Resonant Magnetic Perturbation Coils Research Articles

Effects of edge safety factor on the toroidal flow velocities during the resonant magnetic perturbations and compact torus injection experiments on the STOR-M tokamak

ABSTRACTThe effects of the edge safety factor on the toroidal flow velocity modification due to resonant magnetic perturbation (RMP) and tangential compact torus injection (CTI) have been investigated on the Saskatchewan Torus-Modified (STOR-M) tokamak. The (l = 2, n = 1) RMP coils are wound against the outer surface of the vacuum vessel. The safety factor has been varied by changing the plasma current at a fixed toroidal magnetic field. As the edge safety factor is reduced, the magnetic perturbations on the q = 2 surface are expected to shift radially outwards, moving closer towards the RMP coils. The evolution of the plasma flow velocity was measured through ion Doppler spectroscopy (IDS). It has been found that RMP changes the flow velocity towards the direction of the plasma current direction and this effect is enhanced when the edge safety factor is reduced. When CT was injected tangentially along the plasma current direction, similar changes in the flow velocity have been found. However, the change is not sensitive to the edge safety factor in the CT injection case.

Design of Current-Pulse Power Supply for Tearing Mode Control on the J-TEXT Tokamak

A new method to suppress tearing mode and accelerate magnetic island rotation has been explored. To verify this method on the J-TEXT tokamak, a current-pulse power supply is designed to drive the resonant magnetic perturbation coils with a frequency range from 1 to 5 kHz and amplitude of 3 kA, which can create 0.75 G of magnetic perturbation. The current-pulse power supply topology is modified by H-bridge inverter, which can create a bipolar pulsed current. A set of boost capacitors with an isolation diode is added on dc bus just before the inverter. During the current changing time, the boost capacitors can store the energy of inductive load to steepen the current falling edge and create high voltage to accelerate the current rising speed. This modified topology has a rapid current changing edge and the wide range of operating frequency. A small power prototype is built to verify the topology.

Design and Implementation of the Resonant Magnetic Perturbations Feedback Control System for Tearing Mode Suppression on J-TEXT

Tearing modes (TMs) degrade the performance of tokamak plasma, and can even lead to disruption. Using externally exerted resonant magnetic perturbations (RMPs) to suppress TM is a promising and effective way. In order to suppress the 2/1 TM, 2/1 RMP must be applied in given phase regions to stabilize magnetic island and accelerate island rotation. The RMP feedback control system acquires the multiple-channel poloidalMirnov signal, processes the acquired data and calculates the magnetic island phase in real time, and switches on the RMP power supply when the phase is in the designated region. The feedback control system is based on NI cRIO and developed mainly using LabVIEW field-programmable gate array. The typical 2/1 mode magnetic island on J-TEXT rotates at a frequency from 2 to 10 kHz. To ensure the control precision within 2°, the control period must be within 500 ns. Due to the noisy characteristic of the Mirnov signal, the feedback control system uses a series of error correction methods in real time to obtain accurate phase. Various control strategies have been adopted to exploit the RMP coil and power supply. Observable result is presented in this paper.

Insights into type‐I edge localized modes and edge localized mode control from JOREK non‐linear magneto‐hydrodynamic simulations

Edge localized modes (ELMs) are repetitive instabilities driven by the large pressure gradients and current densities in the edge of H‐mode plasmas. Type‐I ELMs lead to a fast collapse of the H‐mode pedestal within several hundred microseconds to a few milliseconds. Localized transient heat fluxes to divertor targets are expected to exceed tolerable limits for ITER, requiring advanced insights into ELM physics and applicable mitigation methods. This paper describes how non‐linear magneto‐hydrodynamic (MHD) simulations can contribute to this effort. The JOREK code is introduced, which allows the study of large‐scale plasma instabilities in tokamak X‐point plasmas covering the main plasma, the scrape‐off layer, and the divertor region with its finite element grid. We review key physics relevant for type‐I ELMs and show to what extent JOREK simulations agree with experiments and help reveal the underlying mechanisms. Simulations and experimental findings are compared in many respects for type‐I ELMs in ASDEX Upgrade. The role of plasma flows and non‐linear mode coupling for the spatial and temporal structure of ELMs is emphasized, and the loss mechanisms are discussed. An overview of recent ELM‐related research using JOREK is given, including ELM crashes, ELM‐free regimes, ELM pacing by pellets and magnetic kicks, and mitigation or suppression by resonant magnetic perturbation coils (RMPs). Simulations of ELMs and ELM control methods agree in many respects with experimental observations from various tokamak experiments. On this basis, predictive simulations become more and more feasible. A brief outlook is given, showing the main priorities for further research in the field of ELM physics and further developments necessary.

