MHD-FiT: MHD-based dynamic reconstruction of tokamak plasma configuration

This paper introduces an innovative method for reconstructing 2D magnetic flux contours and plasma parameters of dynamically moving tokamak plasmas. While conventional methods like EFIT, based on the Grad–Shafranov equation, are suitable for plasma equilibria with a single magnetic axis, our approach utilizes the MHD equations and shows promise for tokamak plasmas in motion or containing multiple magnetic axes, which may not strictly adhere to plasma equilibria. By utilizing limited edge magnetic probe measurements, our developed model successfully reconstructs the time evolution of two merging plasma toroids in the TS-6 experiment. A comparison with direct 2D magnetic probe measurements in a low β regime reveals a reconstruction error of approximately 3%.


Introduction
Magnetic configuration reconstruction is a vital process in toroidally symmetric magnetic confinement experiments, involving the determination of the 2D or 3D spatial profile of the magnetic field and related plasma parameters.In the case of tokamak plasmas, it is essential to obtain accurate measurements of their 2D configurations [1][2][3].However, inserting a 2D magnetic probe array directly inside the separatrix of high-temperature tokamaks is challenging due to the significant plasma perturbations it can cause.
The motional Stark effect (MSE) measurement technique [4] was developed in the 1990s for 1D magnetic field measurements based on certain models.Nonetheless, it remains incapable of providing a comprehensive 2D internal magnetic field profile.
In our efforts to reconstruct the 2D magnetic configuration within a tokamak, we have traditionally relied on the Grad-Shafranov equation, notably through the use of EFIT reconstruction software [5,6].This approach is primarily based on two key components.(i): Magnetic Field Measurements: We collect magnetic field data from outside the separatrix of high-temperature tokamak plasmas using various instruments, including magnetic probes and flux loops/Rogowski coils installed on the vacuum vessel.Importantly, these measurements are made without disrupting the plasma.(ii): Internal Plasma Diagnostics: Additionally, we utilize internal plasma diagnostics techniques such as Thomson scattering, Electron Cyclotron Emission (ECE) [7], Doppler tomography [8,9], and Motional Stark Effect (MSE) measurements.These diagnostic methods are carefully chosen as they do not perturb the behavior of the tokamak plasmas [10].
The equilibrium reconstruction techniques built upon these data aim to determine the magnetic configuration of 2D toroidally symmetric equilibrium.This is achieved by integrating the measured magnetic field and other relevant data into the Grad-Shafranov equation.Consequently, we can reconstruct essential parameters like plasma position, shape, and current density profile as a 2D axisymmetric equilibrium state [11,12].These reconstructions provide a detailed picture of the plasma's equilibrium, including information about temperature, density, magnetic field strength, and other relevant parameters, and can enable a deeper exploration of plasma instabilities, turbulence, and other dynamic behaviors [13].
Our novel approach introduces the use of the 2D Magnetohydrodynamic (MHD) system of equations for the reconstruction of dynamically changing 2D magnetic configurations and plasma parameters.This new methodology aligns with the evolving time-dependent nature of the measured magnetic field and other data.Unlike the Grad-Shafranov equation, the MHD system of equations does not impose constraints on plasma flow and magnetic axis.This opens up the possibility of reconstructing the magnetic configuration of active plasma phenomena, such as tokamak plasma formation, merging/compression containing multiple magnetic axes, relaxation, and equilibrium.
This approach stands in stark contrast to the standard EFIT model, which is built upon the foundation of the Grad-Shafranov equation.However, it is noteworthy that the recent EFIT can incorporate plasma rotation [14].Through a rigorous comparison of our model's results with direct 2D internal magnetic field measurements conducted in TS-6 [15], we have fine-tuned and improved this MHD-based reconstruction method.Additionally, it is worth noting that other equilibrium reconstruction techniques have also incorporated flow [16,17].However, all endeavors were restricted to addressing the magnetic configuration in the presence of a single magnetic axis.
In this study, we introduce an innovative computational model named 'MHD-FiT' designed to reconstruct the 2D magnetic configuration and associated plasma parameters within tokamak devices.This model leverages the MHD system of equations and utilizes data collected from measurements conducted at the plasma edge.Following the model's introduction, we proceed to assess its capabilities by applying it to the reconstruction of two merging tokamak plasma configurations observed in the University of Tokyo TS-6 experiment [8,15,18].This experiment serves as an illustrative example of dynamically changing tokamak plasma with active flow, a scenario that does not adhere to typical plasma equilibrium conditions.

