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Error field measurements with rotating RMP fields for DIII-D H-mode
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.
3D modeling of n = 1 RMP driven heat fluxes on the SPARC tokamak PFCs using HEAT
3D heat flux calculations at the lower outer divertor plate of SPARC using the HEAT code show that 3D fields generated from error field correction coils can lead to enhanced peak heat fluxes up to 15 times larger compared to the axisymmetric case. Previously employed to simulate axisymmetric heat flux on 3D plasma facing components, the HEAT code can now predict 3D heat flux generated by non-axisymmetric plasmas. This is achieved via a new HEAT module which leverages the 3D field line tracing capabilities of MAFOT starting from an M3D-C1 (MHD resistive code) perturbed equilibria. The resulting heat flux is assigned using the magnetic footprint and the heat flux layer model, an extension of the 2D heat flux model also known as the Eich, to 3D non-axisymmetric plasmas. For SPARC, the new capabilities of HEAT are used to calculate the 3D heat loads resulting from n = 1 perturbation fields (with n indicating the toroidal periodicity) applied through a toroidal array of six picture frame coils with different amplitude. The comparison with the unperturbed case shows significant changes in shape and intensity of the heat flux profile. The results show that the application of n = 1 3D field leads to a localized enhancement of the heat flux peak, influenced by the wetted area impacted by the magnetic footprint, and the appearance of a secondary heat flux peak, whose intensity depends on amplitude of the applied 3D field and toroidal location.
Fast and Invertible Simplicial Approximation of Magnetic‐Following Interpolation for Visualizing Fusion Plasma Simulation Data
We introduce a fast and invertible approximation for fusion plasma simulation data represented as 2D planar meshes with connectivities approximating magnetic field lines along the toroidal dimension in deformed 3D toroidal spaces. Scientific variables (e.g., density and temperature) in these fusion data are interpolated following a complex magnetic-field-line-following scheme in the toroidal space represented by a cylindrical coordinate system. This deformation in the 3D space poses challenges for root-finding and interpolation. To this end, we propose a novel paradigm for visualizing and analyzing such data based on a newly developed algorithm for constructing a 3D simplicial mesh within the deformed 3D space. Our algorithm generates a tetrahedral mesh that connects the 2D meshes using tetrahedra while adhering to the constraints on node connectivities imposed by the magnetic field-line scheme. Specifically, we first divide the space into smaller partitions to reduce complexity based on the input geometries and constraints on connectivities. Then, we independently search for a feasible tetrahedralization of each partition, considering nonconvexity. We demonstrate our method with two X-Point Gyrokinetic Code (XGC) simulation datasets on the International Thermonuclear Experimental Reactor (ITER) and Wendelstein 7-X (W7-X), and use an ocean simulation dataset to substantiate broader applicability of our method. An open source implementation of our algorithm is available at https://github.com/rcrcarissa/DeformedSpaceTet.
Energetic electron transport in magnetic fields with island chains and stochastic regions
This paper investigates energetic electron transport in magnetized toroidal plasmas with magnetic fields characterized by island chains and regions of stochastic field lines produced by coil perturbations. We report on experiments performed in the DIII-D tokamak, which utilize electron cyclotron heating and current drive pulses to ‘tag’ electron populations within different locations across the discharge. The cross-field transport of these populations is then inferred from electron cyclotron emission measurements and gamma emission signals from scintillator detectors. Two types of energetic particles are distinguished and discussed: non-relativistic suprathermal electrons and relativistic runaway electrons. The magnetic field topology in each discharge is reconstructed with field-line tracing codes, which are also used to determine the location and scale of magnetic islands and stochastic regions. Comparison of simulations and experiments suggests that suprathermal transport is suppressed when the tagging is performed at a smaller radial location than the location of the $q = 1$ island chain and enhanced otherwise. Here q is the safety factor. We further demonstrate that increasing the width of the stochastic region within the edge plasma yields enhancement of the suprathermal electron transport.