Enhanced understanding of non-axisymmetric intrinsic and controlled field impacts in tokamaks

An extensive study of intrinsic and controlled non-axisymmetric field (δB) impacts in KSTAR has enhanced the understanding about non-axisymmetric field physics and its implications, in particular, on resonant magnetic perturbation (RMP) physics and power threshold (Pth) for L–H transition. The n = 1 intrinsic non-axisymmetric field in KSTAR was measured to remain as low as δB/B0 ~ 4 × 10−5 even at high-beta plasmas (βN ~ 2), which corresponds to approximately 20% below the targeted ITER tolerance level. As for the RMP edge-localized-modes (ELM) control, robust n = 1 RMP ELM-crash-suppression has been not only sustained for more than ~90 τE, but also confirmed to be compatible with rotating RMP. An optimal window of radial position of lower X-point (i.e. Rx = m) proved to be quite critical to reach full n = 1 RMP-driven ELM-crash-suppression, while a constraint of the safety factor could be relaxed (q95 = 5 0.25). A more encouraging finding was that even when Rx cannot be positioned in the optimal window, another systematic scan in the vicinity of the previously optimal Rx allows for a new optimal window with relatively small variations of plasma parameters. Also, we have addressed the importance of optimal phasing (i.e. toroidal phase difference between adjacent rows) for n = 1 RMP-driven ELM control, consistent with an ideal plasma response modeling which could predict phasing-dependent ELM suppression windows. In support of ITER RMP study, intentionally misaligned RMPs have been found to be quite effective during ELM-mitigation stage in lowering the peaks of divertor heat flux, as well as in broadening the ‘wet’ areas. Besides, a systematic survey of Pth dependence on non-axisymmetric field has revealed the potential limit of the merit of low intrinsic non-axisymmetry. Considering that the ITER RMP coils are composed of 3-rows, just like in KSTAR, further 3D physics study in KSTAR is expected to help us minimize the uncertainties of the ITER RMP coils, as well as establish an optimal 3D configuration for ITER and future reactors.

Design of rotating resonant magnetic perturbation coil system in the STOR-M tokamak

The interaction between resonant magnetic perturbations (RMP) and plasma is an active topic in fusion energy research. RMP involves the use of radial magnetic fields generated by external coils installed on a tokamak device. The resonant interaction between the plasma and the RMP field has many favorable effects such as suppression of instabilities and, under certain conditions, improvement of discharge parameters in tokamaks. The RMP technique has been successfully implemented in the STOR-M tokamak. A set of (m=2, n=1) helical coils carrying a current pulse was used to study the effects of RMP on magnetic islands, plasma rotation, and other edge plasma parameters. A new RMP system is being developed for the STOR-M tokamak. The system consists of a number of external saddle coils distributed in the poloidal and toroidal directions and powered by AC power supplies to generate a rotating RMP field. Numerical simulations have been carried out to calculate several parameters for the new RMP system such as the magnetic field and the dominant modes generated by the coils. The dominant mode generated by the new RMP coil system may be tuned to (2, 1) with significant contributions from (2, 3) and (2, 5) modes.

