Field Line Tracing Research Articles

Vacuum vessel design with lofted toroidal surfaces for a QHS configuration

A vacuum vessel in between the hot plasma and the magnetic coils is crucial for a fusion reactor. In this work, a tool is presented to perform the initial design of such a vessel automatically. Starting from the last closed flux surface, an algorithm is developed which lofts this manifold out as much as possible. At the same time, the algorithm makes sure that no intersection with the coils takes place. In the presented work, this algorithm is applied to the HSX stellarator and it has been verified that the resulting vessel wall can be built from an engineering perspective. Using field line tracing, the strikepoints on the vessel wall indicate the initial locations for a divertor.

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.

Proposed Resolution to the Solar Open Magnetic Flux Problem

The solar magnetic fields emerging from the photosphere into the chromosphere and corona are comprised of a combination of closed (field lines with both ends rooted at the Sun) and open (field lines with only one end at the Sun) fields. Since the early 2000s, the magnitude of total unsigned open magnetic flux estimated by coronal models has been in significant disagreement with in situ spacecraft observations, especially during solar maximum. Estimates of total open unsigned magnetic flux using coronal hole observations (e.g., using extreme ultraviolet or helium (He) I) are in general, in average agreement with the coronal model results and thus show similar disagreements with in situ observations. This paper provides a brief overview of the problem, summarizes the proposed explanations for the discrepancies, and presents results that strongly support the explanation that the discrepancy is due to dynamics at the open-closed boundary. These results are derived from the determination of the total unsigned open magnetic flux, utilizing the Wang–Sheeley–Arge model at a particular spatial resolution and different field-line tracing methods. One of these methods produces excellent agreement with in situ observations. Our results imply that strong magnetic fields in close proximity to active regions and residing near the boundaries of mid-latitude coronal holes are the primary source of the missing open flux. Furthermore, the results outlined here resolve many of the seemingly contradictory facts that have made the open-flux problem so difficult.

A method for determining the locations and configurations of magnetic reconnection within three-dimensional turbulent plasmas

Context. Three-dimensional (3D) reconnection is an important mechanism for efficiently releasing energy during astrophysical eruptive events, which is difficult to be quantitatively analyzed especially within turbulent plasmas. Aims. In this paper, an efficient method for identifying locations and configurations of 3D reconnection from magnetohydrodynamical (MHD) data is developed. Methods. This method analyzes the local nonideal electric field and magnetic structure at an arbitrary position. As only performing algebraical manipulations on the discrete field data and avoiding computationally expensive operations such as field-line tracing and root-finding, this method naturally possesses high efficiency. To validate this method, we apply it to the 3D data from a high-resolution simulation of a Harris-sheet reconnection and a data-driven simulation of a coronal flux rope eruption. Results. It is shown that this method can precisely identify the local structures of discrete magnetic field. Through the information of nonideal electric field and the geometric attributes of magnetic field, the local structures of reconnection sites can be effectively and comprehensively determined. For fine turbulent processes, both qualitative pictures and quantitative statistical properties of small-scale reconnection structures can be obtained. For large-scale solar simulations, macro-scale magnetic structures such as flux ropes and eruption current sheets can also be recognized. Conclusions. We develop a powerful method to analyze multi-scale structures of 3D reconnection. It can be applied not only in MHD simulations but also in kinetic simulations, plasma experiments, and in situ observations.

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.

Magnetic Field Draping in Induced Magnetospheres: Evidence From the MAVEN Mission to Mars

AbstractThe Mars Atmosphere and Volatile EvolutioN (MAVEN) mission has been orbiting Mars since 2014 and now has over 10,000 orbits which we use to characterize Mars' dynamic space environment. Through global field line tracing with MAVEN magnetic field data we find an altitude dependent draping morphology that differs from expectations of induced magnetospheres in the vertical ( Mars Sun‐state, MSO) direction. We quantify this difference from the classical picture of induced magnetospheres with a Bayesian multiple linear regression model to predict the draped field as a function of the upstream interplanetary magnetic field (IMF), remanent crustal fields, and a previously underestimated induced effect. From our model we conclude that unexpected twists in high altitude dayside draping (>800 km) are a result of the IMF component in the MSO direction. We propose that this is a natural outcome of current theories of induced magnetospheres but has been underestimated due to approximations of the IMF as solely directed. We additionally estimate that distortions in low altitude (<800 km) dayside draping along are directly related to remanent crustal fields. We show dayside draping traces down tail and previously reported inner magnetotail twists are likely caused by the crustal field of Mars, while the outer tail morphology is governed by an induced response to the IMF direction. We conclude with an updated understanding of induced magnetospheres which details dayside draping for multiple directions of the incoming IMF and discuss the repercussions of this draping for magnetotail morphology.