Conceptual design of ELM control coils for the TCABR tokamak
An upgrade of the Tokamak à Chauffage Alfvén Brésilien (TCABR) is being designed to make it capable of creating a well controlled environment where the impact of resonant magnetic perturbation (RMP) fields on edge localised modes can be addressed over a wide range of (i) plasma shapes, (ii) divertor configurations, (iii) RMP coil geometries and (iv) perturbed magnetic field spectra. To this end, a unique set of in-vessel RMP coils is being designed and, in this work, their conceptual design is presented. This unique set of coils is composed of three toroidal arrays of coils on the low field side and three toroidal arrays of coils on the high field side. Each of these six toroidal arrays is composed of 18 coils thus allowing for the creation of RMP fields with toroidal mode numbers n ≤ 9 and with increased control of the poloidal mode number spectrum. To study dynamical effects of RMP fields of different toroidal mode numbers, all rotating simultaneously with different velocities, each of the 108 RMP coils will be powered independently by power supplies that can provide voltages of up to 4 kV and electric currents of up to 2 kA, with frequencies varying continuously from 0Hz up to 10kHz. A set of physical criteria were used to determine the optimal coil geometry and their respective number of turns to reduce the coil currents and voltages during operation with alternate current. Further, the conceptual design was carried out using both the vacuum approach (no plasma response) and the single-fluid response approach, which accounts for the response of a linear, single-fluid, visco-resistive plasma calculated using the M3D-C 1 code.
Integrated ELM and divertor power flux control using RMPs with low input torque in EAST in support of the ITER research plan
Experiments have been carried out at the EAST tokamak to study ITER-relevant scenario integration issues, related to edge localized mode (ELM) control in H-mode plasmas by the application of three-dimensional (3D) resonant magnetic perturbations (RMPs), which have a large impact on the execution of the ITER research plan. The EAST experiments have successfully demonstrated ELM suppression at normalized torque inputs similar to ITER. The application of RMP fields with high toroidal mode number (n = 4) reduces the impact of ELM control on energy and particle confinement compared to those use lower n (n = 1, 2) RMPs. Injection of successive pellets is found to be effective in increasing the plasma density in ELM-suppressed H-modes and reducing the divertor power without triggering large ELMs at EAST. Access to high recycling and radiative divertor conditions while maintaining ELM suppression has been demonstrated in EAST by the use of gas fuelling and neon impurity seeding. Both approaches have been found to be effective in reducing power fluxes to the divertor strike points in near-separatrix lobes for both n = 2 and n = 4 RMPs. Furthermore, reduction of power fluxes in off-separatrix lobes is only effective for n = 4 RMP application, which is consistent with magnetic topology modelling (including plasma response) results showing a shallow penetration into the confined plasma region of field lines connected to these lobes compared to n = 2. The EAST results support the use of high n 3D fields for ELM suppression in ITER high Q DT scenarios since they provide optimum integration features regarding energy and particle confinement, pellet fuelling, radiative divertor operation while eliminating ELM transient power loads and being compatible with low torque input.
Roles of non-axisymmetric perturbations in free drift vertical displacement events on EAST
Abstract The safe operation of most tokamaks, especially the large ones, relies on the feedback control of vertical displacement events (VDEs). However, most of these feedback control systems are based on axisymmetric VDE models. In this study, we use NIMROD simulations to study the role of non-axisymmetric perturbations in free drift vertical displacement events on EAST. The high- n modes in the non-axisymmetric VDE grow first, which drives the formation of high- n magnetic island chains. Subsequently, the magnetic island chains grow and overlap with each other, leading to the destruction of the magnetic flux surface, which induces a minor disruption and accelerates the start of the following major disruption. The magnetic island and the stochastic magnetic field allow the toroidally non-axisymmetric poloidal plasma current to jet towards the hoop force direction, forming finger-like and filamentary structures. Such a plasma current non-axisymmetry strongly depends on the anisotropy in the thermal transport coefficients.
