Poloidal Field Coils Research Articles

Heat Transfer Analysis of MgB2 Coil in Heat Treatment Process for Future Fusion Reactor

State of the art MgB <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> is reviewed as a potential material for the poloidal field (PF) coils of the future fusion reactor due to its high critical temperature and low material cost. The heat treatment process is a crucial step in the development of MgB <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> magnets. The temperature lag in heat treatment of large magnets can lead to insufficient thermal reaction time. It may be infeasible to control the temperature of a magnet according to the heat treatment scheme recommended for the MgB <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> wire. Hence, the heat treatment process of a large magnet needs to be evaluated. Therefore, the dynamic temperature distribution of a MgB <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> PF coil is obtained by simulating the heat transfer in heat treatment process. A suitable heat treatment schedule for a large magnet is proposed and the experimental results of a sub-size Cable-In-Conduit Conductor manufactured with MgB <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> strand confirmed the feasibility of the newly proposed heat treatment process. The results provide a reference for the heat treatment method of a future larger MgB <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> coil.

Electrodynamic Losses of the ITER PF Joints During the Dynamic Plasma Scenario

In large scale fusion magnets wound with cable in conduit conductors, the electrical connections between superconducting cables are critical components for the safe operation of the magnet system. This work presents the results of a numerical study on the electrodynamic losses generated in the twin-box joints of the Poloidal Field (PF) coils of the ITER magnet system during a relevant dynamic plasma scenario. The study was carried out using two numerical models implemented in the THELMA code and in a 3D finite element software; both were previously validated versus experimental data obtained in the SULTAN facility (Swiss Plasma Center, Villigen, Switzerland).

Mutual Induction Caused by IVCC Currents on Quench Detection Circuits of the KSTAR TF Coils

The Quench Detection System (QDS) for the Toroidal Field (TF) coils and the Poloidal Field (PF) coils made of Nb <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> Sn or NbTi cable-in-conduit conductors is using Wheatstone bridges to compensate induced voltages, which are generated by electrical currents of the superconducting coils and a plasma, on the quench detection circuits of the Korea Superconducting Tokamak Advanced Research (KSTAR) device. On the other hand, the KSTAR device is equipped with In-Vessel Control Coils (IVCCs), which consist of 16 segmented windings made of normal conductors, for fast plasma position control, field error correction, and resistive wall mode stabilization. Electrical currents of the middle Field Error correction Coil (FEC) in a part of the IVCCs have strong mutual induction on the quench detection circuits of the TF coils due to the paths of the FEC's conductors, and the middle FEC currents, which had unusually long and very steep ramps, raised an emergency protection sequence of the TF coils in a KSTAR plasma experiment. Quench detection circuits only using traditional Wheatstone bridges are insufficient to cancel out such a mutual induction; whereas, the mutual induction can be numerically compensated in a theoretically straightforward calculation.

Parametric thermal-hydraulic analysis of the DEMO PF coils designed by CEA during the breakdown phase

EU-DEMO - the European DEMOnstration Fusion Power Plant, is being designed as an intermediate stage between the ITER experimental reactor and the future fusion power plant. The fully superconducting magnet system of the DEMO tokamak includes six Poloidal Field (PF) coils. Two different concepts of the DEMO PF winding packs are being developed by the EPFL-SPC (Switzerland) and CEA IRFM (France) teams. The current cycle of the PF coils consists of the following phases: Premagnetization (10 s), Plasma Current Ramp-Up (PCRU, 80 s), plasma burn (7200 s) and dwell (600 s). The PCRU phase starts with the fast breakdown (0.8 s), during which the operating current and magnetic field change very rapidly causing significant heat generation due to AC losses. Thus, the breakdown is potentially the most critical phase of normal operation of PF conductors regarding the temperature margin. This study was focused on the thermal-hydraulic analysis of the PF coils designed by CEA during breakdown. According to the CEA design, based on the 2018 DEMO reference, the PF coils are double-pancake wound with square NbTi Cable-in-Conduit Conductors with a central cooling channel. Operation of conductors designed for each PF coil was simulated with the THEA code by Cryosoft. Since the detailed reference current breakdown scenario for the PF coils is not available yet, the analysis was performed parametrically. We took into account the external or internal magnetic field profile along each PF conductor as well as heat generation due to the AC hysteresis losses and coupling losses (for the trial values of the parameter nτ = 100, 200 and 300 ms). The study was aimed at the estimation of the minimum temperature margin in each PF conductor during the breakdown and verification if it fulfills the performance criterion min(ΔTmarg) ≥ 1.5 K. The results of analysis should help in further improvements and optimization of the PF winding packs design.