Toroidal modeling of plasma response to RMP fields in ITER

A systematic numerical study is carried out, computing the resistive plasma response to the resonant magnetic perturbation (RMP) fields for ITER plasmas, utilizing the toroidal code MARS-F (Liu et al 2000 Phys. Plasmas 7 3681). A number of factors are taken into account, including the variation of the plasma scenarios (from 15 MA Q = 10 inductive scenario to the 9 MA Q = 5 steady state scenario), the variation of the toroidal spectrum of the applied fields (n = 1, 2, 3, 4, with n being the toroidal mode number), the amplitude and phase variation of the currents in three rows of the RMP coils as designed for ITER, and finally a special case of mixed toroidal spectrum between the n = 3 and n = 4 RMP fields. Two-dimensional parameter scans, for the edge safety factor and the coil phasing between the upper and lower rows of coils, yield ‘optimal’ curves that maximize a set of figures of merit, that are defined in this work to measure the plasma response. Other two-dimensional scans of the relative coil current phasing among three rows of coils, at fixed coil currents amplitude, reveal a single optimum for each coil configuration with a given n number, for the 15 MA ITER inductive plasma. On the other hand, scanning of the coil current amplitude, at fixed coil phasing, shows either synergy or cancellation effect, for the field contributions between the off-middle rows and the middle row of the RMP coils. Finally, the mixed toroidal spectrum, by combining the n = 3 and the n = 4 RMP field, results in a substantial local reduction of the amplitude of the plasma surface displacement.

Numerically derived parametrisation of optimal RMP coil phase as a guide to experiments on ASDEX Upgrade

Edge localised modes (ELMs) are a repetitive MHD instability, which may be mitigated or suppressed by the application of resonant magnetic perturbations (RMPs). In tokamaks which have an upper and lower set of RMP coils, the applied spectrum of the RMPs can be tuned for optimal ELM control, by introducing a toroidal phase difference between the upper and lower rows. The magnitude of the outermost resonant component of the RMP field (other proposed criteria are discussed herein) has been shown experimentally to correlate with mitigated ELM frequency, and to be controllable by (Kirk et al 2013 Plasma Phys. Control. Fusion 53 043007). This suggests that ELM mitigation may be optimised by choosing , such that is maximised. However it is currently impractical to compute in advance of experiments. This motivates this computational study of the dependence of the optimal coil phase difference , on global plasma parameters and q95, in order to produce a simple parametrisation of . In this work, a set of tokamak equilibria spanning a wide range of (, q95) is produced, based on a reference equilibrium from an ASDEX Upgrade experiment. The MARS-F code (Liu et al 2000 Phys. Plasmas 7 3681) is then used to compute across this equilibrium set for toroidal mode numbers n = 1–4, both for the vacuum field and including the plasma response. The computational scan finds that for fixed plasma boundary shape, rotation profiles and toroidal mode number n, is a smoothly varying function of (, q95). A 2D quadratic function in (, q95) is used to parametrise , such that for given (, q95) and n, an estimate of may be made without requiring a plasma response computation. To quantify the uncertainty of the parametrisation relative to a plasma response computation, is also computed using MARS-F for a set of benchmarking points. Each benchmarking point consists of a distinct free boundary equilibrium reconstructed from an ASDEX Upgrade RMP experiment, and set of experimental kinetic profiles and coil currents. Comparing the MARS-F predictions of for these benchmarking points to predictions of the 2D quadratic, shows that relative to a plasma response computation with MARS-F the 2D quadratic is accurate to 26.5° for n = 1, and 20.6° for n = 2. Potential sources for uncertainty are assessed.

Plasma response based RMP coil geometry optimization for an ITER plasma

Based on an ITER 15MA Q = 10 inductive scenario, a systematic numerical investigation is carried out in order to understand the effect of varying the geometry of the magnetic coils, used for controlling the edge localized modes in tokamaks, on the plasma response to the resonant magnetic perturbation (RMP) fields produced by these coils. Toroidal computations show that both of the plasma response based figures of merit—one is the pitch resonant radial field component near the plasma edge and the other is the plasma displacement near the X-point of the separatrix—consistently yield the same prediction for the optimal coil geometry. With a couple of exceptions, the presently designed poloidal location of the ITER upper and lower rows of RMP coils is close to the optimum, according to the plasma response based criteria. This holds for different coil current configurations with n = 2, 3, 4, as well as different coil phasing between the upper and lower rows. The coils poloidal width from the present design, on the other hand, is sub-optimal for the upper and lower rows. Modelling also finds that the plasma response amplitude sharply decreases by moving the middle row RMP coils of ITER from the designed radial location (just inside the inner vacuum vessel) outwards (outside the outer vacuum vessel). The decay rate is sensitively affected by the middle row coils’ poloidal coverage for low-n (n = 1, 2) RMP fields, but not for high-n (n = 4) fields.

