Halo Currents Research Articles

The Structure Analysis of the EAST Updated Divertor

After EAST_2012 campaign, the updated divertor (upper part) has been designed and installed in EAST. The updated upper divertor is designed as cassette structure like ITER divertor. The structure analysis has been carried out for divertor cassette design in the worst case loads of disruption with the maximum 1 MA of the plasmas current. A series of finite elements analysis indicates that the divertor cassette is able to withstand the electromagnetic (EM) load resulting from halo current, combined with EM load caused by eddy current, gravity and pressure of cooling water.

Electrical connectors for blanket modules in ITER

Blanket electrical connectors (E-straps, ES) are low-impedance electrical bridges crossing gaps between blanket modules (BMs) and vacuum vessel (VV). Similar ES are used between two parts on each BM: the first wall panel (FW) and shield block (SB). The main functions of E-straps are to: (a) conduct halo currents intercepting some rows of BM, (b) provide grounding paths for all BMs, and (c) operate as electrical shunts which protect water cooling pipes (branch pipes) from excessive halo and eddy currents. E-straps should be elastic enough to absorb 3-D imposed displacements of BM relative VV in a scale of ±2mm and at the same time strong enough to not be damaged by EM loads. Each electrical strap is a package of flexible conductive sheets made of CuCrZr bronze. Halo current up to 137kA and some components of eddy currents do pass through one E-strap for a few tens or hundreds milliseconds during the plasma vertical displacement events (VDE) and disruptions. These currents deposit Joule heat and cause rather high electromagnetic loads in a strong external magnetic field, reaching 9T. A gradual failure of ES to conduct Halo and Eddy currents with low enough impedance gradually redistributes these currents into branch pipes and cause excessive EM loads. When branch pipes will be bent so much that will touch surrounding structures, the Joule heating in accidental electrical contact spots will cause local melting and may lead to a water leak.The paper presents and compares two design options of E-straps: with L-shaped and Z-shaped elastic elements. The latter option was developed in 2012 on the basis of more thoughtful analysis of bi-directional cyclic loading conditions influencing a fatigue lifetime. Detail comparative simulations of current and field patterns and subsequent analysis of the fatigue strength and technological assessment allowed make a final choice for the E-strap design in ITER.

Numerical modelling of electromagnetic loads on fusion device structures

In magnetic confinement fusion devices, during abnormal operations (disruptions) the plasma begins to move rapidly towards the vessel wall in a vertical displacement event (VDE), producing plasma current asymmetries, vessel eddy currents and open field line halo currents, each of which can exert potentially damaging forces upon the vessel and in-vessel components. This paper presents a methodology to estimate electromagnetic loads, on three-dimensional conductive structures surrounding the plasma, which arise from the interaction of halo-currents associated to VDEs with a magnetic field of the order of some Tesla needed for plasma confinement. Lorentz forces, calculated by complementary formulations, are used as constraining loads in a linear static structural analysis carried out on a detailed model of the mechanical structures of a representative machine.

Modeling Technique to Predict Fields, Currents, and Loads for C-Mod's Advanced Outer Divertor During a Disruption With a 2.5-MA Plasma Current and 9-T Toroidal Field

Models have been built using the finite-element software COMSOL to predict fields, currents, and the resulting loads and stresses acting on the C-mod advanced outer divertor (AOD). The AOD is being designed to operate with conditions of a 2.5-MA plasma current and a toroidal field of 9 T while being held at 600 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> C, and so must survive a disruption that occurs in these conditions. In addition to the loads resulting from eddy currents induced in the divertor during a disruption, the divertor will at times need to carry up to 400 kA of halo current, which crosses the toroidal field as it returns to the plasma. The loads resulting from this scenario will be very high, and we have had to develop models to predict the fields, currents, and loads as accurately as possible to ensure that the strength of the new design can withstand these loads. First, the fields and eddy currents are predicted in a COMSOL model of C-mod given two inputs. The first input is the currents for the toroidal and poloidal field coils, which come from measured data taken during a discharge. The second input is the current in the plasma, which comes from another model that solves Maxwell's equations to reconstruct the plasma as 24 current carrying filaments. The advantage of this new modeling technique is that it provides the ability to create a model based on actual measured data and to model whichever type of disruption, whether a midplane disruption or a vertical displacement event, so that the model more accurately reflects operating conditions the AOD will see. In addition to the Lorenz forces due to the induced eddy currents in the AOD, the model can also calculate the large forces due to halo currents that cross C-mod's large toroidal field. The loads due to the halo currents will be the largest loads the divertor sees. With all the loads defined, a structural model of the divertor is run to determine stresses and displacements.