Performance review of the joints for the ITER poloidal field coils

For large scale magnets wound with cable-in-conduit conductors, the safe operation of the joints is of paramount importance to guarantee adequate reliability and stability margin of the whole magnet. For this reason, during the R&D activities undertaken for the development of the ITER magnet system, several experimental campaigns were launched to study the AC and DC performance of the joint and limit the risk of thermal runaways at the joints during the tokamak operation. The joint electrical resistance must be limited below specified values to avoid excessive heating generated by the transport current. Moreover, in presence of time-varying fields, different types of losses arise at the joints, which can be associated to their superconducting and resistive parts. The relative importance of these losses depends on the joint manufacturing solution. The aim of this investigation is to analyze the performance at different working conditions of the joints for the connection of the conductors of the poloidal field (PF) coils of the ITER magnet system. This work presents, for the first time, a wide review of the test campaign performed from 2016 to 2021 on the PF joint samples during the three manufacturing phases, namely pre-qualification, qualification and production. The values of electrical resistances and losses under sinusoidal field variations are reported in the paper at different operating conditions, thus building a useful database to assess the joint performances during the machine operation. The data here collected show the impact of the manufacturing techniques on the joint performances and, furthermore, represent a useful tool for the validation of numerical and analytical models of joints.

Analysis and design of the central stack for the SMART tokamak

The SMall Aspect Ratio Tokamak (SMART) is a new spherical machine that is currently under construction at the University of Seville aimed at exploring negative vs positive triangularity prospects in Spherical Tokamaks (ST). The operation of SMART will cover three phases, with toroidal fields Bϕ≤ 1 T, inductive plasma currents up to Ip= 500 kA and a pulse length up to 500 ms, for a plasma with R = 0.4 m, a = 0.25 m and a wide range of shaping configurations (aspect ratio, 1.4 < R/a < 3, elongation, κ≤ 3, and average triangularity, -0.6 ≤δ≤ 0.6). The magnet system of the tokamak is composed by 12 Toroidal Field Coils (TFC), 8 Poloidal Field Coils (PFC) and a Central Solenoid (CS). With such operating conditions, the design of the central stack, usually a critical part in spherical tokamaks due to space limitations, presents notable challenges. The current SMART central stack has been designed to operate up to phase 2 and it comprises the inner legs of the TFC, surrounded by the CS, two supporting rings, a central pole and a pedestal. To achieve the plasma parameters of this phase (Bϕ=0.4 T with inductive Ipup to 200 kA), the high currents required, combined with the low aspect-ratio of the machine lead to high forces on the conductors that represent an engineering challenge. The loads expected in the central stack are a centring force up to 1.5 MN and a twisting torque up to 7.4 kNm. This work describes the design of the central stack and its mechanical validation with a multiphysics finite element assessment. Using a combined electromagnetic and mechanical assessment, it is shown that the SMART central stack will meet the physics requirements in phase 2.

Modelling, design and simulation of plasma magnetic control for the Spherical Tokamak for Energy Production (STEP)

Magnetic controller performance requirements and design solutions for the Spherical Tokamak for Energy Production (STEP) are driven by the need to produce equilibrium and scenario trajectories, maintaining steady plasma vertical stabilization and shape control for a period of thousands of seconds or longer while avoiding contact with the plasma-facing components (PFCs). Axisymmetric magnetic control schemes including vertical stabilization, plasma current control, plasma shape control and poloidal field coil current control for the STEP Prototype Reactor (SPR) concept are being developed using a suite of control analysis tools (known collectively as TokSys) supporting the integrated plasma control design process. The vertical growth rate based on a linear rigid plasma response model in TokSys is used for assessing the controllability of the vertical instability in SPR. TokSys closed-loop simulations with the axisymmetric non-linear, free-boundary evolution code, GSevolve, are performed for the assessment, identification, and verification of algorithm implementation and controller performance for the various axisymmetric control systems. Dynamic control performance and controllability are shown to be consistent with noise-affected scenario requirements under reasonable power supply and sensor performance assumptions.

Compact Radiative Divertor Experiments at ASDEX Upgrade and Their Consequences for a Reactor.

