Magnetic Field Line Tracing Research Articles

Toroidal distribution of heat load on castellated plasma facing components for lower divertor target in EAST

In tokamak devices, the performance of plasma facing components (PFCs) under high heat loads is a key challenge for achieving long-pulse and high-performance plasma operations. The lower divertor of EAST adopts an ITER-like cassette modules (CMs) structure. However, regular distribution of damage along the toroidal direction have been observed on the divertor target plates, which not only affects the lifespan of PFCs but also limits the long-pulse and high-performance plasma operations. Therefore, investigating the toroidal distribution of the heat load on the divertor target in EAST is crucial for understanding the mechanism of damage on the target plate surface. The toroidal characteristics of heat loads on CMs of the lower divertor in EAST was analyzed using a three-dimensional magnetic field line tracing program (PFCFlux). For the inner vertical target (IVT) and outer vertical target (OVT) within a single CM, the heat load varies monotonically along the toroidal direction. In contrast, the heat load distribution on the outer horizontal target (OHT) is uniform, except at the chamfers, which is directly correlated with the target’s geometric structure and the magnetic field configuration. The surface heat load distribution exhibits toroidal non-uniformity, with the heat deposition pattern being generally consistent and displaying periodic variations. The toroidally uneven heat load distribution is attributed to the change in the magnetic field’s tilt angle. Additionally, the peak heat load is observed at the chamfer positions between cassettes, and an analysis is conducted on the relationship between peak heat load and the size of the chamfer. Smaller tilt angles result in lower surface heat load. Furthermore, a comparative analysis of peak heat loads at the chamfer under different plasma current conditions reveals that higher plasma currents generally result in increased peak heat loads. This investigation into the toroidal heat load distribution on the divertor surface contributes to understanding of the damage mechanism of W PFC as the target plate and provides valuable data for divertor design of future fusion devices.

A New Field Line Tracer for the Study of Coronal Magnetic Topologies

We present a new code for the tracing of magnetic field lines and calculation of related quantities such as the squashing factor in the solar corona. The Universal Fieldline Tracer (UFiT) is an open-source package that can currently take inputs directly from four well-established coronal models, with additional models planned to be made directly accessible in the future. This package contains tools to make use of large-scale three-dimensional field line maps to calculate volumetric quantities, such as the total volume of the open corona, or the fraction that maps to regions on the solar surface within some distance of a coronal hole boundary, which may be relevant to phenomenological models of solar wind speed such as the Wang–Sheeley–Arge model. Synthetic coronagraphs can also be produced rapidly by this package. We have postprocessed long-term magnetofrictional simulations to demonstrate that the separatrix web occupies a larger fraction of the corona during solar maximum than solar minimum.

Conceptual design of poloidal horseshoe limiter layout for JA DEMO

In the development of the JA DEMO fusion reactor, the proposed poloidal horseshoe limiter aims to mitigate the surface heat load localized on the breeding blanket. The limiter protrudes from the first wall toward the plasma to shade the blanket from the charged particles, which account for the majority of the surface heat load. To concretize the limiter design, this study presents a limiter layout that implements a concept that allows for sufficient cooling and remote maintenance. The limiter shape was determined by evaluating the surface heat load using 3-D magnetic field line tracing. A fully poloidal limiter with a width of 300 mm, which corresponds to 2.4 % of the FW area, was selected. The limiter heating, consisting of surface heat load and nuclear heating, was evaluated to discuss the required cooling, and the concept of a limiter cassette and modules for cooling was proposed. For the limiter replacement method, the outboard limiter is designed to be extracted from the upper port with the mounting segment. The inboard limiter is then grasped and transported to reach the upper port after the outboard limiter extraction. Both the inboard and outboard limiter are expected to be replaced without affecting other in-vessel components in this study.

