Electromagnetic load evaluating and optimizing approach of the blanket system during VDEs considering halo current

In most scenarios, the vertical displacement event (VDE) represents the most extreme electromagnetic (EM) event within the tokamak device. The significant EM loads experienced during this event have the potential to compromise the structural stability of in-vessel components. This study investigates the EM loads on the water-cooled ceramic breeder blanket system of China Fusion Engineering Test Reactor (CFETR) using finite element analysis methods in two characteristic events: hot-VDE and cold-VDE. The study discusses the EM load effects resulting from changes in magnetic flux and induced electromotive force, respectively, with a specific focus on halo currents. The results reveal that, with similar current quech time, the difference in EM load on the blanket system during the VDEs primarily depends on the halo currents. When the electrical connection of the back supporting structure (BSS) is open, the halo current path within the blanket system and vacuum vessel (VV) changes, and a substantial portion of the halo current in the blanket system is conducted to the VV via the BSS. Consequently, a portion of the EM load on the blankets and BSS is transferred to the VV due to the transfer of halo current. Inspired by this, the conceptual use of ‘shunts’ is proposed to provide a dedicated circuit for shunting halo currents away from critical device components, such as the VV and blankets. This approach allows for the sharing of EM loads caused by halo currents and reduces the threat posed by halo currents to the structural integrity of these essential components.

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Introduction
With the presence of magnetohydrodynamic (MHD) instability, such as the kink model, tear model, and other microscopic instabilities of the plasma, the magnetic field in the vacuum vessel (VV) becomes complex and variable [1].When undamped plasma instability reaches a critical scale, it can lead to a major disruption accidents or vertical displacement events (VDEs).Among these events, VDEs are particularly critical for tokamak devices, as they impose huge electromagnetic (EM) loads and pose great threat to the structural integrity of in-vessel components [2,3].Furthermore, VDEs are known for their complexity and unpredictability.To simulate the plasma behavior during a VDE, an easy model to establish assumes strict axisymmetry, allowing the theoretically required three-dimensional simulation code to be condensed into a two-dimensional format.Building upon this axisymmetric approach, researchers like Chen, Maione, and Amoskov have investigated the EM load characteristics during VDEs in the context of China Fusion Engineering Test Reactor (CFETR), the EU Demonstration Reactor (DEMO), and the International Thermonuclear Experimental Reactor (ITER) [4][5][6][7].This research also adopts an axisymmetric model for the VDE analysis.
Besides the induced eddy currents in conductors during VDE, the halo current that flows through the scrape-off layer also makes a significant contribution to the EM load on conductors [2,3].The maximum values of I h /I p 0 (where I h is the halo current and I p 0 is the pre-disruption plasma current) for JET, COMPASS-D, JT-60U, and ITER typically hover around 0.45 [8][9][10][11][12][13][14][15][16][17][18][19].Taking this into consideration, it becomes evident that halo current is a crucial factor that cannot be disregarded when simulating the EM load on first wall (FW) structures and VV during VDE.However, existing plasma simulation codes (e.g., DINA, TSC, TOKSYS, etc) that can self-consistently describe plasma evolution often struggle to effectively evaluate the EM load on detailed structures caused by halo current.Thus, the halo current is typically simplified as a current or voltage source load on the FW, with the halo current within the plasma being ignored [20][21][22][23].Under the assumption that halo current is equivalent to a 'power-supply load,' research has been conducted on the EU-DEMO and ITER to investigate the load effects of halo current.These effects vary significantly due to the distinct electrical structures of these devices [24][25][26][27].Consequently, when considering the EM load contribution of halo current, understanding its path within in-vessel components becomes of paramount importance [21].In CFETR, the path of the halo current is determined by the back supporting structure (BSS), which connects the isolated blanket modules with VV [28].Therefore, this research places particular emphasis on assessing the EM load effects associated with the halo current path.
In this study, the EM load on the water-cooled ceramic breeder (WCCB) blanket of CFETR during VDEs is investigated using the finite element (FE) method.The analysis is conducted under the assumption of an axisymmetric VDE with the halo current serving as the power supply.Both hot-VDE and cold-VDE scenarios are employed as examples to perform a detailed evaluation of the Lorentz load on the blanket system.The study explores the distinctive characteristics of EM loads on the blanket during different plasma quench events and examines the impact of halo current on these loads.Finally, approaches for load optimization are examined, with a particular emphasis on the influence of halo current.