Lazy Cohomology Generators Enable the Use of Complementarity for Computing Halo Current Resistive Distribution in Fusion Reactors

This paper presents a methodology to efficiently calculate the resistive distribution of halo currents in 3-D conductive structures that surround the plasma in magnetic confinement fusion devices. The domain of the problem is so complicated that two complementary formulations are used to monitor the discretization error. It turns out that thousands of cohomology generators are needed by the electric vector potential electrokinetic formulation, which would require an enormous amount of memory and computing power to retrieve them even using state-of-the-art algorithms. To solve this challenging problem, we present a novel algorithm to generate the absolute second cohomology group generators exploiting the idea of lazy cohomology generators stored as sparse vectors. The proposed algorithm allows a saving of between four and five orders of magnitude computational time.

Numerical Simulation Approaches to Evaluating the Electromagnetic Loads on the EAST Vacuum Vessel

Numerical simulation approaches are developed to compute the electromagnetic forces on the EAST vacuum vessel during major disruptions and vertical displacement events, with the halo current also considered. The finite element model built with ANSYS includes the vacuum vessel, the plasma facing components and their support structure, and the toroidal and poloidal field coils. The numerical methods are explained to convince of its validity. The eddy current induced by the magnetic flux variation and the conducting current caused by the halo current are also presented for discussion. The electromagnetic forces resulting from the numerical simulation are proven to be useful for structure design optimization. Similar methods can be applied in the upgrades of the EAST device.

Electromagnetic load calculation of the ITER machine using a single finite element model including narrow slits of the in-vessel components

We evaluate electromagnetic (EM) loads on the main systems of the ITER machine using a single finite element model. The 20° sector of the full ITER machine includes the main in-vessel components as well as the vacuum vessel. Narrow slits of the in-vessel components are effectively modeled by using the element splitting method without significant increase of computation memory and time as well as without sacrificing the accuracy. Furthermore, the halo current is taken into account at the same time together with the plasma current. To apply both currents concurrently, dedicated conversion codes are utilized to transfer the plasma simulation results by DINA to the electromagnetic analysis by ANSYS-EMAG used here. The electromagnetic loads on the ITER machine are calculated for various disruption scenarios. Investigation on the analysis results is made to find the worst plasma disruption case and the design-driving load component for each system as well as to compare load contribution from eddy and halo currents. The effect of the narrow slits on load reduction is also examined.

Overview of physics results from the conclusive operation of the National Spherical Torus Experiment

Research on the National Spherical Torus Experiment, NSTX, targets physics understanding needed for extrapolation to a steady-state ST Fusion Nuclear Science Facility, pilot plant, or DEMO. The unique ST operational space is leveraged to test physics theories for next-step tokamak operation, including ITER. Present research also examines implications for the coming device upgrade, NSTX-U. An energy confinement time, τE, scaling unified for varied wall conditions exhibits a strong improvement of BTτE with decreased electron collisionality, accentuated by lithium (Li) wall conditioning. This result is consistent with nonlinear microtearing simulations that match the experimental electron diffusivity quantitatively and predict reduced electron heat transport at lower collisionality. Beam-emission spectroscopy measurements in the steep gradient region of the pedestal indicate the poloidal correlation length of turbulence of about ten ion gyroradii increases at higher electron density gradient and lower Ti gradient, consistent with turbulence caused by trapped electron instabilities. Density fluctuations in the pedestal top region indicate ion-scale microturbulence compatible with ion temperature gradient and/or kinetic ballooning mode instabilities. Plasma characteristics change nearly continuously with increasing Li evaporation and edge localized modes (ELMs) stabilize due to edge density gradient alteration. Global mode stability studies show stabilizing resonant kinetic effects are enhanced at lower collisionality, but in stark contrast have almost no dependence on collisionality when the plasma is off-resonance. Combined resistive wall mode radial and poloidal field sensor feedback was used to control n = 1 perturbations and improve stability. The disruption probability due to unstable resistive wall modes (RWMs) was surprisingly reduced at very high βN/li > 10 consistent with low frequency magnetohydrodynamic spectroscopy measurements of mode stability. Greater instability seen at intermediate βN is consistent with decreased kinetic RWM stabilization. A model-based RWM state-space controller produced long-pulse discharges exceeding βN = 6.4 and βN/li = 13. Precursor analysis shows 96.3% of disruptions can be predicted with 10 ms warning and a false positive rate of only 2.8%. Disruption halo currents rotate toroidally and can have significant toroidal asymmetry. Global kinks cause measured fast ion redistribution, with full-orbit calculations showing redistribution from the core outward and towards V∥/V = 1 where destabilizing compressional Alfvén eigenmode resonances are expected. Applied 3D fields altered global Alfvén eigenmode characteristics. High-harmonic fast-wave (HHFW) power couples to field lines across the entire width of the scrape-off layer, showing the importance of the inclusion of this phenomenon in designing future RF systems. The snowflake divertor configuration enhanced by radiative detachment showed large reductions in both steady-state and ELM heat fluxes (ELMing peak values down from 19 MW m−2 to less than 1.5 MW m−2). Toroidal asymmetry of heat deposition was observed during ELMs or by 3D fields. The heating power required for accessing H-mode decreased by 30% as the triangularity was decreased by moving the X-point to larger radius, consistent with calculations of the dependence of E × B shear in the edge region on ion heat flux and X-point radius. Co-axial helicity injection reduced the inductive start-up flux, with plasmas ramped to 1 MA requiring 35% less inductive flux. Non-inductive current fraction (NICF) up to 65% is reached experimentally with neutral beam injection at plasma current Ip = 0.7 MA and between 70–100% with HHFW application at Ip = 0.3 MA. NSTX-U scenario development calculations project 100% NICF for a large range of 0.6 < Ip(MA) < 1.35.