We present a novel concept to tackle the power exhaust challenge of a magnetically confined fusion plasma. It relies on the prior establishment of an X-point radiator that dissipates a large fraction of the exhaust power before it reaches the divertor targets. Despite the spatial proximity of the magnetic X point to the confinement region, this singularity is far away from the hot fusion plasma in magnetic coordinates and therefore allows the coexistence of a cold and dense plasma with a high potential to radiate. In the compact radiative divertor (CRD) the target plates are placed close to this magnetic X point. We here report on high performance experiments in the ASDEX Upgrade tokamak that indicate the feasibility of this concept. Despite the shallow (projected) field line incidence angles of the order of θ_{⊥}=0.2°, no hot spots were observed on the target surface monitored by an IR camera, even at a maximum heating power of P_{heat}=15 MW. And even with the X point located exactly on the target surface and without density or impurity feedback control, the discharge remains stable, the confinement good (H_{98,y2}=1), hot spots absent, and the divertor in a detached state. In addition to its technical simplicity, the CRD scales beneficially to reactor-scale plasmas that would benefit from an increased volume of the confined plasma, more space for breeding blankets, smaller poloidal field coil currents, and-potentially-an increased vertical stability.

Demonstration of ITER Real-Time Framework with application of PF coil control in KSTAR

ITER Real-Time Framework (RTF) is a middleware for developing fast real-time control applications such as plasma control system (PCS). In this framework, applications are built by creating and assembling Function Blocks (FBs) as atomic components of the application. The RTF can easily configure the application to be operated with multi-thread, multi-process, or multi-node processing under real-time mode. In this paper, we demonstrated capability of the RTF on the Poloidal Field (PF) coil Magnetic Power Supply (MPS) system of KSTAR. First, we fully implemented the KSTAR PF coil control logic from the KSTAR PCS into an independent RTF application. By configuring the real-time mode and multi-thread processing, 11 PF coils can be simultaneously controlled with a 20 KHz execution cycle. Second, we applied a built-in exception handler in the RTF to implementing protection from specified off-normal events such as PF Power Supply Fault (PSF) and PF OverCurrent Fault (OCF). Third, we integrated the standard real-time network interfaces of the KSTAR, the Reflective Memory (RFM) network, with the RTF application. Finally, we made a shot automation interface in order to run the RTF application according to the KSTAR shot sequence stages. This interface also has a snapshot functionality to store and load all experimental parameters for each shot number. We evaluated the effectiveness of the RTF application through a single PF MPS test connected with a 40 mH dummy load coil.

Vertical control of DIII-D discharges with strong negative triangularity

Through predictive modeling validated by a series of experiments on DIII-D, the vertical stability of low β diverted plasmas with strong negative triangularity (NT) () is assessed. As a result of their unique magnetic geometry, NT plasmas feature larger Shafranov shifts and more elongated inner flux surfaces than positive triangularity counterparts, typically leading to enhanced vertical instability growth rates. However, coupling with the non-conformal vessel DIII-D wall reduces these growth rates to controllable values, providing a path forward for stabilizing strongly NT plasma with a diverted geometry. These discharges are used to validate GSdesign (part of the TokSys code suite) stability calculations in strong NT plasmas on DIII-D, with errors of no more than ∼20% observed between modeled and experimentally measured growth rates. Additions of diagnostic noise and power supply tuning to the TokSys model are needed to accurately capture the time dependence of DIII-D NT discharges, assisting with the design of control schemes specific to the DIII-D poloidal field coils. Finally, implications of these results on a future NT reactor are briefly described.

Analysis of edge transport in L-mode negative triangularity TCV discharges

One of the major problems for future tokamak devices are ELMs (Edge Localized Modes) as they can lead to large, uncontrolled heat fluxes at the machine targets. For this reason, different techniques and alternative magnetic configurations are under study to mitigate or avoid these phenomena. One of the most promising among these studies is the Negative Triangularity (NT) configuration, which exhibits a global confinement comparable with H-Mode operation and, staying in L-mode, could enable an easier power exhaust dissipation due to a possible bigger heat flux decay length with respect to the conventional Positive triangularity (PT) H-mode. In this work, the fluid code SOLEDGE2D-EIRENE is used to study edge transport. Studies are made on discharges performed in the TCV device (Tokamak à configuration variable), which can create a variety of different plasma geometries thanks to 16 independently powered poloidal field coils and its open vacuum vessel. In order to understand if and how power and particle exhaust in NT differs with respect to those of the PT shape, four discharges in single null magnetic divertor configuration with fixed lower triangularity (δbot=+0.5) but with different upper triangularity (from δup=-0.28 to δup=+0.45) have been modelled. All of them are ohmically heated, L-mode deuterium plasmas, and in the high recycling regime. Moreover, these discharges were previously used in [4] to measure the heat flux decay length by IRT (Infrared Thermography), allowing us to make comparisons with modelling results.

