier components. The time evolution of the radial penetration was supportive of this hypothesis.
The magnetic field topology and error fields are measured in the MUSE permanent magnet stellarator with an electron beam and fluorescent rod. The effective magnetization of the magnets is determined by measuring rational flux surface locations. Electron magnetic drift effects must be considered self-consistently due to the small magnetic shear on MUSE. Error fields are characterized by flux surface shape deviation and magnetic island chain width and phase. Error fields are then corrected by adjusting the permanent magnet (PM) holders as rigid bodies. Resonant error fields are on the order of or smaller than 3 x 10 -6 of the toroidal field after correction and surface shape matches well with the design. Resonant components of the quasi-symmetry deviation are estimated, using a novel magnetic drift measurement, to be in the 10 −4 range. The PM approach is validated as a low-cost and precise way to build optimized stellarators.
© 2002-2011 IEEE. In the framework of the high-luminosity upgrade of the large hadron collider, the U.S. LARP collaboration and CERN are jointly developing a 150-mm aperture Nb3Sn quadrupole for the Large Hadron Collider (LHC) interaction regions. Due to the large beam size and orbit displacement in the final focusing triplet, MQXF has challenging targets for field quality at nominal operation conditions. Three short model magnets have been tested and around 30 coils have been built, allowing a first analysis of the reproducibility of the coil size and turns positioning. The impact of the coil shimming on field quality is evaluated, with special emphasis on the warm magnetic measurements and the correlation to field measurements at cold and nominal field. The variability of the field harmonics along the magnet axis is studied by means of a Monte-Carlo analysis and the effects of the corrective actions implemented to suppress the low-order unallowed multipoles are discussed.
The presence of error fields has been shown to degrade plasma confinement and drive instabilities. Error fields can arise from many sources, but are predominantly attributed to deviations in the coil geometry. In this paper, we introduce a Hessian matrix approach for determining error field sensitivity to coil deviations. A primary cost function used for designing stellarator coils, the surface integral of normalized normal field errors, was adopted to evaluate the deviation of the generated magnetic field from the desired magnetic field. The FOCUS code [Zhu et al., Nucl. Fusion 58(1):016008 (2018)] is utilized to provide fast and accurate calculations of the Hessian. The sensitivities of error fields to coil displacements are then determined by the eigenvalues of the Hessian matrix. A proof-of-principle example is given on a CNT-like configuration. We anticipate that this new method could provide information to avoid dominant coil misalignments and simplify coil designs for stellarators.
Error fields have been detected and quantified using the flux surface mapping diagnostic system on Wendelstein 7-X (W7-X). A low-field '${\rlap{-}\ \iota} =1/2$ ' magnetic configuration (${\rlap{-}\ \iota} =\iota /2\pi $ ), sensitive to error fields, was developed in order to detect their presence using the flux surface mapping diagnostic. In this configuration, a vacuum flux surface with rotational transform of n/m = 1/2 is created at the mid-radius of the vacuum flux surfaces. If no error fields are present a vanishingly small n/m = 5/10 island chain should be present. Modeling indicates that if an n = 1 perturbing field is applied by the trim coils, a large n/m = 1/2 island chain will be opened. This island chain is used to create a perturbation large enough to be imaged by the diagnostic. Phase and amplitude scans of the applied field allow the measurement of a small $\sim 0.04$ m intrinsic island chain with a ${{130}^{\circ}}$ phase relative to the first module of the W7-X experiment. Lastly, these error fields are determined to be small and easily correctable by the trim coil system.