Impact and mitigation of disruptions with the ITER-like wall in JET

Disruptions are a critical issue for ITER because of the high thermal and magnetic energies that are released on short timescales, which results in extreme forces and heat loads. The choice of material of the plasma-facing components (PFCs) can have significant impact on the loads that arise during a disruption. With the ITER-like wall (ILW) in JET made of beryllium in the main chamber and tungsten in the divertor, the main finding is a low fraction of radiation. This has dropped significantly with the ILW from 50–100% of the total energy being dissipated during disruptions in CFC wall plasmas, to less than 50% on average and down to just 10% for vertical displacement events (VDEs). All other changes in disruption properties and loads are consequences of this low radiation: long current quenches (CQs), high vessel forces caused by halo currents and toroidal current asymmetries as well as severe heat loads. Temperatures close to the melting limit have been locally observed on upper first wall structures during deliberate VDE and even at plasma currents as low as 1.5 MA and thermal energy of about 1.5 MJ only. A high radiation fraction can be regained by massive injection of a mixture of 10% Ar with 90% D2. This accelerates the CQ thus reducing the halo current and sideways impulse. The temperature of PFCs stays below 400 °C. MGI is now a mandatory tool to mitigate disruptions in closed-loop operation for currents at and above 2.5 MA in JET.

Tokamak halo currents

A halo current flows for part of its path through the plasma edge and for part through the chamber walls and can be as large as tenths of the plasma current. The primary interest in halo currents is the large force that they can exert on machine components. Two discordant constraints are central to the theory: (1) Halo currents must produce the magnetic field distribution required to maintain plasma force balance—a distribution that depends on the two angular coordinates of a torus. (2) Halo currents must flow along the magnetic field lines in the plasma, which implies a dependence on a linear combination of the two angular coordinates—only one angular coordinate is free. The physics basis of these two constraints is explained as is their application to the calculation of the properties of halo currents, such as their broad toroidal spectrum. Existing codes could be used to (1) provide detailed comparisons with experiments to validate that the critical elements of physics are adequately included, (2) allow more complete predictions for future machines such as ITER, and (3) design shunts and resistive elements to ensure halo currents follow paths that are the least damaging to the machine. The physics of halo currents implies that it may be possible to feedback stabilize resistive wall modes beyond the ideal-wall limit.

Sideways wall force produced during tokamak disruptions

A critical issue for ITER is to evaluate the forces produced on the surrounding conducting structures during plasma disruptions. We calculate the non-axisymmetric ‘sideways’ wall force Fx, produced in disruptions. Simulations were carried out of disruptions produced by destabilization of n = 1 modes by a vertical displacement event (VDE). The force depends strongly on γτwall, where γ is the mode growth rate and τwall is the wall penetration time, and is largest for γτwall = constant, which depends on initial conditions. Simulations of disruptions caused by a model of massive gas injection were also performed. It was found that the wall force increases approximately offset linearly with the displacement from the magnetic axis produced by a VDE. These results are also obtained with an analytical model. Disruptions are accompanied by toroidal variation of the plasma current Iφ. This is caused by toroidal variation of the halo current, as verified computationally and analytically.