Non-axisymmetric ideal equilibrium and stability of ITER plasmas with rotating RMPs

The magnetic perturbations produced by the resonant magnetic perturbation (RMP) coils will be rotated in ITER so that the spiral patterns due to strike point splitting which are locked to the RMP also rotate. This is to ensure even power deposition on the divertor plates. VMEC equilibria are calculated for different phases of the RMP rotation. It is demonstrated that the off harmonics rotate in the opposite direction to the main harmonic. This is an important topic for future research to control and optimize ITER appropriately. High confinement mode (H-mode) is favourable for the economics of a potential fusion power plant and its use is planned in ITER. However, the high pressure gradient at the edge of the plasma can trigger periodic eruptions called edge localized modes (ELMs). ELMs have the potential to shorten the life of the divertor in ITER (Loarte et al 2003 Plasma Phys. Control. Fusion 45 1549) and so methods for mitigating or suppressing ELMs in ITER will be important. Non-axisymmetric RMP coils will be installed in ITER for ELM control. Sampling theory is used to show that there will be significant a harmonic sideband. There are nine coils toroidally in ITER so . This results in a significant n = 6 component to the applied field and a significant n = 5 component to the applied field. Although the vacuum field has similar amplitudes of these harmonics the plasma response to the various harmonics dictates the final equilibrium. Magnetic perturbations with toroidal mode number n = 3 and n = 4 are applied to a 15 MA, burning ITER plasma. We use a three-dimensional ideal magnetohydrodynamic model (VMEC) to calculate ITER equilibria with applied RMPs and to determine growth rates of infinite n ballooning modes (COBRA). The case shows little change in ballooning mode growth rate as the RMP is rotated, however there is a change with rotation for the case.

Observation of spectrum effect on the measurement of intrinsic error field on EAST

Intrinsic error field on EAST is measured using the ‘compass scan’ technique with different n = 1 magnetic perturbation coil configurations in ohmically heated discharges. The intrinsic error field measured using a non-resonant dominated spectrum with even connection of the upper and lower resonant magnetic perturbation coils is of the order and the toroidal phase of intrinsic error field is around . A clear difference between the results using the two coil configurations, resonant and non-resonant dominated spectra, is observed. The ‘resonant’ and ‘non-resonant’ terminology is based on vacuum modeling. The penetration thresholds of the non-resonant dominated cases are much smaller than that of the resonant cases. The difference of penetration thresholds between the resonant and non-resonant cases is reduced by plasma response modeling using the MARS-F code.

Three-dimensional modeling of plasma edge transport and divertor fluxes during application of resonant magnetic perturbations on ITER

Results from three-dimensional modeling of plasma edge transport and plasma–wall interactions during application of resonant magnetic perturbation (RMP) fields for control of edge-localized modes in the ITER standard 15 MA Q = 10 H-mode are presented. The full 3D plasma fluid and kinetic neutral transport code EMC3-EIRENE is used for the modeling. Four characteristic perturbed magnetic topologies are considered and discussed with reference to the axisymmetric case without RMP fields. Two perturbation field amplitudes at full and half of the ITER ELM control coil current capability using the vacuum approximation are compared to a case including a strongly screening plasma response. In addition, a vacuum field case at high q95 = 4.2 featuring increased magnetic shear has been modeled.Formation of a three-dimensional plasma boundary is seen for all four perturbed magnetic topologies. The resonant field amplitudes and the effective radial magnetic field at the separatrix define the shape and extension of the 3D plasma boundary. Opening of the magnetic field lines from inside the separatrix establishes scrape-off layer-like channels of direct parallel particle and heat flux towards the divertor yielding a reduction of the main plasma thermal and particle confinement. This impact on confinement is most accentuated at full RMP current and is strongly reduced when screened RMP fields are considered, as well as for the reduced coil current cases.The divertor fluxes are redirected into a three-dimensional pattern of helical magnetic footprints on the divertor target tiles. At maximum perturbation strength, these fingers stretch out as far as 60 cm across the divertor targets, yielding heat flux spreading and the reduction of peak heat fluxes by 30%. However, at the same time substantial and highly localized heat fluxes reach divertor areas well outside of the axisymmetric heat flux decay profile. Reduced RMP amplitudes due to screening or reduced RMP coil current yield a reduction of the width of the divertor flux spreading to about 20–25 cm and cause increased peak heat fluxes back to values similar to those in the axisymmetric case. The dependencies of these features on the divertor recycling regime and the perpendicular transport assumptions, as well as toroidal averaged effects mimicking rotation of the RMP field, are discussed in the paper.