MHD-FiT model
The governing MHD system of equations of the MHD-FiT approach is solved using the two-dimensional implementation of high-order finite difference framework BOUT++ [19][20][21].In this approach, equations are normalized by presenting each dimensional variable ξ as ξ = ξ 0 ξ, where ξ 0 is a dimensional constant and ξ is the normalized variable.Normalizing to a reference mass density ρ 0 gives an Alfvén time scale τ A = √ ρ 0 µ 0 , for example, the dimensional constant for the toroidal current density is µ 0 .Therefore, the normalized MHD system of equation is defined as follows (1) Here, n is the plasma density, v-the plasma velocity, B is the magnetic field, p is the total pressure, j = ∇ × B is the current density, E the electric field and ϵ is the total energy.In this set of equations, η and ν are the normalized Braginskii resistivity and viscosity, and γ = 5/3.It is imperative to acknowledge that the formulation of initial and boundary conditions hinges upon the specific device's type and geometric attributes.As an innovative paradigm for magnetic configuration reconstruction, the 2D MHD simulation effectively predicts the holistic behavior of both plasma and magnetic fields for dynamically evolving plasma configurations observed in tokamaks, spheromaks [22,23], reversed field pinches (RFPs), and field-reversed configurations (FRCs) [24], aligning harmoniously with the measurements of plasma parameters.This method makes judicious use of a limited array of plasma diagnostics, encompassing external magnetic measurements (via external magnetic probes, magnetic flux loops, and Rogowski coils) and internal plasma parameter measurements that do not perturb the toroidal plasma, such as MSE, Thomson scattering, and ECE, to name a few.This is achieved through the integration of a comprehensive set of prior information as initial conditions, encompassing details of the vacuum vessel, coil characteristics, positioning, and current distribution, along with relevant plasma parameters including density, initial temperature, and more.
Figure 1 illustrates the generalized flowchart of MHD-FiT for essential coils in spherical tokamaks.Upon completion of the generation of the intended two-dimensional mesh, coupled with the standard initial condition for the plasma such as density, temperature, and resistivity [19], the installation of active coils assumes significance.Within the framework of the MHD-FiT tool, the construction of the numerical coils is based on the utilization of a cluster of point coils, designed to represent the coils' geometrical configuration.These mathematical coils, characterized by their negligible size, emulate the properties of the coils or magnetic probe arrays.It is assumed that the precise placement, number of turns, and configurations of these coils have been established beforehand.However, the magnitude and waveform of the current traversing through the coils, being a critical parameter, may or may not have been verified depending on the operation.
In this case, the implementation of magnetic diagnostic systems, such as flux cores or magnetic probe arrays positioned in proximity to the active coils, enables the estimation of the waveform associated with the coils situated at a variable distance.The utilization of this methodology is crucial for approximating the waveform of the poloidal field (PF) coil generating the plasma rings in the merging start-up scenario.
A collection of coils can be employed to generate an equilibrium field, simulating the behavior of physical EF (Equilibrium Field) coils placed at their respective positions if the waveform of the current flowing in EF coils is known.Alternatively, in the absence of current characteristics, a sequence of non-physical coils can imitate the magnetic probe arrays instead, whereby the current waveform within these coils generates signals that mimic the registered measurements obtained at those specific locations to produce the locally measured equilibrium field as used in the current test model.
Once the procedure of implementing the experimental measurement in the current model is finalized, solving the MHD system of equations provides us with the magnetic configuration and plasma parameters inside the vacuum vessel.In this case, the accuracy of the reconstruction is examined through a condition loop, comparing the total plasma current over the reconstructed domain with the measured current experimentally by using the Rogowski coil.