Electromagnetic and structural analyses of the vacuum vessel and plasma facing components for EAST

During plasma disruptions, time-varying eddy currents are induced in the vacuum vessel (VV) and Plasma Facing Components (PFCs) of EAST. Additionally, halo currents flow partly through these structures during the vertical displacement events (VDEs). Under the high magnetic field circumstances, the resulting electromagnetic forces (EMFs) and torques are large. In this paper, eddy currents and EMFs on EAST VV, PFCs and their supports are calculated by analytical and numerical methods. ANSYS software is employed to evaluate eddy currents on VV, PFCs and their structural responses. To learn the electromagnetic and structural response of the whole structure more accurately, a detailed finite element model is established. The two most dangerous scenarios, major disruptions and downward VDEs, are examined. It is found that distribution patterns of eddy currents for various PFCs differ greatly, therefore resulting in different EMFs and torques. It can be seen that for certain PFCs the transient reaction force are severe. Results obtained here may set up a preliminary foundation for the future dynamic response research of EAST VV and PFCs which will provide a theoretical basis for the future engineering design of tokamak devices.

The ITER EC H&CD upper launcher: Structural system

After approval of the preliminary design of the ITER EC H&CD Upper Launcher, ECHUL-CA, a consortium of several European research institutes, was founded to pool resources for approaching the final design. At the end of 2011 the consortium has signed a 2 years contract with F4E to go ahead with the work on the launcher. The contract deals with design work on both the port plug, forming the structural system, and the mm-wave-system, which injects the RF-power into the plasma. Within the period of this contract all components being part of the Tritium confinement, of which the closure plate, the support flange, the diamond windows and the waveguide feed-throughs are the most outstanding ones, will get the status of the final design.Important steps to be done for the structural system are the optimization of the mechanical behavior of the launcher, leading to minimum deflections of the port plug during plasma disruptions and optimum seismic resistance. To reduce the effect of halo currents it was decided to recess the first wall of 100mm compared to the regular blanket tangent. This recess requires substantial changes of the cooling system and the thermo-hydraulic design of the launcher. Also the layout of the shielding arrangement and the integration of the mm-wave system need significant revision. Moreover manufacturing aspects and enhanced remote handling capability are taken into account.For the final design also quality aspects must be considered; thus the design is elaborated with respect to applicable codes and standards, material specifications, risk analyses and the RAMI (reliability, availability, maintainability and inspectability) analysis to guarantee maximum performance of the device.This paper outlines the present status of the structural system of the EC H&CD upper launcher and represents the most recent steps towards its final design.

The ITER EC H&CD upper launcher: EM disruption analyses

In the frame of the new grant started in November 2011 between Fusion for Energy (F4E) and the ECHUL-CA consortium, the development process of the Electron Cyclotron Heating and Current Drive (EC H&CD) upper launcher (UL) in ITER has moved a step toward the final design phase.Based on the 2009 preliminary design review version, the new configuration of the UL now features a thicker single-wall mainframe (up to 90mm), a recessed first wall panel (100mm, to reduce the impact of halo currents) and a new arrangement of the internal shield blocks. The main design drivers for the structural components are still the electromagnetic (EM) loads, which need to be reassessed for the new configuration of the UL.In this paper the results of a new EM 20° sector model of ITER, specialized for the UL, are shown. Six different disruption scenarios are considered in this work: upward linear (36ms) and exponential (36ms) vertical displacement events (VDE), upward linear (36ms) and exponential (16ms) major disruptions (MD), category II upward slow and slow–fast VDEs. Comparing the analyses’ results allowed to define a set of structural loads to be used as a reference for the forthcoming structural calculations.

Dynamics of the disruption halo current toroidal asymmetry in NSTX

This paper describes the dynamics of disruption halo current non-axisymmetries in the lower divertor of the National Spherical Torus Experiment (Ono et al 2000 Nucl. Fusion 40 557). The halo currents typically have a strongly asymmetric structure where they enter the divertor floor, and this asymmetry has been observed to complete up to eight toroidal revolutions over the duration of the halo current pulse. However, the rotation speed and toroidal extent of the asymmetry can vary significantly during the pulse. The rotation speed, halo current pulse duration, and total number of revolutions tend to be smaller in cases with large halo currents. The halo current pattern is observed to become toroidally symmetric at the end of the halo current pulse. It is proposed that this symmeterization is due to the loss of most or all of the closed field line geometry in the final phase of the vertical displacement event.