Structural optimisation of the DEMO alternative divertor configurations based on FE and RBF mesh morphing

The DEMO tokamak exhibits extraordinary complexity due to the constraints and requirements pertaining to different fields of physics and engineering. The multidisciplinary nature of the DEMO system makes its design phase extremely challenging since different and often opposite requirements need to be accounted for. Toroidal field (TF) coils generate the toroidal magnetic field required to magnetically confine the plasma particles and support at the same time the poloidal field coils. They must bear tremendous loads deriving from electromagnetic interactions between the coil currents and the generated magnetic field. An efficient tokamak design aims at minimizing the energy stored in its magnetic field and hence at reducing the toroidal volume within the TF coils whose shape would hence ideally mimic co-centrically the shape of the plasma. In order to bear the enormous forces a D-shape is most suitable for the TF coils as it allows them to resist the very large compression on the inner side and to carry the electro-magnetic (EM) pressure mainly by membrane stresses preventing large bending to occur on the outer side. At the same time the divertor structures must fit within the TF coils and this requires adaptations of the TF coil shape in the case of so-called advanced divertor configurations (ADCs), which require larger divertor structures. This article shows the TF coils adapted to ADCs using a structural optimisation procedure applied to the reference shape. The introduced strategy takes as structural optimum the iso-stress profile associated to each coil. A continuous transformation, based on radial basis functions mesh morphing, turns the baseline finite element (FE) model into its iso-stress counterpart, with a series of intermediate configurations available for electromagnetic and structural investigations as output. The adopted strategy allowed to determine, for each of the ADC cases, a candidate shape. Static membrane stress levels during magnetization could be reduced significantly from more than 700 MPa to below 450 MPa.

Commissioning and first operational experience with the new thyristor converter Group 7 of ASDEX Upgrade

Due to the continuously expanding experimental program of ASDEX Upgrade (AUG), the high current converters came to their limits. At the same time, the risk of failure increased because of the equipment aging. In order to reduce this risk and to extend the area of operation, a new thyristor converter called “Group 7″, equipped with a recently developed digital control system, was installed. While the design was already published on SOFT 2018, this paper will describe in detail the commissioning results and the first operational experience of the new thyristor converter. The manufacturing and on site installation of Group 7 started in 2018 and was finished in spring 2021 by the delivery of the transformers. In parallel to the construction process the main components were type-tested. One of four converter modules was extensively verified during the factory acceptance tests. In order to be able to test the digital control system independently of the construction of the power converter, a scale model was built. All functions of the control system were tested on it. It was also useful to investigate the problems arising during commissioning and to verify firmware fixes. After finishing the site installation work, the converter was proved in all possible configurations on a test coil. These tests were performed in local and remote control. Attention was also paid to the effect of power factor improvement by neutral-point vs. regular bridge (B6) thyristor configuration. For this reason, all tests were performed with and without operation of the neutral-point thyristors. The last step was to operate the converter on the magnet coils of AUG. In an intensive test program over a period of six month, all poloidal field and OH coils of AUG were operated with the new converter in the required operation mode.

Application of integrated simulation environment SIEMNED to the analysis of the MEPHIST-0 tokamak operation

This paper presents the results of numerical simulation of plasma equilibrium and stability in the MEPHIST-0 tokamak with SIEMNED software and comparison of simulation results with experiments. The determined characteristics of the vacuum chamber show that it significantly affects the entire discharge. For various scenarios of the inductor operation, a comparison of experimental data and simulated currents and magnetic fields induced in the chamber was carried out. For steady-state tokamak operation, a numerical study of equilibrium plasma configurations was carried out depending on the currents in the poloidal magnetic field coils and plasma current. The vertical plasma instability was investigated. The limiting values of plasma ellipticity preventing the vertical plasma instability were numerically determined. Numerical simulations show that plasma equilibrium is supported by induced currents. It was shown numerically that magnetic configuration with ‘zero of higher order’ were obtained before the plasma shot, suggesting consistency between the simulation results and observations.