Prediction and Verification of Parker Solar Probe Solar Wind Sources at 13.3 R⊙

AbstractDrawing connections between heliospheric spacecraft and solar wind sources is a vital step in understanding the evolution of the solar corona into the solar wind and contextualizing in situ timeseries. Furthermore, making advanced predictions of this linkage for ongoing heliospheric missions, such as Parker Solar Probe (Parker), is necessary for achieving useful coordinated remote observations and maximizing scientific return. The general procedure for estimating such connectivity is straightforward (i.e., magnetic field line tracing in a coronal model) but validating the resulting estimates is difficult due to the lack of an independent ground truth and limited model constraints. In its most recent orbits, Parker has reached perihelia of 13.3R⊙ and moreover travels extremely fast prograde relative to the solar surface, covering over 120° longitude in 3 days. Here we present footpoint predictions and subsequent validation efforts for Parker Encounter 10, the first of the 13.3R⊙ orbits, which occurred in November 2021. We show that the longitudinal dependence of in situ plasma data from these novel orbits provides a powerful method of footpoint validation. With reference to other encounters, we also illustrate that the conditions under which source mapping is most accurate for near‐ecliptic spacecraft (such as Parker) occur when solar activity is low, but also require that the heliospheric current sheet is strongly warped by mid‐latitude or equatorial coronal holes. Lastly, we comment on the large‐scale coronal structure implied by the Encounter 10 mapping, highlighting an empirical equatorial cut of the Alfvèn surface consisting of localized protrusions above unipolar magnetic separatrices.

Effect of discreteness and misalignment on magnetic field and charged particle confinement in CFQS quasi-axisymmetric stellarator

The Chinese first quasi-axisymmetric stellarator (CFQS), which will be the first quasi-axisymmetric (QA) stellarator in the world, is now under construction. The primary task of the CFQS project is to realize a QA configuration and to examine its physical properties. Based on this task, two important issues were investigated in this work in order to estimate the robustness of the CFQS design from a physical perspective. One was the toroidal field (TF) ripple due to the discreteness of modular coils (MCs) which could potentially degrade the charged particle confinement in the CFQS configuration. The other was a possible MC misalignment in the assembly that would affect the magnetic field and charged particle confinement in the CFQS. Moreover, since the stellarator symmetry might be broken by the MC misalignment, such a case was also investigated in this work. By performing a magnetic field line tracing and charged particle orbit tracing calculation, it was found that the TF ripple does not affect the confinement property significantly and the magnetohydrodynamics equilibrium was robust against possible MC misalignments. These results are helpful in defining the reasonable tolerance of assembly accuracy.

Development of Poloidal Horseshoe Limiter Concept for JA DEMO

In the development of a DEMO fusion reactor, mitigating the heat load deposited on the breeding blanket at steady-state operation is one of the challenging issues because of the localized high heat flux brought by charged particles and low thermal conductivity of the reduced activation ferritic/martensite (RAFM) steel structural material. This study proposes a concept of limiter for JA DEMO; a horseshoe-shaped limiter which is continuous poloidally in the first wall (FW) except for the diverter area, and discretized toroidally. The limiter is protruded from the FW to shade the blankets from the charged particles, which move along the magnetic field lines. To enhance the heat removal capability and neutron irradiation tolerance, a tungsten mono-block using RAFM heat sink was applied as the plasma-facing unit (PFU) on the limiters. The heat removal capability of the limiter’s PFU was evaluated as 4.6 MW/m2. The limiter shape satisfying this value was determined basing on the utilization of heat load evaluation with 3-D magnetic field line tracing. Three limiter shape parameters; protrusion height, protrusion width and the FW set-back, were investigated to understand the variation of charged particle load distribution. Both cylindrical and box-shaped blanket concepts were considered, and design windows for the limiter shape were acquired to discuss the optimum parameter. The optimum limiter shape fulfilling the requirement of steady-state operation has been defined, and the limiter’s occupied area amounts to 1.2% of the FW area for both blanket options.

Energy deposition and melt deformation on the ITER first wall due to disruptions and vertical displacement events

An analysis workflow has been developed to assess energy deposition and material damage for ITER vertical displacement events (VDEs) and major disruptions (MD). This paper describes the use of this workflow to assess the melt damage to be expected during unmitigated current quench (CQ) phases of VDEs and MDs at different points in the ITER research plan. The plasma scenarios are modeled using the DINA code with variations in plasma current I p, disruption direction (upwards or downwards), Be impurity density n Be, and diffusion coefficient χ. Magnetic field line tracing using SMITER calculates time-dependent, 3D maps of surface power density q ⊥ on the Be-armored first wall panels (FWPs) throughout the CQ. MEMOS-U determines the temperature response, macroscopic melt motion, and final surface topology of each FWP. Effects of Be vapor shielding are included. Scenarios at the baseline combination of I p and toroidal field (15 MA/5.3 T) show the most extreme melt damage, with the assumed n Be having a strong impact on the disruption duration, peak q ⊥ and total energy deposition to the first wall. The worst-cases are upward 15 MA VDEs and MDs at lower values of n Be, with q ⊥,max = 307 MW m−2 and maximum erosion losses of ∼2 mm after timespans of ∼400–500 ms. All scenarios at 5 MA avoided melt damage, and only one 7.5 MA scenario yields a notable erosion depth of 0.25 mm. These results imply that disruptions during 5 MA, and some 7.5 MA, operating scenarios will be acceptable during the pre-fusion power operation phases of ITER. Preliminary analysis shows that localized melt damage for the worst-case disruption should have a limited impact on subsequent stationary power handling capability.