Numerical setup for TS-6(TS-3U) spherical tokamak
The TS-6 device comprises a cylindrical vacuum vessel with toroidal dimensions of 0.75 × 1.44 m (diameter × height).Positioned at the center of the vessel is a central rod with a diameter of 0.11 m, which consists of a combination of slim-CS (30 turns ×2) and TF coil (12 rods).Inside the chamber, there are two sets of poloidal field coils, namely PF with four turns.Additionally, the device includes a pair of equilibrium field coils (EF: 234 turns) located at the top left and right, as depicted in figure 2(a) [8].
The PF coils are connected to capacitor banks with a voltage of 40 kV and a capacitance of 18.75 µF.At t = 0.0 µs, the power supplies initiate the discharge process.Through the induction of the PF coils, initial toroidal plasma rings are generated.These plasma rings are propelled towards the midplane by the negative half swing of the LC discharge current of PF and the vertical field provided by the EF coils (with a magnitude of 35.1 kA • turn).
When the two PF coil currents turn negative, two separate tokamak plasmas are pinched off from the PF coils and then subsequently merge in the axial direction.This merging process is facilitated by the drag force exerted by the attraction of parallel toroidal plasma current and the compressive force exerted by the PF and EF coils.
In the more intricate 'merging-compression' scenario currently employed in the ST-40 device, controlled ejection, reconnection, and confinement of plasmas are utilized to initiate plasma current and initialize plasma heating [23,[25][26][27].There have been endeavors to reconstruct the magnetic configuration at the equilibrium state of merging compression in the ST-40 device.However, akin to prior works, the primary focus has predominantly centered on the equilibrium stage [28].
We employed a high-density discharge and low plasma β for testing the MHD-FiT reconstruction method, leading to the zero-β assumption in MHD equations.Its typical plasma parameters are set as follows: the electron temperature (T e ), ion temperature (T i ), and reference temperature (T 0 ) are all equal to 10 eV.The electron density (n e ) is set to 5 × 10 20 m −3 .The normalized Braginskii resistivity is chosen as 4 × 10 −4 , while the normalized viscosity is set to 5 × 10 −2 .The computational domain for the MHD-FiT model is a 2D rectangle mesh (white rectangle in figure 1(a)) with uniform grid geometry and (n Z × n R ) of 256 × 128 grid size in toroidal geometry, covering the measurement area within the range of R = [0.07,0.33] m and Z = [−0.23,0.25] m away from the actual perfect conducting boundary of the vacuum vessel.These dimensions define the spatial extent of the simulation grid where the plasma parameters are calculated during the reconstruction process [19].Spherical tokamaks employ a magnetic field configuration organized into an array consisting of toroidal (B t ) and poloidal The central TF coil is primarily responsible for generating the intense toroidal magnetic field.Once the tokamak plasmas are formed, the poloidal magnetic field component is predominantly generated by the toroidal plasma current and is further augmented by the in-vessel PF coils.
To measure the magnetic field during the merging operation in the TS-6 device, a high-resolution 2D magnetic probe array system is strategically positioned on the R − Z plane between the two in-vessel PF coils, as depicted in figure 2(c).The magnetic probe array includes pick-up coils designed for measuring the reconnecting component of the magnetic field (B Z ).These pick-up coils have a cylindrical hollow structure with 300 turns and dimensions of 5 mm in length, 1.9 mm outer diameter, and 1 mm inner diameter.Additionally, there are pickup coils for measuring the toroidal component of the magnetic field (B t ), which have an elliptical structure with 200 turns, 5 mm length, 2 mm outer diameter, and 1 mm inner diameter [15,29].
The magnetic pick-up coils are fixedly positioned outside the tokamak plasmas and cover the region between the PF coils, specifically at Z-coordinates ranging from −0.23 m to 0.25 m and R-coordinates ranging from 0.07 m to 0.33 m with a relative spatial resolution of ∆ ∼ 1 cm.In the high-density (approximately 5 × 10 20 m −3 ) and low-temperature (around 10 eV) merging experiment conducted in TS-6, the impact of 2D probe insertion is nearly negligible, accounting for less than 5% of the magnetic field.
The TS-6 merging experiment offers the advantage of operating in both low and high-temperature regimes, enabling simultaneous measurement of magnetic characteristics in both the core and edge regions [30].Among the 224 pick-up coils positioned at the mid-plane, only 72 are situated outside the separatrix region and are referred to as 'external magnetic probes,' as illustrated by red and orange rectangles in figure 2(c).
As the detailed waveform of the PF coils is unknown in the TS-6 merging experiment, the signal obtained from the external magnetic probes positioned on the radial axis (8 probes on each side) will be utilized to extrapolate the current of the PF coils located outside the measurement region.Figure 2(c-2) shows the time evolution of the extrapolated PF coil current [31], obtained from the signals received by the external probes at known distances from the PF coils at each time step.This data is then fitted with an expression used as the current flowing in a pair of PF coils.The physical characteristics of the PF coils are critical as they can directly affect the shape of the formed plasma rings.
In the case of the equilibrium field, the situation is more straightforward as a pair of physical coils might not be required.The 28 external probes positioned on the upper Zaxis (R ∼ 0.33 m) can function as small-scaled non-physical coils, contributing to the generation of the equilibrium field inside the domain and radial balance of the plasma.As depicted in figure 2(c-1), the 1D profile of the poloidal flux along the axial axis at R ∼ 0.33 m, calculated during the plasma formation (t = 453 µs), exhibits a close match with the reconstructed profile generated by the MHD-FiT model [31].In this case, only the measured magnetic field data by using the upper external probes are utilized to provide and adjust the equilibrium field.
In addition to the magnetic parameters discussed previously, the plasma current measured by the Rogowski coil serves as a reliable filter with low error.It guarantees that the reconstruction process is carried out only when the reconstructed plasma current closely aligns with the value measured by the Rogowski coil, with a tolerance of within 5% at each time step, the reconstruction terminates when the error exceeds the tolerance value.This ensures the accuracy and reliability of the reconstructed magnetic configuration.