Diagnostics for Burning Plasmas
Here, recent progress in the design and manufacturing development of in-vessel diagnostic components by the U.S. ITER team is reported. Design and manufacturing choices are driven by engineering challenges stemming from ITER’s burning plasma mission, which entails levels of plasma neutron emission, pulse lengths, and size scales well beyond the existing database. Challenges include port access limitations, neutron irradiation and activation risks, nuclear heating of components, complex interfaces, remote handling compatibility, and constraints on component and processing materials. Responses to these challenges are presented using examples from the low field side reflectometer, toroidal interferometer polarimeter, and electron cyclotron emission diagnostics. Relevance of the experience from ITER diagnostics engineering to the design of future integrated fusion facilities based on burning plasmas is addressed.
3D Modelling of the Lithium Injection Experiment in H-Mode Plasma of EAST
Investigations of lithium transport in H-mode plasma of EAST tokamak have been performed by the three-dimensional fluid code EMC3-EIRENE. The simulation results show that the toroidally-localized lithium injection at the low field side (LFS) leads to a toroidally non-axisymmetric distribution of the Li 1+ and Li 2+ ions. The field line tracing approach is utilized to carry out a detailed study on the distributions of the Li 1+ and Li 2+ ions. It is found that Li 1+ ions mainly reside at the LFS while Li 2+ ions can transport from LFS to the high field side. The relationship between mean free path and connection length for Li 1+ and Li 2+ ions has been discussed. Here, the 3D line-integration images of deuterium and lithium emission spectra modelled by EMC3-EIRENE are in qualitative consistency with the experiment results.
First observation of RMP ELM mitigation on MAST Upgrade
Abstract The first experimental attempts at controlling edge localised modes (ELMs) via the application of resonant magnetic perturbations on the MAST Upgrade tokamak are reported. Using the linear MHD model MARS-F, the phase shift between the upper and lower coil rows ΔΦ was optimised for toroidal mode number n = 1 and n = 2 fields, to provide forward guidance to experiments. In low β N discharges, the application of n = 1 3D fields caused the ELM frequency f E L M to increase by over a factor 20 relative to the reference, and also induced a locked mode, which did not cause a plasma termination nor an H-L back transition. However when β N was raised, this induced locked mode caused plasma termination which precluded mitigation access. Initially, applying a numerically optimised n = 2 field had no effect. However applying a rigid toroidal shift to this field caused a locked mode disruption, demonstrating the presence of a substantial n = 2 error field. Coil current ramps were conducted with ΔΦ set at 6 different values, resulting in either locked mode disruptions or no effect, but mitigation with n = 2 fields was not established.
AC compensation of 3D magnetic diagnostic signals in DIII-D and National Spherical Torus Experiment-Upgrade (NSTX-U) for real-time application
A time domain algorithm has been developed to remove the vacuum pickup generated by both coil current (DC) and induced vessel current (AC) in real time from three dimensional (3D) magnetic diagnostic signals in the National Spherical Torus Experiment-Upgrade (NSTX-U) and DIII-D tokamaks. The possibility of detecting 3D plasma perturbations in real time is essential in modern and future tokamaks to avoid and control MHD instabilities. The presence of vacuum field pickup, due to toroidally asymmetric (3D) coils or to misalignment between sensors and axisymmetric (2D) coils, pollutes the measured plasma 3D field, making the detection of the magnetic field produced by the plasma challenging. Although the DC coupling between coils and sensors can be easily calculated and removed, the AC part is more difficult. Here, an algorithm based on a layered low-pass filter approach for the AC compensation and its application for DIII-D and NSTX-U data is presented, showing that this method reduces the vacuum pickup to the noise level. Comparison of plasma response measurements with and without vacuum compensation shows that accurate mode locking detection and plasma response identification require precise AC and DC compensations.