Nanocomposite Beta Nb50Ti based SWCNTs by FAST-SPS-FCT

The synthesis of β-type phase NbxTi (x= 50 at%) / SWCNTs (Single Walled Carbon Nanotubes) intermetallic matrix nanocomposite by mechanical alloying to ensure the effective distribution of (SWCNTs) within the matrix. It has been stated by several researchers that during ball-milling of NbxTi (x =50 at%) powder mixtures, Nb-Ti intermetallic compound formation occurs either gradually along milling time of mechanical allowing (MA), or suddenly through amechanically self-propagating reaction (MSPR), which occurs after a ignition time of MA. For this purpose, 0.4and 0.8 at% of SWNTs was added to the powder mixture after the completion of reactionbetween Nb and Ti. The obtained powders Nb50Ti intermetallic compound mixed with SWCNTs powder and then was also ball-milled. Bulk samples were compacted and then sintered by (FAST-SPS-FCT) method (Field Assisted Sintering Technics-Sparck Plasma Sintering- Furnace, Advanced Ceramics for High-Temperature) at the temperature range (1273-1473 °K) with some time that retained the integrity of SWNTs in the intermetallic matrix.Structural and mechanical and vibronic changes of the nanocomposites were investigated by X-ray diffractometery (XRD). Field emission scanning electron microscopy (FESEM) micrographs showed that the offered MA approach caused the SWNTs to be uniformly embedded in the in situ synthesized NbTi intermetallic matrix. Meanwhile better distribution of SWCNTs resulted in higher density of FAST-SPS-FCT bulk nanocomposite as well higher hardness up to 2.75GPa compared to 2.4 of Nb50Ti intermetallic alloy obtained after MA time. The total porosity, compressive strength, and compressive elastic modulus of the FAST-SPS-FCT manufactured material were determined as 7%, 600 MPa, and 120 MPa, respectively. The alloy’s and its intermetallic nanocomposite have Young’s elastic modulus is comparable to that of healthy cancellous bone which makes it applicable in the biomedical field. The in vitro biocomptability will be performed in the near future. The comparable results for the FAST-SPS-FCT nanocomposites were 3%, 650 MPa, and 130 MPa. The alloy’s elastic modulus is comparable to that of healthy cancellous bone. This difference in mechanical properties results from different porosity and phase composition of the bot β-phase NbxTi (x= 50 at%) and NbxTi (x= 50 at%)/SWCNTs intermetallic matrix nanocomposite. More other nanotechnologies applications of the nanocomposite will be focused in the study of the superconducting type I for the ITER Poloidal Field Coils by measuring of Jc (T, B) characteristics.

Techno-Economic Optimization of the NbTi DTT Feeders

The superconducting (SC) coils of the Divertor Tokamak Test (DTT) facility will be connected to the current leads by a set of SC feeders, currently designed as cable-in-conduit conductors wound using commercial NbTi strands to be cooled by Supercritical Helium at 4.5 K. The feeders are immersed in the magnetic field generated by the SC coil and plasma outside of magnet system, so that the maximum field on the most loaded feeder can reach 4 T at the full rated current (including the self-field effect). Here the performance of the feeder conductors is assessed during a plasma pulse, based on the DTT standard single-null operating scenario, for the most loaded feeder of the Central Solenoid and of the Toroidal and Poloidal Field coils, computing the minimum temperature margin to current sharing throughout the plasma scenario. Several alternative cabling configurations are analyzed, designed to withstand the nominal current at the peak field with a different number of SC and stabilizer strands. A figure of merit is built parametrically based on the variation of the minimum temperature margin as a function of the material, manufacturing and operational costs of the different alternative feeder layouts. Based on such techno-economical characterization, the optimal (cheapest) design of the feeder cables is identified.

Development of a removable three-dimensional magnetic probe system for measuring field null on the NanChang Spherical Tokamak.