Structure of intermittent variation of floating potential in a converging field following a magnetic beach ECR plasma source

In the converging field configuration of cylindrical plasma following an ECR plasma source, intermittent variation of floating potential, which is a negative spike with about a ten microsecond duration, is observed. The event is ubiquitous; independent of measurement position and magnetic field. Cross-correlation analysis for two floating potentials at separate positions reveals that a strong correlation exists within the event timescale. The correlation along the magnetic field line suggests an axially elongated structure. The radial extent of the structure is clarified by the radial correlation profile. Different FWHM of the radial profile at the plasma production region and the downstream converging field region is essentially explained by field line tracing.

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.

Improvement in the simulation tools for heat distribution predictions and control of baffle and middle divertor loads in Wendelstein 7-X

In the first divertor campaign in Wendelstein 7-X (W7-X), unexpected significant heat loads were observed at particular plasma-facing components (e.g. baffle tiles and middle divertor part) which were not designed to receive high heat flux. In a prior investigation, it was concluded that the previous diffusive field line tracing (DFLT) model used for divertor design in W7-X cannot reproduce these loads, due to the missing physics in simulating the heat transport in the shaded flux tubes. To tackle this issue, two new efficient codes (DFLT_rev and EMC3-Lite) are introduced and validated against various experimental heat distributions in different magnetic configurations. The new tungsten baffle tiles have been designed with these codes and mounted in the machine, aiming for mitigated heat loads in the upcoming campaign.

Forecast of the Energetic Electron Environment of the Radiation Belts

AbstractDifferent modeling methodologies possess different strengths and weakness. For instance, data based models may provide superior accuracy but have a limited spatial coverage while physics based models may provide lower accuracy but provide greater spatial coverage. This study investigates the coupling of a data based model of the electron fluxes at geostationary orbit (GEO) with a numerical model of the radiation belt region to improve the resulting forecasts/pastcasts of electron fluxes over the whole radiation belt region. In particular, two coupling methods are investigated. The first assumes an average value for L* for GEO, namely = 6.2. The second uses a value of L* that varies with geomagnetic activity, quantified using the Kp index. As the terrestrial magnetic field responds to variations in geomagnetic activity, the value of L* will vary for a specific location. In this coupling method, the value of L* is calculated using the Kp driven Tsyganenko 89c magnetic field model for field line tracing. It is shown that this addition can result in changes in the initialization of the parameters at the Versatile Electron Radiation Belt model outer boundary. Model outputs are compared to Van Allen Probes MagEIS measurements of the electron fluxes in the inner magnetosphere for the March 2015 geomagnetic storm. It is found that the fixed coupling method produces a more realistic forecast.

Tripolar guide magnetic fields due to island coalescence in solar wind current sheets: Simulation and theory

Reconnecting current sheets (CSs) in the solar wind near 1 AU have been previously identified that exhibit a modified Hall magnetic field perturbation of the nominal guide field characterized by a “tripolar” structure with depressions on both sides of a central maximum [Eriksson et al., Astrophys. J. 805, 43 (2015)]. Such CSs were inferred to contain multiple interacting islands based on measurements from all four Cluster satellites. A new set of 2D particle-in-cell simulations have been performed providing the foundation for a theoretical model for the origin of the tripolar guide-field perturbation. The simulations are initialized with a thin CS unstable to the formation of many small islands that undergo pairwise coalescence and growth. The guide field depressions develop as the result of a balance between the electrostatic (curl-free or irrotational) and electromagnetic (divergence-free or solenoidal) components of the parallel electric field. Field-line and flow-line tracing provide additional support for the model by demonstrating how a level of charge separation sufficient to support a large electrostatic potential can be maintained following island coalescence. A parameter study reveals that the plasma beta is the primary quantity controlling the evolution of the tripolar field. Dependence on the initial guide-field strength is also investigated.

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.

X-point and divertor filament dynamics from gas puff imaging on TCV

A new gas puff imaging diagnostic has been installed on the TCV tokamak, providing two-dimensional insights into scrape-off-layer (SOL) turbulence dynamics above, at and below the magnetic X-point. A detailed study in L-mode, attached, lower single-null discharges shows that statistical properties have little poloidal variations, while vast differences are present in the 2D behaviour of intermittent filaments. Strongly elongated filaments, just above the X-point and in the divertor far-SOL, show a good consistency in shape and dynamics with field-line tracing from filaments at the outboard midplane, highlighting their connection. In the near-SOL of the outer divertor leg, short-lived, high frequency and more circular (diameter ∼15 sound Larmor radii) filaments are observed. These divertor-localised filaments appear born radially at the position of maximum density and display a radially outward motion with velocity ≈400 m s−1 that is comparable to radial velocities of upstream-connected filaments. Conversely, in these discharges ( pointing away from the divertor), these divertor filaments’ poloidal velocities differ strongly from those of upstream-connected filaments. The importance of divertor-localised filaments upon radial transport and profile broadening is explored using filament statistics and in situ kinetic profile measurements along the divertor leg. This suggests that these filaments contribute significantly to electron density profile broadening in the divertor.