Stabilization of vertical plasma position in the PHiX tokamak with saddle coils

Saddle coils (SCs) are proposed as coils with a stabilizing effect of a vertical plasma position. This effect comes from an average magnetic field along a magnetic field line. Magnetic field line tracing was performed to investigate the structure and the quantitative values of the averaged magnetic field generated by SCs and toroidal magnetic field coils (TFCs). Experiments to stabilize the vertical position of the plasma were also carried out in a small tokamak device, PHiX. It was experimentally demonstrated that the averaged magnetic field generated with SCs and TFCs could stabilize the vertically unstable plasmas. In addition, three-dimensional equilibrium calculation using VMEC suggested that the plasmas were vertically elongated on the toroidal average when the vertical positions were stabilized by SCs. From the above results, it was shown that the non-axisymmetric magnetic fields generated by SCs could realize the plasmas with stable vertical position and an elongated cross-section.

Numerical analysis of heat load distribution in Heliotron J with magnetic field tracing and plasma transport modeling

We model and characterize the heat load patterns on the vacuum chamber wall in an advanced helical device, Heliotron J, based on the peripheral transport code EMC3-EIRENE, in three typical magnetic configurations with different toroidal mirror ratios (bumpiness). The heat flux distribution on the vacuum chamber wall evaluated with the EMC3-EIRENE code shows several groups of heat flux footprints, some of which are not seen in the connection length distribution obtained with the magnetic field tracing code. This clearly shows the necessity for plasma modeling in addition to magnetic field line tracing in the design of three-dimensional devices. At high electron density, a displacement and an expansion of the heat flux distribution in both the toroidal and poloidal directions are observed. As a result of the heat flux expansion, the peak value of the heat flux decreases at high electron density. Further, an approach that uses the heat distribution function is proposed to evaluate the global power distribution in the entire vacuum chamber. The evaluation results confirm a decrease in the peak heat flux and an increase in the plasma-wetted area at high electron density. The heat flux distribution expansion is larger for the low-bumpiness configuration, in which the peak heat value is by more than lower than that for the high-bumpiness configuration.

Symplectic Gaussian process regression of maps in Hamiltonian systems.

We present an approach to construct structure-preserving emulators for Hamiltonian flow maps and Poincaré maps based directly on orbit data. Intended applications are in moderate-dimensional systems, in particular, long-term tracing of fast charged particles in accelerators and magnetic plasma confinement configurations. The method is based on multi-output Gaussian process (GP) regression on scattered training data. To obtain long-term stability, the symplectic property is enforced via the choice of the matrix-valued covariance function. Based on earlier work on spline interpolation, we observe derivatives of the generating function of a canonical transformation. A product kernel produces an accurate implicit method, whereas a sum kernel results in a fast explicit method from this approach. Both are related to symplectic Euler methods in terms of numerical integration but fulfill a complementary purpose. The developed methods are first tested on the pendulum and the Hénon-Heiles system and results compared to spectral regression of the flow map with orthogonal polynomials. Chaotic behavior is studied on the standard map. Finally, the application to magnetic field line tracing in a perturbed tokamak configuration is demonstrated. As an additional feature, in the limit of small mapping times, the Hamiltonian function can be identified with a part of the generating function and thereby learned from observed time-series data of the system's evolution. For implicit GP methods, we demonstrate regression performance comparable to spectral bases and artificial neural networks for symplectic flow maps, applicability to Poincaré maps, and correct representation of chaotic diffusion as well as a substantial increase in performance for learning the Hamiltonian function compared to existing approaches.

Experimental implementation of a real-time power flux estimator for the ITER first wall on the TCV tokamak

A control-oriented approach to the monitoring of wall power flux densities on ITER has been successfully developed. It is based on real-time equilibrium reconstruction in 2-D which is then used to describe the deposited heat flux as a poloidal flux function with user specified parameters for the power exhausted into the scrape-off layer (SOL) and the SOL heat flux width. To account for the real 3-D geometry of the plasma-facing components (PFC), appropriate weighting factors are derived from magnetic field line tracing in 3-D. Integration of the 3-D effect is performed with a new GUI-based software environment, SMITER, incorporating a field line tracer and permitting import and meshing of PFC CAD models. The paper discusses the experimental demonstration of the model-based wall heat flux algorithm on the TCV tokamak, reporting on the benchmarking of the new code package, SMITER against infra-red camera heat flux measurements and the derivation of the component shaping weighting factors. A comparison of the real-time estimation of the peak power flux and its spatial location against the off-line infra-red measurement for limiter plasma configurations is presented.