The critical n=1, n=2, and n=3 error-field amplitudes needed to trigger error-field penetration in ITER and SPARC, steady-state, ohmically heated plasmas are calculated using a standard asymptotic matching approach. The calculation incorporates plasma impurities, trapped particles, the bootstrap current, and neoclassical poloidal flow-damping. The energy confinement time is specified by the neo-Alcator scaling law in the low-density linear ohmic confinement (LOC) regime, and by the ITER-89P L-mode scaling law in the high-density saturated ohmic confinement regime (SOC) regime. The response of the plasma in the inner region is calculated using a linearized version of the four-field model. At the normal operating electron number density, diamagnetic levels of rotation are found to be sufficient to protect ITER and SPARC ohmically heated plasmas from m=2/n=1 error-field penetration. On other hand, SPARC, and especially ITER, ohmically heated plasmas may be vulnerable to n>1 error-field penetration. ITER and SPARC ohmically heated plasmas are also slightly more susceptible to error-field penetration when the electron fluid at the rational surface rotates in the ion diamagnetic direction, rather than the electron diamagnetic direction. At electron number densities that are sufficiently low that the plasma lies in the LOC confinement regime, the error-field penetration threshold increases with increasing density. However, as soon as the electron number density becomes large enough that the plasma enters the SOC regime, the increase in the error-field penetration threshold with increasing density levels off.
The role of error fields in stellarators is explored in this work through simulations of, and experiments performed on, the Wendelstein 7-X (W7-X) stellarator. Previous experimental results, based on limiter plasmas in W7-X, suggest that error fields are small in the experiment based on limiter plasmas. In this work, we document results from the first divertor campaign on W7-X with a focus on error fields resonant with the edge island divertor structure. Measurements obtained using divertor thermocouples corroborate earlier limiter results that the error fields are small and correctable, requiring only 5% of the total rated current of the trim coil system. The effect of these error fields on magnetic geometry and topology are investigated using the flux surface measurement technique. The resulting divertor thermal load asymmetry is modeled via field line diffusion and compared to experimental data.
Error fields are predominantly attributed to inevitable coil imperfections. Controlling error fields during coil fabrication and assembly is crucial for stellarators. Excessively tight coil tolerance increases time and cost, and, in part, led to the cancellation of the National Compact Stellarator Experiment and delay of W7-X. In this paper, we improve the recently proposed Hessian matrix method to rapidly identify important coil deviations. Two of the most common figures of merit, magnetic island size and quasi-symmetry, are analytically differentiated over coil parameters. By extracting the eigenvectors of the Hessian matrix, we can directly identify sensitive coil deviations in the order of the eigenvalues. The new method is applied to the upcoming Chinese First Quasi-axisymmetric Stellarator configuration. Important perturbations that enlarge n/m = 4/11 islands and deteriorate quasi-axisymmetry of the magnetic field are successfully determined. The results suggest each modular coil should have separate tolerance and some certain perturbation combinations will produce significant error fields. By relaxing unnecessary coil tolerance, this method will hopefully lead to a substantial reduction in time and cost.
In this project, we improve beam stability for the Electron-Ion Collider. Magnetic field errors can reduce beam stability, making it essential to identify the field errors that have the greatest impact on accelerator performance. However, this is particularly challenging because beam stability depends on the complex interactions of many magnetic field errors, resulting in a high-dimensional and nonlinear optimization problem. We determine which field errors are the most influential for the large physical aperture superconducting magnet B2PF, a critical magnet in the Interaction Region (IR) in the Hadron Storage Ring (HSR). We complete and analyze nearly 30,000 simulations on the Brookhaven National Laboratory Linux Cluster by varying 18 nonlinear magnetic field errors. We evaluate beam stability using the dynamic aperture and the tune diffusion. We identify the field errors that most strongly influence beam stability and establish quantitative field error tolerances that improve accelerator performance.