Simulation model and method
The EF commercial software ANSYS is employed to simulate the EM field of CFETR.The entire model of CFETR exhibits toroidal cyclic symmetry with a 22.5-degree cycle, leading to the establishment of a 1/16 model.To simplify the internal structure of the WCCB blanket, the 'equivalent material' approach is employed.The EM characters, magnetization M eq and resistance ρ eq of the equivalent model are determined based on the corresponding volume V i and conductive crosssection S i of each material, following the equations: where M i and ρ i is the magnetization and resistance of each material, respectively, with i referring to each material employed in the blankets.While the complete electrical structure connecting in-vessel components is retained.Detailed information regarding the comprehensive geometric structure and material characteristics of the model can be found in [29].
The modeling utilizes a cylindrical coordinate system, which incorporates an additional poloidal direction perpendicular to the toroidal direction to facilitate the description of the halo current path (refer to figure 1).This cylindrical coordinate system serves both for the modeling and the analysis of simulation results, encompassing parameters such as current, magnetic field, forces, moments, and various other physical quantities.The transient changes in the plasma current evolution during VDEs are simulated with the DINA code.The DINA code is a two-dimensional computational program that relies on the axisymmetric model and MHD theory.The key plasma parameters are detailed in table 1 [30].Based on the coordinates and current intensity of plasma obtained from the DINA code, the toroidal plasma current is discretized into a set of current filaments.The variation in current density within these filaments simulates the plasma quench and vertical displacement Definition of cylindrical coordinate system, r is the radial direction, φ is the toroidal direction, z is the vertical direction, θ is the poloidal direction perpendicular to the φ .5.4 Field on axis B (T) 6.5 [31].For strictly axisymmetric VDEs, the loading of halo current on the FW should be evenly distributed along the toroidal direction, while the poloidal halo current on the FW aligns with the magnitude of the halo current in the plasma.As depicted in figures 2(a) and (b), vertical instability leads to an upward movement of the plasma in Case 1 at approximately 0.8 s.The plasma experiences a thermal quench (TQ) around 0.995 s, followed by an increase in plasma current to 13.8 MA.By 1.1 s, the plasma reaches the FW, triggering a current quench (CQ).In Case 2, the plasma disrupts before making contact with the FW at 0.03 s.Notably, the ratio I h /I p 0 in Case 2 is greater than that in Case 1.
ANSYS provides SOLID236, a three-dimensional element capable of modeling EM fields.This element type includes both magnetic and electric degrees of freedom.Magnetic degrees of freedom are based on the edge-flux (AZ) formulation, while the electric degree of freedom corresponds to the electric potential (VOLT) defined at each node [32].To ensure accurate and stable simulations, several conditions and constraints are applied: 1.The AZ at the central symmetric axis of the FE model is set to zero, preventing abrupt flux changes in this region.2. The AZ on the external surface of the air field is fixed at zero, and the size of air field is set to approximately twelve times that of the device.This configuration establishes an infinite boundary condition.3. To achieve periodic symmetry, the AZ values on both toroidal ends of the model are set equal, defining the periodic symmetry boundary of the model.4. The VOLT at both ends of the VV are coupled.5.The complex electrical connections between the BSS and the VV are compressed, are abstracted as VOLT coupling.