The Harmonic Analysis of RMP Coil Power Supply in EAST TOKAMAK

In EAST TOKAMAK, resonant magnetic perturbation (RMP) coils, which are powered by RMP coil power supply (PS), are set to research edge localized mode, resistive wall mode and error field correction. In order to meet the requirements of fast response and output voltage ripple proposed by physical experimenters, the structure of multiple modules using cascaded carrier phase-shifted PWM H-bridges is adopted, which enhances the equal switch-frequency of the PS and improves the quality of output voltage. In the paper, theoretical calculation applying Fourier analysis is given to analyze its harmonics. Both simulation results on Matlab and test results of output voltage ripple show that the RMP coil PS can meet the requirements.

Conceptual Design and Engineering Analysis for CFETR Upper RMP Coils

Different means of active control of MHD instabilities have been developed in lots of experimental research of tokomak. Resonant magnetic perturbation (RMP) is one of basic tools which has been widely used in control of edge localized modes, resistive wall mode and error field correction and it may well be applied in China Fusion Engineering Test Reactor (CFETR). A set of RMP coils has been conceptual physical designed for CFETR, which refers to the design experience of EAST and ITER, yet the structural strength needs to be assessed. Hence, finite element method was introduced, taking the issues above into careful consideration. Electro-magnetic, hydraulic-thermal and mechanical analysis were conducted to check whether the critical components meet the mechanical requirements.

Overview of the recent research on the J-TEXT tokamak

The experimental research over last two years on the J-TEXT tokamak is summarized and presented in the paper. The high-performance polarimeter-interferometer developed on J-TEXT, aiming to measure electron density and Faraday angle simultaneously, has time response up to 1 µs, phase resolution <0.1° and spatial resolution ∼3 cm. Such high resolution permits investigations of fast equilibrium dynamics as well as magnetic and density perturbations associated with magnetohydrodynamic instabilities. Particle transport due to the sawtooth crashes is analysed. The sawteeth only partially flatten the core density profile and recovery between crashes implies an inward pinch velocity extending to the centre. The resonant magnetic perturbation (RMP) system on J-TEXT can generate a rotating helical field perturbation with a maximum rotation frequency up to 6 kHz, and dominant resonant modes of m/n = 2/1, 3/1 or 1/1. It is found that tearing modes can be easily locked and then rotate together with a rotating RMP. The effects of RMPs on plasma flows and fluctuations are studied with Langmuir probe arrays at the plasma edge. The toroidal velocity increases and the radial electric field decreases with RMP coil current when the RMP current is no more than 5 kA. When the RMP current reaches 6 kA, the toroidal velocity profile becomes flattened near the last closed flux surface. The geodesic acoustic mode is damped in most of the edge region, while the low frequency zonal flow is damped inside the islands, but increases at its boundary.

Combination of helical ferritic-steel inserts and flux-tube-expansion divertor for the heat control in tokamak DEMO reactor

Edge localized modes (ELMs) in the H-mode operation of tokamak reactors may be suppressed/mitigated by the resonant magnetic perturbation (RMP), but RMP coils are considered incompatible with DEMO reactors under the strong neutron flux. We propose an innovative concept of the RMP without installing coils but inserting ferritic steels of the helical configuration. Helically perturbed field is naturally formed in the axisymmetric toroidal field through the helical ferritic steel inserts (FSIs). When ELMs are avoided, large stationary heat load on divertor plates can be reduced by adopting a flux-tube-expansion (FTE) divertor like an X divertor. Separatrix shape and divertor-plate inclination are similar to those of a simple long-leg divertor configuration. Combination of the helical FSIs and the FTE divertor is a suitable method for the heat control to avoid transient ELM heat pulse and to reduce stationary divertor heat load in a tokamak DEMO reactor.