Reconstruction of magnetic field parameters
In the TS-6 merging experiment, simultaneous measurements of internal and external magnetic fields enable the reconstruction of the internal magnetic field using externally measured data.This reconstruction allows for subsequent comparison with internally measured profiles, providing a means to assess and validate the performance and accuracy of the innovative MHD-FiT model.Figure 3(a) illustrates the reference timescale of the merging completion ratio (ratio of the reconnected to the peak poloidal flux) calculated from the experimental and reconstructed poloidal flux values.When all the flux lines involved in the reconnection process merge, the merging ratio reaches 100%, indicating the completion of merging that transforms two tokamak plasmas into a single plasma.During the ramp-down of the PF coil current, two tokamak plasmas are inductively generated and detach from the PF coils at the pinch-off moment (t = 453 µs).
Following this event, the tokamak plasmas undergo motion towards the mid-plane due to the mutual attraction of parallel current density [9].At t = 460 µs, the tokamak plasmas merge, resulting in the formation of a unified plasma in both experimental and numerical frameworks.The agreement observed between the experimental and reconstructed merging ratios provides validation that the employed model effectively captures the timescale of the merging process.This tool holds promise for applications in devices where an accurate understanding of the internal process completion is crucial for enhancing performance and stability.
Plasma current is a critical parameter in fusion devices, and in certain spherical tokamaks like TS-6 [32], MAST [33], and ST-40 [25], the merging process has been utilized to initiate plasma current, aiming for higher values compared to traditional methods [28].The measurement of this parameter is performed directly using the Rogowski coil positioned inside the vacuum vessel, where the plasma exists after its inductive formation.Following the completion of the merging process at t = 460 µs, the plasma current enters a 'flat-top' state before gradually damping.This parameter serves as a quality indicator within the MHD-FiT tool, ensuring the accuracy of the reconstruction process.
Interestingly, as shown in figure 3(b), the directly measured and reconstructed time evolution of the plasma current exhibit an excellent agreement, even without directly incorporating this parameter into the reconstruction process.During the flat-top phase t = [460, 466] µs, a slight increase in deviation to approximately 2% is observed, attributed to additional plasma damping processes occurring within the vacuum vessel.
The magnetic configuration is a fundamental determinant in fusion devices, exerting a significant influence on plasma confinement, heating, and stability.It serves as a critical source of information regarding the core plasma shape, position, and size within the confines of the vacuum vessel.Currently, the reconstruction of the magnetic configuration using the standard EFIT method focuses exclusively on the plasma equilibrium state, disregarding the magnetic configuration preceding the equilibrium state.
In figure 4, the left panel depicts the 2D contour of poloidal flux lines derived from data collected by 156 internal magnetic probe arrays positioned at the R − Z plane.The poloidal flux Ψ is obtained from Ψ = 2π ´RB Z dR, where B Z is the measured axial component of the magnetic field measured by magnetic probe arrays.The right panel showcases the reconstructed flux lines obtained through the implementation of the MHD-FiT model, employing information acquired from 72 external magnetic probes.
At t = 450 µs, the poloidal flux in the system is solely generated by the PF coils positioned outside the measurement domain at Z = ±0.3 m.Comparing the profiles obtained from measurements and reconstructions reveals minimal deviation between the two.Subsequently, a reduction in the PF current induces the formation of two tokamak plasmas that detach from the coils at t = 453 µs and move towards the mid-plane for merging.The intermediate figures display the two tokamak plasmas during the active merging phase.
As anticipated, the profiles exhibit good agreement, albeit with a slight asymmetry observed in the experimental data.This asymmetry can be attributed to measurement errors in individual probes, resulting in a deviation of approximately 2% in the positions of the flux lines.
Subsequently, after the merging process, the single plasma ring undergoes relaxation to attain tokamak plasma equilibrium.The temporal evolution of the plasma current in figure 3(b) has already demonstrated an increasing deviation after merging due to faster damping in the experimental setup.
Figure 4(a) for time t = 465 µs shows the poloidal flux contours at the equilibrium state.As anticipated, the deviation between the measured and actual profiles is higher at this time step.For example, the measured flux at the magnetic axis reaches Ψ = 1.954 mW, while the reconstructed value is approximately Ψ = 1.99 mW, resulting in a relative deviation of 1.81%.The conventional EFIT assumes a single magnetic axis inside the reconstruction domain therefore EFIT is unable to reconstruct the merging process containing two magnetic axes.Since there is only a single magnetic axis at this time, EFIT can also be used for magnetic configuration reconstruction.In this case, the flux at the magnetic axis reconstructed by EFIT is Ψ = 2.03 mW, resulting in a reconstruction error of 3.74%, which is twice the MHD-FiT reconstruction error at this time step.
Figure 4(b) illustrates the temporal evolution of the 2D position of the magnetic axes of each plasma ring from the pinch-off time until the equilibrium state.This depiction offers insights into the core plasma's position.The measured and reconstructed axial locations of the magnetic axes coincide, with an average radial deviation of 2% observed for the position of the magnetic axes.
The comparison between the directly measured magnetic field parameters and the reconstructed values during the dynamic phases of the merging start-up within the TS-6 spherical Tokamak validated the efficacy of the developed MHD-FiT model.This model can reconstruct core plasma  parameters using limited external magnetic diagnostic data and solve the 2D MHD system of equations.Notably, the model cannot account for the effects of 3D configurations and kinetic processes prevalent in later stages.Nonetheless, the low reconstruction error of less than 4% affirms the model's ability to accurately reconstruct the core plasma in hightemperature devices.
Furthermore, the model demonstrates its capability to reconstruct vital stability parameters, such as the safety factor q, which is crucial in assessing plasma stability within fusion devices.The safety factor q, a fundamental parameter, describes the rotational transform of magnetic field lines in toroidal plasmas [34].It is determined by the ratio of the poloidal magnetic field to the toroidal magnetic field and quantifies the number of twists experienced by the magnetic field lines around the toroidal direction [34].Figure 5 illustrates the safety factor profile after the end of merging, which is found to be greater than 1 in the TS-6 spherical tokamak.Notably, a small reconstruction error is observed between the measured and reconstructed q profiles as a function of normalized poloidal flux Ψ N , while the reconstructed profile by EFIT has a much larger error 5.1% in comparison to the MHD-FiT 1.4% which is most likely due to the presence of plasma motion (not equilibrium state) and paramagnetic internal toroidal field [20] at this time step.