Thermo-mechanical limits of a magnetically driven fast-ion loss detector in the ASDEX Upgrade tokamak

A real-time control system is being developed for a magnetically driven Fast-Ion Loss Detector (FILD) at the ASDEX Upgrade tokamak. The insertion of the diagnostic head will be adjusted in real-time to react to changes in the graphite head temperature, plasma position and appearance of MHD instabilities. The graphite probe head of the detector is exposed to an intense heat flux (located ∼3–5 cm from separatrix). The control algorithm performance is constrained by: the graphite head sublimation temperature, the ultimate stress limit, the reaction time of the controller and the retraction time. In this work, the temperature and thermal induced stress distribution on the probe head are assessed to determine what temperature-related magnitude is the limiting factor. The heat flux at the probe head has been estimated using the time-averaged parallel heat flux measured at the divertor target via infrared thermography. A field line tracing algorithm determines which regions of the probe head receives a weighted heat flux due to shadowing (self-induced or from other structures) and the incidence angle of the field lines. A finite element model is used to simulate the temporal evolution of the graphite head temperature and to obtain the induced thermal stress. The temperature spatial distribution at the probe head is validated against measurements of the probe head for different FILD systems showing a good agreement. These measurements have been obtained from visible cameras with an infrared filter. The model concludes that the maximum stress (∼100 MPa) does not overcome the graphite mechanical limit (170 MPa) and that the probe head is not affected by fatigue. Therefore, the graphite sublimation temperature (2000 °C) is set as the limiting factor of the new control system.

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.

A fast multi-dimensional magnetohydrodynamic formulation of the transition region adaptive conduction (TRAC) method

We have demonstrated that the transition region adaptive conduction (TRAC) method permits fast and accurate numerical solutions of the field-aligned hydrodynamic equations, successfully removing the influence of numerical resolution on the coronal density response to impulsive heating. This is achieved by adjusting the parallel thermal conductivity, radiative loss, and heating rates to broaden the transition region (TR), below a global cutoff temperature, so that the steep gradients are spatially resolved even when using coarse numerical grids. Implementing the original 1D formulation of TRAC in multi-dimensional magnetohydrodynamic (MHD) models would require tracing a large number of magnetic field lines at every time step in order to prescribe a global cutoff temperature to each field line. In this paper, we present a highly efficient formulation of the TRAC method for use in multi-dimensional MHD simulations, which does not rely on field line tracing. In the TR, adaptive local cutoff temperatures are used instead of global cutoff temperatures to broaden any unresolved parts of the atmosphere. These local cutoff temperatures are calculated using only local grid cell quantities, enabling the MHD extension of TRAC to efficiently account for the magnetic field evolution, without tracing field lines. Consistent with analytical predictions, we show that this approach successfully preserves the properties of the original TRAC method. In particular, the total radiative losses and heating remain conserved under the MHD formulation. Results from 2D MHD simulations of impulsive heating in unsheared and sheared arcades of coronal loops are also presented. These simulations benchmark the MHD TRAC method against a series of 1D models and demonstrate the versatility and robustness of the method in multi-dimensional magnetic fields. We show, for the first time, that pressure differences, generated during the evaporation phase of impulsive heating events, can produce current layers that are significantly narrower than the transverse energy deposition.

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.

Modeling the toroidal asymmetry of the heat load impacted by nitrogen injection in EAST using EMC3-EIRENE

The effects of nitrogen injection on the heat load in the scape-off layer are systematically investigated in the EAST double-null divertor configuration using EMC3-EIRENE code. Nitrogen impurities injected near the separatrix line and away from the separatrix line give rise to a non-axisymmetric distribution of heat load on the target plate. With impurity injection near the separatrix line, the occurrence of the toroidal asymmetric heat load is observed only nearby the toroidal injection location, while with injection away from the separatrix line the regions of the asymmetric heat load extend and deviate from the toroidal injection position. The competition between the friction force and the ion temperature gradient force has been analyzed. It shows that when impurities are injected away from the separatrix line more impurities can be parallelly transported to a further toroidal location, which results in the extension and deviation of the non-symmetric electron temperature. When the input power is increased, the non-symmetric phenomenon of the heat load turns to be insignificant due to the reduction of the impurity density in the downstream regions, as illustrated by the field line tracing technique. Furthermore, by scanning various injection positions in the EAST tokamak, the optimum location of impurity injection has been discovered.