Physics of toroidal gap heat loading on castellated plasma-facing components

Abstract Because the gaps between plasma-facing components in fusion devices are comparable in size to the ion Larmor radius (of the order of 1 mm), magnetic field line tracing, the so-called approximation, cannot accurately predict the fine scale heat load distribution around the gap edges. Finite Larmor radius effects dominate ion deposition. The poloidal component of the ion flux striking the surface is always in the diamagnetic/EXB drift direction, meaning that ions preferentially load one side of the gap. Usually electrons can be described optically due to their smaller Larmor radius. Depending on the local inclination of magnetic flux surfaces, it is possible that ions and electrons wet the same side of the gap, or opposite sides. Two-dimensional particle-in-cell simulations and dedicated experiments performed in the COMPASS tokamak are used to better understand processes responsible for plasma deposition on the sides of toroidal gaps between castellated plasma-facing components in tokamaks. The different contributions of the total incoming flux along a toroidal gap have been observed experimentally for the first time in COMPASS. These experimental results confirm the model predictions, demonstrating that in specific cases the heat deposition does not necessarily follow the optical approximation. The role played by electric fields in the deposition pattern is marginal, contrary to local non-ambipolarity that can change the asymmetrical plasma deposition from one side of the toroidal gap to the other.

Web Services for 3D MHD Equilibrium Data at Wendelstein 7-X

Consistent physics and engineering models are required for many use cases at Wendelstein 7-X. Web service technology is used to provide convenient access to common software components and experiment data. The usage of standard web protocols allows the integration in client software written in any programming language. This leads to a better reusability of expert codes and experiment data by a large international team. At W7-X, web services provide common functions such as Biot–Savart calculations and magnetic field line tracing. Further services provide access to databases for diagnostic data or machine models. A new web service was implemented for the creation of 3D magnetohydrodynamic (MHD) equilibrium calculations and a user-friendly access to the results. Consistent interface definitions allow an orchestration of the W7-X web services by user code, as well as a seamless integration into a data analysis framework. In this paper, we present the current state of the MHD equilibrium web services at Wendelstein 7-X.

Comparison of divertor heat flux splitting by 3D fields with field line tracing simulation in KSTAR

We present the experimental and numerical analysis of divertor heat flux spitting by 3D magnetic fields in KSTAR. A dedicated experiment to measure the modification of the divertor heat flux profile in the n = 2 resonant and non-resonant field configurations has been conducted. The measured heat flux profiles were directly compared to the magnetic field line tracing (FLT) simulation using the POCA-FLT code, which fully considers vacuum and ideal plasma response models. Measurements indicate that the 3D fields induce strong splitting of heat flux on the divertor target due to the formation of stochastic field layers. Splitting characteristics largely depend on the applied 3D field structure and its alignment to the axisymmetric magnetic pitch. The modeling of the field line connection length shows good agreement with measurements, reproducing well the pattern of heat flux splitting. Simulations with the ideal plasma response better reproduce measured heat flux profiles by excitation of non-resonant field components in the non-resonant 0° phase and shielding of resonant field components in the resonant 90° phase.

Accuracy Assessment of Numerical Tracing of Three-Dimensional Magnetic Field Lines in Tokamaks with Analytical Invariants

We consider the problem of the accurate tracing of long magnetic field lines in tokamaks, which is in general crucial for the determination of the plasma boundary as well as for the magnetic properties of the scrape-off layer. Accurate field line tracing is strictly related to basic properties of ordinary differential equation (ODE) integrators, in terms of preservation of invariant properties and local accuracy for long-term analysis. We introduce and discuss some assessment criteria and a procedure for the specific problem, using them to compare standard ODE solvers with a volume-preserving algorithm for given accuracy requirements. In particular, after the validation for an axisymmetric plasma, a three-dimensional (3-D) configuration is described by means of Clebsch potentials, which provide analytical invariants for assessing the accuracy of the numerical integration. A standard fourth-order Runge-Kutta routine at fixed step is well suited to the problem in terms of reduced computational burden, with extremely good results for accuracy and volume preservation. Then we tackle the problem of field line tracing in the determination of plasma-wall gaps for a 3-D configuration, demonstrating the effective feasibility of the plasma boundary evaluation in tokamaks by tracing field lines with standard tools.