Integrated Procedure for Halo Current Reconstruction in ITER

This paper describes an integrated procedure for the reconstruction of halo currents expected in ITER. The procedure is based on simulation and reconstruction codes, partially adapted from existing codes and partly developed specifically for this purpose. The ultimate goal of this integrated procedure is the assessment of the performance and the possible optimization of the halo current diagnostic system foreseen in ITER. The preliminary results indicate that an alternative distribution of the present layout of halo current sensors could improve the reconstruction capability of this diagnostic system.

Numerical modeling of 3D halo current path in ITER structures

Disruptions represent one of the main concerns for Tokamak operation, especially in view of fusion reactors, or experimental test reactors, due to the electro-mechanical loads induced by halo and eddy currents. The development of a predictive tool which allows to estimate the magnitude and spatial distribution of the halo current forces is of paramount importance in order to ensure robust vessel and in-vessel component design. With this aim, two numerical codes (CARIDDI, CAFE) have been developed, which allow to calculate the halo current path (resistive distribution) in the passive structures surrounding the plasma. The former is based on an integral formulation for the eddy currents problem particularized to the static case; the latter implements a pair of 3D FEM complementary formulations for the solution of the steady-state current conduction problem. A simplified plasma model is adopted to provide the inputs (halo current injected into the first wall). Two representative test cases (ITER symmetric and asymmetric VDEs) have been selected to cross check the results of the proposed approaches.

Status of the EU domestic agency electromagnetic analyses of ITER vacuum vessel and blanket modules

This paper presents the results of the electromagnetic analyses of the ITER vacuum vessel and blanket modules. A wide collection of electromagnetic transients has been simulated: VDEs and MDs belonging to cat III, II and I, and a magnet fast discharge. Eddy and halo currents and corresponding Lorentz forces have been computed using 3D solid FE models implemented in ANSYS and CARIDDI. The plasma equilibrium configurations (displacement and quench of the plasma current, toroidal flux variation due to the β drop and halo currents wetting the first wall) used as an input for the EM analyses have been supplied by the 2D axisymmetric code DINA. The paper describes in detail the methodology used for the analyses and the main results obtained.

Simulation of VDE under intervention of vertical stability control and vertical electromagnetic force on the ITER vacuum vessel

Vertical displacement events (VDEs) and disruptions usually take place under intervention of vertical stability (VS) control and the vertical electromagnetic force induced on vacuum vessels is potentially influenced. This paper presents assessment of the force that arises from the VS control in ITER VDEs using a numerical simulation code DINA. The focus is on a possible malfunctioning of the ex-vessel VS control circuit: radial magnetic field is unintentionally applied to the direction of enhancing the vertical displacement further. Since this type of failure usually causes the largest forces (or halo currents) observed in the present experiments, this situation must be properly accommodated in the design of the ITER vacuum vessel. DINA analysis shows that although the ex-vessel VS control modifies radial field, it does not affect plasma motion and current quench behavior including halo current generation because the vacuum vessel shields the field created by the ex-vessel coils. Nevertheless, the VS control modifies the force on the vessel by directly acting on the eddy current carried by the conducting structures of the vessel. Although the worst case was explored in a range of plasma inductance and pattern of VS control in combination with the in-vessel VS control circuit, the result confirmed that the force is still within the design margin.

R&D and maintenance on graphite tile of divertor region at EAST

EAST, with full superconducting magnetic coils, had been designed and constructed to address the scientific and engineering issues under steady state operation. The in-vessel components are full graphite tiles as first wall had been operated successfully. In the experiment campaign of 2010, the H mode operation and 1MA operation have been gotten on EAST. However, in some case, some of the graphite tiles of divertor region are damaged with the plasma parameter enhanced. As most of the damaged graphite tiles are in the divertor region, they are probably damaged by the electro-magnetic force of the halo current when the VDEs occur. The force of the halo current is re-estimated. The structure analysis has been done by the ANSYS software. From the analysis result. It can be obtained that the stress is larger than the allowable stress when the halo current on the graphite tile is larger than 2.7kA. The tensile testing of the graphite also has been done. As the result, the graphite tiles are damaged when the forces are up to 2400N. To deal with the problem, two proposes are accepted. In the one hand, the new type graphite material is used, whose tensile strength is up to 45MPa. In the other hand, the structure of the graphite tiles is optimized.