Results and discussions
During a VDE, conductors such as blankets experience significant EM loads primarily due to the Lorentz force, as described by Lorentz's equation: where the Lorentz force ⃗ f is influenced by the current density ⃗ j and the magnetic field ⃗ B. In these conductors, taking into account the selfinductance effect of current, there are where I is the total current in the conductor, with subscripts φ z, θ, and rφ denoting the toroidal-vertical, poloidal (verticalradial), and radial-toroidal components of I, respectively.Similarly, subscripts for R and L denote their corresponding components, I S is the current source, which represents the 'power supply' load from the halo current in the plasma, R is the resistance of the corresponding I loop, L is the self-inductance of the corresponding I loop, Φ is the magnetic flux, with subscripts r, φ , and z representing the radial, toroidal, and vertical components of Φ , respectively.
In equation ( 2), the first term on the left side accounts for the counteractive effect of induced electromotive force on current decay, while the second term represents the contribution of flux change to the current.The third term corresponds to the contribution of the halo current, which consists solely of the poloidal component.
In the in-vessel conductors, the flux change drives only the eddy current I e .Thus, the total current I is composed of and similarly for the poloidal halo current I h θ : where bold type, such L/R, I, R, and Φ are abbreviations representing the corresponding matrices in equation (2).Assuming a constant permeability µ for in-vessel conductors, and the flux change term in equation ( 3) is primarily driven by the plasma current J p under stable magnet system, as expressed by: where B represents the magnetic induction intensity reflecting the value of Φ .Based on equations ( 3) and ( 5), when the plasma current quenching trend (dJ p /dt) is similar, different plasma disruption events within one tokamak result in comparable behavior of the I e .Consequently, there is a corresponding similarity in the patterns of EM forces generated by I e , and this is primarily premised by the similarity of the magnetic field within the device.However, it is important to note that the time response of in-vessel conductors (including blankets, BSS, etc.) to EM forces may exhibit variations due to their distinct spatial positions within the tokamak.While Case 1 (hot-VDE) and Case 2 (cold-VDE) display similar plasma current quenching trends (as seen in figure 1(a)), the blankets experience significantly different EM loads, primarily due to the presence of substantial halo currents, as detailed in figure 3 and table 2.
The halo current within the FW follows a sequential path through the blankets, the BSS, and the VV, ultimately connecting with the halo current in the plasma region to create a closed   loop.The 3#, 4#, 5#, 6#, and 7# blanket is the blanket modules which halo current mainly flows through.Among these blankets, the halo current predominantly flows through blanket modules 4# and 5#.Therefore, special attention is given to analyze the total current within blanket modules 4# and 5# due to their substantial EM load, as depicted in figure 4.
All the current curves exhibit two prominent peaks.The first peak arises from the eddy current generated by the rapid plasma quenching, while the second peak is a result of the halo current.When there are no additional current sources present, the behavior of current in the conductor can be described by the form of equation (4).By removing I S and then integrating equation ( 4) over time, we obtain: where I 0 represents the peak current before attenuation, and t 0 is the initiation time of attenuation.The descending portion of the current curve exhibits a consistent monotonic exponential decay.Therefore, the emergence of the second peak can be attributed to the influence of the halo current.The curves following the first peak can be approximately divided into two distinct exponential attenuation curves: one corresponds to the eddy current, and the other to the halo current.
It is important to highlight that, in Case 2, the 4# blanket exhibits a higher total current intensity compared to the 5# blanket, despite experiencing less EM force.Typically, within a tokamak, the toroidal field intensity B φ significantly outweighs other components.According to the principles of vector cross-multiplication, the contribution of poloidal current J θ often surpasses that of toroidal current J φ .Consequently, even when the total current is relatively small, the resulting EM force can be substantial when driven by significant poloidal currents.
Before the halo current flows in, the EM load is primarily driven by the eddy current.This is especially true during the early stage of plasma quench, particularly during the TQ phase when ∆t (time interval) is very small.When we integrate equation (3) over time t, we can express it as equation ( 7), with the minor term involving ∆t omitted: Equation ( 7) clearly indicates that the change ∆I e in conductor current is mainly influenced by the change ∆Φ in magnetic flux during the TQ phase.This explains the observed reversal in current direction, as depicted in figure 5, during TQ.
In the case of a cold-VDE (Case 2), the plasma undergoes a dramatic disruption before it contacts the FW.Consequently, the plasma with a higher current density reaches the blankets more rapidly during the initial stages of the VDE.This rapid arrival causes a momentary reversal in the current direction within the IB blankets.This observation aligns with the findings in [6].However, in the case of a hot-VDE (Case 1), where there is plasma current displacement during TQ, the change in the magnetic field generated by plasma displacement ∆d is insufficient to counterbalance the decrease in magnetic field caused by plasma current decay ∆I p .Consequently, the reversal in eddy current direction does not occur.Furthermore, the variation of a change in current direction does not occur in the OB blankets since both ∆I p and ∆d contribute equally to the magnetic field of the OB blankets.
Figure 6 illustrates the Lorentz forces and moments experienced by the different blanket system segments during the VDE.A comparison of the EM loads on the blanket system between Case 1 and Case 2 reveals that the EM response characteristics of the corresponding blanket segments remain consistent, with only variations in response amplitude.These variations can be attributed to differences in time-varying flux and halo current between the two cases.Notably, the differences in ∆ ( I h /I p 0 ) between these two events result in more pronounced load differences in the IB blankets compared to the OB blankets.Furthermore, during the transition from the TQ to the CQ phase, the EM force acting on the IB blankets undergoes significant fluctuations, and noticeable variations in the amplitude of the Lorentz load are experienced by the blanket system, with the maximum amplitude approaching the MN magnitude.The causes of these fluctuations can be attributed to changes in magnetic flux and the inflow of halo current.