Impact of RMP magnetic field simulation models on fast ion losses

Two opposing approaches to include resonant magnetic perturbations (RMPs) in fast ion simulations are compared, one where the vacuum field caused by the RMP current coils is added to the axisymmetric MHD equilibrium, the other where the MHD equilibrium includes the plasma response within the 3D deformation of its flux-surfaces. The first model admits large regions of stochastic field-lines that penetrate the plasma without alteration. The second assumes nested flux-surfaces with a single magnetic axis, which excludes stochastic field-lines, and embeds the RMPs within a 3D saturated ideal MHD state. The two descriptions of RMPs have been implemented in the VENUS-LEVIS guiding-centre orbit code. Simulations of fast ion populations resulting from MAST neutral beam injection have been applied to MAST n = 3 RMP coil configuration. At low beam energies, particle losses are dominated by parallel transport due to the stochasticity of the field-lines (vacuum-RMP model), whereas at higher energies, losses are accredited to the 3D structure of the perturbed plasma and the resulting drifts (equilibrium-RMP model).

Design of Connecting Cable for RMP Power Supply in EAST TOKAMAK

In EAST TOKAMAK, resonant magnetic perturbation (RMP) coils are set to research edge localized mode, resistive wall mode and error field correction. The connecting cable is used to connect the power supply and RMP coils. This paper has theoretical calculation and simulation results for different kinds of cables. According to the design requirements of thermal stability and mechanical stability, the water cooling copper coaxial-cable is chosen. The temperature rise test proves that the design scheme is feasible and reasonable.

ELM mitigation via rotating resonant magnetic perturbations on MAST

The application of resonant magnetic perturbations (RMPs) produces splitting of the divertor strike point due to the interaction of the RMP field and the plasma field. The application of a rotating RMP field causes the strike point splitting to rotate, distributing the particle and heat flux evenly over the divertor. The RMP coils in MAST have been used to generate a rotating perturbation with a toroidal mode number n=3. The ELM frequency is doubled with the application of the RMP rotating field, whilst maintaining the H mode. During mitigation, the ELM peak heat flux is seen to be reduced by 50% for a halving in the ELM energy and motion of the strike point, consistent with the rotation of the applied RMP field, is seen using high spatial resolution (1.5mm at the target) heat flux profiles measured using infrared (IR) thermography.

Modelling of three dimensional equilibrium and stability of MAST plasmas with magnetic perturbations using VMEC and COBRA

It is known that magnetic perturbations can mitigate edge localized modes (ELMs) in experiments, for example, MAST [Kirk et al., Nucl. Fusion 53, 043007 (2013)]. One hypothesis is that the magnetic perturbations cause a three dimensional corrugation of the plasma and this corrugated plasma has different stability properties to peeling-ballooning modes compared to an axisymmetric plasma. It has been shown in an up-down symmetric plasma that magnetic perturbations in tokamaks will break the usual axisymmetry of the plasma causing three dimensional displacements [Chapman et al., Plasma Phys. Controlled Fusion 54, 105013 (2012)]. We produce a free boundary three-dimensional equilibrium of a lower single null MAST relevant plasma using VMEC [S. P. Hirshman and J. C. Whitson, Phys. Fluids 26, 3553 (1983)]. The safety factor and pressure profiles used for the modelling are similar to those deduced from axisymmetric analysis of experimental data with ELMs. We focus on the effect of applying n = 3 and n = 6 magnetic perturbations using the resonant magnetic perturbation (RMP) coils. A midplane displacement of over ±1 cm is seen when the full current is applied. The current in the coils is scanned and a linear relationship between coil current and midplane displacement is found. The pressure gradient in real space in different toroidal locations is shown to change when RMPs are applied. This effect should be taken into account when diagnosing plasmas with RMPs applied. The helical Pfirsch-Schlüter currents which arise as a result of the assumption of nested flux surfaces are estimated for this equilibrium. The effect of this non-axisymmetric equilibrium on infinite n ballooning stability is investigated using COBRA [Sanchez et al., J. Comput. Phys. 161, 576–588 (2000)]. The infinite n ballooning stability is analysed for two reasons; it may give an indication of the effect of non-axisymmetry on finite n peeling-ballooning modes, responsible for ELMs; and infinite n ballooning modes are correlated to kinetic ballooning modes which are thought to limit the pressure gradient of the pedestal [Snyder et al., Phys. Plasmas 16, 056118 (2009)]. The ballooning mode growth rate gains a variation in toroidal angle. The equilibria with midplane displacements due to RMP coils have a higher ballooning mode growth rate than the axisymmetric case and the possible implications are discussed.