Discussion and conclusion
This paper introduces the novel MHD-FiT model designed for reconstructing 2D magnetic field and plasma configuration, particularly magnetic field parameters of dynamically changing tokamak plasmas in motion.We performed a point-topoint comparison between directly measured and reconstructed magnetic parameters during a merging experiment in the University of Tokyo TS-6 spherical Tokamak, as an example of dynamically changing tokamak plasma.It was observed that this model enables the reconstruction of internal magnetic configuration with high accuracy (less than 5% error) despite using only a limited number of externally measured magnetic field data.
Despite the numerous advantages offered by MHD-FiT in reconstructing core plasma parameters, certain limitations persist as a result of its reliance on 2D reconstruction using MHD equations and the constrained scope of available plasma diagnostics that have minimal impact on tokamak plasmas.These limitations include the inability to account for kinetic processes, electron dynamics, and three-dimensional effects.However, future iterations of our reconstruction tool aim to address these limitations.Notwithstanding these limitations, the current version of the model has demonstrated its effectiveness in reconstructing global plasma parameters essential for enhancing confinement, stability, and heating.
In this study, we have specifically examined the application of MHD-FiT in the context of two merging tokamak plasmas.Nevertheless, this model can be employed for various types of dynamically changing toroidal plasmas described by the MHD system of equations, including several tokamak, spherical tokamak, spheromak, and FRC experiments.The typical examples of moving toroidal plasmas are TS-6 [8,9], UTST [35], and even larger-scale commercial devices like MAST [33] and ST-40 [25,26] spherical tokamak.
It is important to note that accurate reconstruction of 2D magnetic and plasma configurations is achievable with other 2D/3D-MHD models [36].This is possible as long as strategically installed external and internal magnetic diagnostic systems can provide essential information as initial conditions for the reconstruction model without introducing unnecessary perturbations.In this regard, MHD-FiT holds an advantage over other models since it can incorporate time-dependent values from in situ measurements without affecting the physical parameters of the plasma and magnetic field.Some equilibrium reconstruction methods, such as the LIUQE Grad-Shafranov equilibrium solver [37,38] used in the TCV Tokamak, enable the reconstruction of magnetic configurations with multiple magnetic axes.This is achieved through iterative solutions of the Poisson equation and linearization of the plasma current density under pressure constraints.However, this technique has limitations in accuracy if the equilibrium is highly nonlinear.Moreover, the linear parametrization of the current density in the LIUQE method is unstable against vertical gross motion due to the elongated shape of the magnetic configuration, necessitating engineering solutions for vertical stability [37].
In contrast, MHD-FiT can operate in resistive/Hall-MHD modes, providing a wide range of magnetic and plasma parameters during linear and nonlinear processes without requiring any engineering modifications to the device, fitting an equilibrium model, or a prior distribution of equilibria, as is necessary with other common models.Instead, MHD-FiT only requires the characteristic information of the active coils and their plasma current.It does not experience limitations in fitting data, even in complex scenarios involving vacuum vessels with varying resistivities and image currents, and plasma characteristics such as the presence or absence of active flows, local instabilities and plasmoids, and multiple global magnetic axes.The general MHD simulation nature of the MHD-FiT reconstruction code reduces the complexity of the calculation scheme and decreases computation time.