An interpretation of spacecraft and ground based observations of multiple omega band events

The source of the auroral phenomenon known as omega bands is not yet known. We examine in detail five different intervals when omega bands were observed on March 9th, 2008 between 0400UT and 1100UT over central Canada using both ground and space-based instrumentation. The THEMIS all sky imagers show the development of some of the omega bands from north–south streamers. Spherical elementary currents derived from ground magnetometer data indicate that the omega bands lie near the interface between the region 1 and region 2 currents in the post-midnight sector. THEMIS spacecraft data from the pre-midnight sector display multiple high speed flows and dipolarization features associated with high levels of geomagnetic activity, whereas four GOES geosynchronous spacecraft show multiple injections and dipolarization features. Magnetic field line tracing suggests that the magnetospheric location of the omega bands is at or just beyond geosynchronous orbit. We discuss in detail two potential source mechanisms for the omega bands: plasma sheet velocity shears and high speed flows in the magnetotail and relate the available data to those mechanisms. Our data and a magnetohydrodynamic (MHD) simulation support high speed flows in the magnetotail as the most likely generation mechanism, although the distribution of the magnetotail spacecraft does not provide unambiguous support for our interpretation of the source mechanism.

Ideal plasma response to vacuum magnetic fields with resonant magnetic perturbations in non-axisymmetric tokamaks

Ideal plasma shielding and amplification of resonant magnetic perturbations in non-axisymmetric tokamak is presented by field line tracing simulation with full ideal plasma response, compared to measurements of divertor lobe structures. Magnetic field line tracing simulations in NSTX with toroidal non-axisymmetry indicate the ideal plasma response can significantly shield/amplify and phase shift the vacuum resonant magnetic perturbations. Ideal plasma shielding for n = 3 mode is found to prevent magnetic islands from opening as consistently shown in the field line connection length profile and magnetic footprints on the divertor target. It is also found that the ideal plasma shielding modifies the degree of stochasticity but does not change the overall helical lobe structures of the vacuum field for n = 3. Amplification of vacuum fields by the ideal plasma response is predicted for low toroidal mode n = 1, better reproducing measurements of strong striation of the field lines on the divertor plate in NSTX.

MAGNETIC FIELD LINE RANDOM WALK IN MODELS AND SIMULATIONS OF REDUCED MAGNETOHYDRODYNAMIC TURBULENCE

The random walk of magnetic field lines is examined numerically and analytically in the context of reduced magnetohydrodynamic (RMHD) turbulence, which provides a useful description of plasmas dominated by a strong mean field, such as in the solar corona. A recently developed non-perturbative theory of magnetic field line diffusion is compared with the diffusion coefficients obtained by accurate numerical tracing of magnetic field lines for both synthetic models and direct numerical simulations of RMHD. Statistical analysis of an ensemble of trajectories confirms the applicability of the theory, which very closely matches the numerical field line diffusion coefficient as a function of distance z along the mean magnetic field for a wide range of the Kubo number R. This theory employs Corrsin's independence hypothesis, sometimes thought to be valid only at low R. However, the results demonstrate that it works well up to R = 10, both for a synthetic RMHD model and an RMHD simulation. The numerical results from the RMHD simulation are compared with and without phase randomization, demonstrating a clear effect of coherent structures on the field line random walk for a very low Kubo number.

Modification of the helical divertor footprint induced by the net toroidal plasma current in the LHD heliotron

In this study, the modification of the helical divertor footprint induced by the net toroidal plasma current was investigated in the Large Helical Device (LHD). The divertor footprint shifted a few centimetres when the net toroidal plasma current, as measured by Rogowski coils, was induced via the neutral-beam injection. The shift direction was related to the plasma current direction, and the shift width showed almost linear dependence on the plasma current divided by the toroidal field strength. Magnetic field line tracing calculation considering the plasma current within a simple model revealed that the modification of the edge field line structure causes the footprint shift. The predicted and experimental shift widths agreed qualitatively.

Visualization of the Flux Rope Generation Process Using Large Quantities of MHD Simulation Data

We present a new concept of analysis using visualization of large quantities of simulation data. The time development of 3D objects with high temporal resolution provides the opportunity for scientific discovery. We visualize large quantities of simulation data using the visualization application 'Virtual Aurora' based on AVS (Advanced Visual Systems) and the parallel distributed processing at Space Weather Cloud in NICT based on Gfarm technology. We introduce two results of high temporal resolution visualization: the magnetic flux rope generation process and dayside reconnection using a system of magnetic field line tracing.