The approach for decreasing the blanket EM load added by the halo current
The blanket system of CFETR employs a single-module segmentation (SMS) design, connecting the IB or OB blankets within the same segment [33].According to Ohm's law, ⃗ E = ρ ⃗ J, the path taken by the halo current is primarily determined by the distribution of resistance within the conductor.Since halo current predominantly flows in parallel through most structural conductors which is parallel connection, they establish a fairly straightforward connection as described below: In equation (8), I h (i ) and R h (i ) represent the currents and associated resistances of parallel conductors, respectively.It is worth noting that resistance is essentially proportional to the length of the path.Consequently, the main paths for the formation of circuits for halo current in the SMS design are through the two shorter paths labeled A and B (as shown in figure 7).However, when path A is severed, the BSS transitions to a multi-module segmentation (MMS) design.In the MMS configuration, halo current primarily flows through path B. As a result of this transition, the EM load transmitted to the VV increases.Specifically, in Cases 1 and 2, the EM load on the VV increases by 21% and 98%, respectively.Conversely, the EM load on the 5# blanket, which is predominantly affected by halo current, experiences a significant reduction of 75% and 70% in Cases 1 and 2, respectively (as depicted in figures 8(a)-(d)).
Furthermore, there are some notable differences in the EM load between the SMS and MMS BSS, as illustrated in figures 8(e) and (f ).The path of halo current predominantly follows a poloidal direction due to the isolated blanket segments along the toroidal direction.Additionally, as the discrete blankets running perpendicular to the toroidal direction are interconnected by the BSS, the halo current exerts a significant impact on the EM load of the BSS.The force experienced by the BSS undergoes substantial changes when the halo current flows in.Moreover, the presence of electric gaps intercepts the path of halo current within the BSS, resulting in a relief of the EM load on the BSS.Interestingly, the alterations in the electrical structure of the BSS hardly affect its eddy currents.This conclusion can be drawn from the observation that the force curve of the BSS remains almost unchanged before the halo current flows into it.
In order to reduce the EM load on the blanket system during VDE, it is imperative to limit the impact of the enormous halo current directly on the blanket system.Drawing inspiration from the path change of halo current observed in the MMS configuration, a strategy can be devised to divert the halo current to other conductors, thereby reducing its contribution to the EM force acting on the blankets.Specifically, by completely segregating the blanket modules of one segment and ensuring that each blanket independently, the halo current can be isolated within the blanket system, to avoid  forming closed loops.Furthermore, a circuit can be designed for each blanket to conduct the halo current towards stable conductor structures capable of withstanding significant EM loads.However, it is essential to avoid transferring the load from the blanket to the VV, as VV components are typically designed as irreplaceable standing components in the tokamak.Moreover, VV also experiences a substantial EM load during VDE.Taking these factors into consideration, an effective solution appears to be the incorporation of a low-resistance electrical structure 'shunts' that runs in parallel to both the blanket system and VV, as depicted in figure 9.This arrangement allows for the diversion of halo current away from critical components while ensuring that the EM load is appropriately managed.
A significant portion of the I h is directed towards the shunt, exploiting its low resistance, and the resulting EM load generated by I h is predominantly absorbed by the shunt, which carries I h 2 .It is important to note that the current design of the VV and blanket system does not currently accommodate the envisioned shunts, there is not enough space for the shunts [34].As of now, the shunts remain a conceptual component.However, after reasonable design adjustment, the engineering verification for shunts will be carried out.