The field null configuration of a poloidal magnetic field is one of the critical conditions for achieving Ohmic breakdown during the initial discharge of a new tokamak. The issue of the Ohmic breakdown on the NanChang Spherical Tokamak (NCST) is still not solved satisfactorily although plasma currents of about 2kA were found. Hence, a removable three-dimensional magnetic probe (RTMP) system consisting of 25 magnetic probes was designed, calibrated, and constructed on the NCST to evaluate the field null inside a vacuum vessel. After repeated tests, the RTMP system exhibited outstanding performance in terms of accuracy and stability with errors of about 1%. Meanwhile, the RTMP system successfully measured the toroidal field (TF) coil ripples at the magnetic axis. During experiments, the stray field arising from the TF coil implied a strong link between the flexible connection of the TF coil and the Ohmic breakdown on the NCST. After the field null was effectively modified by using a new flexible connection of the TF coil and controlling the induced current in the poloidal field coil, the NCST tokamak reproducibly obtained 20kA plasma current with the limiter configuration during the plasma current flat-top phase.

Design of the HL-2M Support System

The HL-2M tokamak was constructed at Southwestern Institute of Physics. The support system is one of the main subsystems of the device. The magnetic coils and vacuum vessel are located and integrated by the support system. According to its function, the support system is divided into gravity support, support for poloidal field coils, and anti-torque structure for toroidal field coils. The structure design and the finite element analysis of the support system is introduced in this paper.

Misalignment of magnetic field in DIII-D assessed by post-mortem analysis of divertor targets

We assess the toroidal magnetic field B t asymmetry in DIII-D due to a misalignment of the toroidal field coils with respect to the poloidal magnetic field coils and vacuum vessel. The peak-to-peak variation of the divertor strike point (SP) radius is measured to be 1 cm, with an n = 1 toroidal pattern. We use the centre of a narrow carbon deposition band on tungsten-coated divertor tiles just inside the outer strike point (OSP) as a proxy for the divertor SP location. The band occurred in a series of reverse B t discharges with the OSP positioned on the divertor inserts due to strong E × B drift transport of C from the inner to the outer SP through the private flux region. The variation in band radius (and hence the magnetic SP) is a (4.89 ± 0.31) mm shift toward (310 ± 4)° toroidal direction. These measurements agree well with previous measurements of the 3D magnetic field distribution (Luxon 2003 Nucl. Fusion 43 1813), simulations performed by the mafot field line integration code, and recent Langmuir probe measurements in the small-angle-slot (SAS) divertor (Watkins et al 2019 Nucl. Mater. Energy 18 46). Comparison of these measurements in the SAS divertor also indicates that there is the possibility of a tilt (in conjunction with the shift) of the B t coil field of (0.04 ± 0.07)° towards the toroidal angle of (215 ± 25)°. Previous measurements suggested a field misalignment of (4.6 ± 0.3) mm in the 270° toroidal direction, and a tilt of (0.06 ± 0.02)° toward the 114° toroidal direction, which is similar to the results reported here. These studies will be important for better understanding the radial variation of the toroidal strike line in DIII-D, for designing the new generation of SAS divertor, and for developing an understanding of the impact of error fields on tokamaks with tightly baffled slot divertors.

Methodology of Plasma Shape Reachability Area Estimation in D-Shaped Tokamaks

This paper suggests and develops a new methodology of estimation for a multivariable reachability region of a plasma separatrix shape on the divertor phase of a plasma discharge in D-shaped tokamaks. The methodology is applied to a spherical Globus-M/M2 tokamak, including the estimation of a controllability region of a vertical unstable plasma position on the basis of the experimental data. An assessment of the controllability region and the reachability region of the plasma is important for the design of tokamak poloidal field coils and the synthesis of a plasma magnetic control system. When designing a D-shaped tokamak, it is necessary to avoid the small controllability region of the vertically unstable plasma, because such cases occur in practice at a restricted voltage on a horizon field coil. To make the estimations mentioned above robust, PID-controllers for vertical and horizontal plasma position control were designed using the Quantitative Feedback Theory approach, which stabilizes the system and provides satisfactory control indexes (stability margins, setting time, overshoot) during plasma discharges. The controllers were tested on a series of plasma models and nonlinear models of current inverters in auto-oscillation mode as actuators for plasma position control. The estimations were made on these models, taking into account limitations on control actions, i.e., voltages on poloidal field coils. This research is the first step in the design of the plasma shape feedback control system for the operation of the Globus-M2 spherical tokamak. The developed methodology may be used in the design of poloidal field coil systems in tokamak projects in order to avoid weak achievability and controllability regions in magnetic plasma control. It was found that there is a strong cross-influence from the PF-coils currents and the CC current on the plasma shape; hence, these coils should be used to control the plasma shape simultaneously.