The measurement and correction of error fields in Wendelstein 7-X (W7-X) is critical to long pulse high beta operation, as small error fields may cause overloading of divertor plates in some configurations. Accordingly, as part of a broad collaborative effort, the detection and correction of error fields on the W7-X experiment has been performed using the trim coil system in conjunction with the flux surface mapping diagnostic and high resolution infrared camera. In the early commissioning phase of the experiment, the trim coils were used to open an n/m = 1/2 island chain in a specially designed magnetic configuration. The flux surfacing mapping diagnostic was then able to directly image the magnetic topology of the experiment, allowing the inference of a small similar to 4 cm intrinsic island chain. The suspected main sources of the error field, slight misalignment and deformations of the superconducting coils, are then confirmed through experimental modeling using the detailed measurements of the coil positions. Observations of the limiters temperatures in module 5 shows a clear dependence of the limiter heat flux pattern as the perturbing fields are rotated. Plasma experiments without applied correcting fields show a significant asymmetry in neutral pressure (centered in module 4) and light emission (visible, H-alpha, CII, and CIII). Such pressure asymmetry is associated with plasma-wall (limiter) interaction asymmetries between the modules. Application of trim coil fields with n = 1 waveform correct the imbalance. Confirmation of the error fields allows the assessment of magnetic fields which resonate with the n/m = 5/5 island chain.
3D magnetic sensors are employed to identify the amplitude and toroidal phase of error fields (EF) by analyzing the torque balance for magnetic islands entrained by rotating resonant magnetic perturbations (RMPs) in DIII-D H-mode plasmas. This technique of torque balance allows for efficient error field identification, offering a valuable tool for scenario-specific and optimized error field compensation (EFC) and requires only magnetic diagnostics. The torque balance used in this work includes the contribution from electromagnetic torque due to error fields, wall response, RMP fields, and viscous. Results show that viscous torque plays a crucial role, particularly during locked modes and H-mode plasmas, ensuring accurate data fits with lower residuals. The torque balance technique reveals that the L- and H-mode plasmas have distinct EF configurations, and consistent with a model-based EF analysis including MHD response in IPEC and the SURFMN EF simulation. This technique shows great robustness in measuring the intrinsic EF amplitude regardless of its amplitude or toroidal phase. Repeated discharges with EFC disparities exhibit consistent results of intrinsic error field within a reasonable range near the “standard” error field compensation. Additionally, the use of a rotating n = 1 resonant magnetic perturbation offers the advantage of reducing disruption risks by entraining saturated magnetic islands. These findings are instrumental for optimizing EF correction in fusion devices, thereby enhancing tearing mode suppression and overall plasma stability.
A tokamak relies on the axisymmetric magnetic fields to confine fusion plasmas and aims to deliver sustainable and clean energy. However, misalignments arise inevitably in the tokamak construction, leading to small asymmetries in the magnetic field known as error fields (EFs). The EFs have been a major concern in the tokamak approaches because small EFs, even less than 0.1%, can drive a plasma disruption. Meanwhile, the EFs in the tokamak can be favorably used for controlling plasma instabilities, such as edge-localized modes (ELMs). Here we show an optimization that tailors the EFs to maintain an edge 3D response for ELM control with a minimized core 3D response to avoid plasma disruption and unnecessary confinement degradation. We design and demonstrate such an edge-localized 3D response in the KSTAR facility, benefiting from its unique flexibility to change many degrees of freedom in the 3D coil space for the various fusion plasma regimes. This favorable control of the tokamak EF represents a notable advance for designing intrinsically 3D tokamaks to optimize stability and confinement for next-step fusion reactors.
Optimal error field correction (EFC) is thought to be achieved when coupling to the least-stable “dominant” mode of the plasma is nulled at each toroidal mode number (n). The limit of this picture is tested in the DIII-D tokamak by applying superpositions of in- and ex-vessel coil set n = 1 fields calculated to be fully orthogonal to the n = 1 dominant mode. In co-rotating H-mode and low-density Ohmic scenarios, the plasma is found to be, respectively, 7× and 20× less sensitive to the orthogonal field as compared to the in-vessel coil set field. For the scenarios investigated, any geometry of EFC coil can thus recover a strong majority of the detrimental effect introduced by the n = 1 error field. Despite low sensitivity to the orthogonal field, its optimization in H-mode is shown to be consistent with minimizing the neoclassical toroidal viscosity torque and not the higher-order n = 1 mode coupling.