Conclusion
The study focuses on analyzing the EM load of CFETR blanket system during VDEs with an axisymmetric VDE model and considering the power supply for halo current.The result shows that the significant EM load during VDE results from both the magnetic flux variation in the blanket module due to the vertical displacement and attenuation of plasma current and the inflow of halo current into the blanket FW.Additionally, the variation in EM load is primarily influenced by the halo current, assuming a similar plasma quench trend.The study also delves into the characteristics of three independent excitation sources contributing to the EM load: magnetic flux change, induced electromotive force, and halo current.It observes that the EM load evolution in both Cases 1 (hot-VDE) and Case 2 (cold-VDE) follows similar patterns over time, with differences primarily in response amplitude.The presence of an electrical gap in the BSS significantly alters the path of halo current and its impact on conductor loads.Disconnecting the BSS connecting blankets 4# and 5# reduces the load on the blankets while increasing the load on the VV.As a result, the EM load optimization for halo current should initially focus on halo current diversion.A proposed solution involves implementing a 'shunt' that runs parallel to both the VV and the blanket system, which can help mitigate the EM load on the blanket system.This study provides specific data support for CFETR blanket system design, it also offers insights into how to optimize blanket EM load under extreme EM conditions.

Figure 1 .
Figure1.Definition of cylindrical coordinate system, r is the radial direction, φ is the toroidal direction, z is the vertical direction, θ is the poloidal direction perpendicular to the φ .

Figure 2 (
a) illustrates the plasma current and the halo current, with Case 1 representing the hot-VDE and Case 2 representing the cold-VDE.The paths of the halo current and the locations of the inboard (IB) blankets (1#∼6#) and outboard (OB) blankets (7#∼11#) are depicted in figure 2(c).

Figure 2 .
Figure 2. (a) Plasma current I p and halo current I h during hot-VDE (Case 1) and cold-VDE (Case 2), (b) plasma current density distribution at initial state (t = 0 s) and the moment of touching FW [30], (c) the halo current path in the plasma and in-vessel components, and x ∼ z points out the compressed support structures which halo current flows through.

Figure 5 .
Figure 5.The vector map (vertical view, −Z direction) of the total current density in the IB and OB blanket during TQ (clockwise, CW; counterclockwise, CCW).

Figure 6 .
Figure 6.Lorentz forces and moments of blanket segments, outboard-center (OBc) blankets are the blankets located at the toroidal center segment of the model, outboard-side (OBs) blankets are the blankets located at the toroidal side segments of the model.

Figure 7 .
Figure 7.The halo current path of (a) SMS and (b) MMS.

Figure 9 .
Figure 9.The conceptual diagram of the I h , I h 1 , I h 2 and I h 3 is the halo current flows through the vacuum vessel, shut resistance, and blanket system, respectively.

Table 1 .
The main parameters of plasma.

Table 2 .
Maximum Lorentz forces of blanket system in VDEs (units: kN).