Inverse aspect-ratio expanded tokamak equilibria
Following Greene et al. [Phys. Fluids 14, 671 (1971)] and Connor et al. [Phys. Plasmas 31, 577 (1988); Plasma Phys. Control. Fusion 34, 161 (1992); and Nucl. Fusion 33, 1533 (1993)], the Grad-Shafranov equation for an axisymmetric tokamak plasma equilibrium is solved via an expansion in the, supposedly small, inverse aspect-ratio of the plasma, ϵ. The displacements of equilibrium magnetic flux-surfaces due to plasma shaping are assumed to be $\mathcal{O}$(ϵ) smaller than the minor radii of the surfaces, but no other restriction is placed on the nature of the shaping. The solution of the Grad-Shafranov equation is matched to a vacuum solution that extends to infinity, and consists of an expansion in toroidal functions. The external poloidal magnetic field generated by a finite set of discrete external poloidal magnetic field-coils is calculated, and incorporated into the toroidal function expansion. In this manner, the shape of a large aspect-ratio tokamak plasma is directly related to the currents flowing in the external poloidal field-coils. Finally, a pedestal in the plasma pressure, and the associated spike in the bootstrap current, are incorporated into the model.
Experimental demonstration of transient CHI start-up using a floating biased electrode configuration
Transient coaxial helicity injection (CHI) current start-up in a spherical tokamak (ST) has been demonstrated for the first time using a reactor-relevant floating single biased (FSB) electrode configuration on QUEST. Unlike previous applications of CHI on HIT-II and on NSTX in which the entire ST vessel was split in two using two toroidal ceramic rings as vacuum breaks, in the FSB electrode configuration on QUEST, only the lower outer divertor plate is electrically insulated from the rest of the vessel. This is the CHI injector region. A CHI discharge is generated by driving current, using an external power supply, along magnetic field lines that connect the inner and outer divertor plates in the CHI injector region. The CHI plasma evolution and closed flux formation on QUEST are very similar to those on NSTX and have generated toroidal currents of 150 kA with 100 kA of current flowing on closed flux surfaces. An alternate, force-free model approach has been used to derive the CHI scaling relations. The resulting CHI scaling relations from the model are consistent with the conventional CHI scaling relations, which state that the CHI generated toroidal current is proportional to the CHI injector flux and the CHI injector current is inversely proportional to the toroidal field. These results from QUEST bode well for the application of CHI in a new generation of compact high field STs and low aspect ratio tokamaks in which the space for the central solenoid is very restricted.
Reversed Field Pinch Research in MST (Final Technical Report)
This is the Final Technical Report for the cooperative agreement DE-FC02-05ER54814 titled “Reversed Field Pinch Research in MST” spanning the funding period 4/1/2005 to 12/14/2019. It summarizes key results from MST research, major publications and presentations, and the mentoring of graduate students and postdocs. The Madison Symmetric Torus (MST) is unique within the U.S. and world fusion plasma program. As one of just five operating reversed field pinch (RFP) experiments, and the only one in the U.S., MST has had an important role in advancing the fundamental understanding of the RFP plasma configuration. The MST research program targets topics that intersect with all three goals. While MST provides a unique opportunity to advance the science and fusion potential of the RFP, as a cousin to the tokamak and stellarator plasma configurations the RFP is a valuable partner in establishing validated predictive capability for fusion science more generally. Specific combinations of the major variables in toroidal confinement, like magnetic field strength, plasma current, and shaping, define the different configurations. By exploring adjacent regions in this major variable parameter space, the RFP exposes dependencies not otherwise accessible in the tokamak and stellarator. This diversity enlarges the arena for scientific discovery, both for fusion and plasma physics. The basic science emphasis for MST research has been the self-organizing behavior of RFP plasmas. This inspired MST’s participation in the NSF Physics Frontier Center for Magnetic Self-Organization in Laboratory and Astrophysical Plasmas (CMSO), which ran from 2004-2016 and motivated a substantial fraction of MST’s research goals and capabilities. By all measures the MST Program has been remarkably successful in publications, community engagement, and mentoring of young scientists. While the DOE-FES’s proof-of-principle program for the RFP now languishes through the cessation of this cooperative agreement, operation of MST continues as one of two devices included in the new Wisconsin Plasma Physics Laboratory (WiPPL) basic science user facility. The scope of present research for MST in WiPPL is narrowed to the basic science associated with the RFP magnetic configuration and the advancement of specific fusion topics, which now includes studies of disruptions in tokamak plasmas. The world’s effort in RFP fusion research continues, despite a lack of U.S. federal support to investigate the RFP configuration for fusion application, most notably through a major upgrade to the RFX-mod2 facility in Italy [1] and the recent construction of the KTX facility at USTC in China. First plasmas for RFX-mod2 are anticipated in 2021.