Figure 1 .
Figure 1.General Flowchart of MHD-FiT model to reconstruct the 2D configurations of toroidal plasmas in motion.The black arrows show the path taken for the current device.

Figure 2 .
Figure 2. The vertical cross-section of the TS-6 (TS-3U) device (a), in addition to a high-speed camera image capturing the experiment (b), is accompanied by a 2D map of a high-resolution magnetic probe array (internal and external probes) (c).The red-colored indicators denote the placement of the external magnetic probes employed for MHD-Fit reconstruction.(c-1) Axial profiles of the measured poloidal flux at the upper boundary (R = 0.33 m), calculated from 2D magnetic probe measurement and reconstructed using the MHD-FiT model.(c-2) Temporal evolution of the PF coil current, extrapolated analytically (blue) and the time-dependent expression used in the MHD-FiT model (orange), based on the signals received from the external probes.The complete 2D probe array was then employed to juxtapose the directly measured 2D magnetic field contours with those reconstructed through the MHD-Fit method.

Figure 3 .
Figure 3. (a) Temporal evolution of the merging ratio, expressed as a percentage, in the TS-6 merging experiment and MHD-FiT model.(b) Time-dependent variation of experimentally measured and MHD-FiT model-reconstructed total plasma current in the TS-6 merging experiment.

Figure 4 .
Figure 4. (a) The 2D poloidal flux contours obtained from the internal magnetic probe array data (left) and reconstructed using the MHD-FiT model (right) at various time points: plasma formation (t = 450 µs), merging (t = 458 µs), and the plasma equilibrium state (t = 465 µs).(b) Time evolution of 2D position of the magnetic axes from the pinch-off to the equilibrium state of the single plasma.

Figure 5 .
Figure 5.The safety factor as a function of normalized poloidal flux Ψ N , obtained from magnetic measurements, reconstructed using the MHD-FiT model and EFIT at t = 461 µs.