Nonlinear coupling of tearing modes in reversed field pinch plasmas with stepped pressure profiles
A theory of the three-wave coupling of triplets of tearing modes in toroidal pinches [i.e., either reversed field pinches (RFPs) or tokamaks] was proposed by R. Fitzpatrick [Phys. Plasmas 6, 1168 (1999)]. However, this theory only applies to toroidal pinches with negligible equilibrium plasma pressure gradients. Such a limitation is particularly inappropriate to RFPs. This paper generalizes the analysis of R. Fitzpatrick [Phys. Plasmas 6, 1168 (1999)] in order to take the equilibrium pressure gradient into account. However, for the sake of simplicity, a stepped pressure profile, rather than a continuous profile, is employed. In the limit in which the number of steps becomes very large, the results obtained from the generalized theory are presumably equivalent to those that would have been achieved using a continuous pressure profile. The generalized theory is used to investigate the formation of the characteristic toroidally localized pattern of phase-locked m = 1 and m = 0 tearing modes in RFP plasmas that is known as the “slinky” pattern. The incorporation of the equilibrium plasma pressure into the analysis is found to be of crucial importance when determining the properties of the pattern. This is the case because the plasma pressure controls the number of unstable m = 1 and m = 0 tearing modes, and also significantly affects the strength of three-wave coupling, as well as the phase relation between the phase-locked m = 1 and m = 0 modes.
R&D Needs for a US Fusion Magnet Base Program
Significant technology maturation efforts are underway by privately funded fusion startups with the goal to demonstrate mature HTS magnet technology. To support the private sector development effort and the DOE milestone based program, a U.S. Fusion Magnet Community Workshop was held on March 14-15, 2023 in Princeton, NJ. This was the first U.S. community workshop focused on fusion magnet technologies aimed at determining the structure and technical direction for a public program designed to complement the private fusion industry landscape. Based on the wide range of different contributions, a set of general themes and fusion magnet R&D needs were identified and discussed. Feedback received to the workshop charge questions highlighted critical magnet R&D gaps such as availability of existing large cable and coil test facilities, a magnet education program that can generate a trained and essential workforce by leveraging R&D capabilities of universities, U.S. national labs, and fusion industry. Other opportunities synergistic and complementary with high energy physics, high field magnets that are open for a broad range of science drivers. The defined R&D gaps underpin the need for a mid-term and long-term public program in fusion magnet development, which reflects the purpose of the workshop in developing the rationale and consent for such a base program. A self-consistent, fusion specific U.S. fusion magnet program will complement and de-risk fusion pilot plants (FPPs) of promising magnetic configurations developed by private companies on a timeline consistent with the NASEM report on bringing fusion to the U.S. grid. We describe the magnet challenges presented and R&D needs discussed in the workshop. In conclusion, these challenges and R&D needs provide focus for the development of U.S. mid-term and long term roadmaps on enabling HTS for high field fusion.