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The radio frequency current condensation effect reported in Reiman and Fisch (2018 Phys. Rev. Lett. 121 225001) is modeled in the nonlinear resistive magnetohydrodynamic code. A series of numerical investigations have been performed to investigate the enhancement of electron cyclotron current drive (ECCD) by the current condensation effect during the control of neoclassical tearing mode (NTM) in tokamak plasmas. In the numerical model, both the parallel transport and the perpendicular transport of electron temperature are considered. The EC driven current and driven perturbed electron temperature can nonlinearly evolve within the given magnetic configuration and eventually reach saturation states. The input power threshold of ECCD and the fold bifurcation phenomenon are numerically verified via nonlinear simulations. The numerical results show good agreements with the analytical results. Moreover, spatial distributions of EC current for the two solutions at different condensed level are displayed. The control effectiveness of ECCD for large NTM islands has been evaluated while considering the current condensation effect. While taking into account current condensation effect, for a sufficiently large input power, a larger island can be more effectively stabilized than a smaller one, which suggests a reassessment of the previous idea that the ECCD should always be turned on as early as possible. The potential physics mechanism behind the ECCD control have all been discussed in detail. Furthermore, the condensation effect is found to have favorable effects on the radial misalignment of ECCD. In the consideration of the situation for extremely localized control needs, a highly peaked heating profile is adopted to verify that the fold bifurcation phenomenon still exists and the current condensation effect can still take effect in this extreme condition. [ABSTRACT FROM AUTHOR]

Electron cyclotron emission (ECE) diagnostics for ITER serve two key purposes. The diagnostics will measure plasma electron temperature with high spatial and temporal resolution. Additionally, they will be used to detect neoclassical tearing modes (NTMs), a deleterious and nonlinearly unstable mode causing the growth of magnetic ‘seed’ islands. Interpreting ECE requires anticipation of physical limits including frequency cut-offs and harmonic overlap. In high temperature plasmas, the relativistic shift and broadening of the emission must also be considered to accurately reconstruct the electron temperature spatial profile. Accounting for these effects allows ECE diagnostics to be used for accurate measurement of the equilibrium electron temperature profile, as well as fluctuations about this equilibrium. One such fluctuation is caused by the fast radial transport of heat across rotating magnetic islands. ECE diagnostics can detect this change as an oscillation at the plasma rotation frequency to determine the existence and location of NTMs. This paper presents work on a synthetic diagnostic for ECE. The synthetic diagnostic tests simulated ECE signals, which are inferred from ITER scenarios perturbed by magnetic islands after accounting for all ECE physics. The synthetic diagnostic tests conventional ECE detection algorithms for NTMs in real-time on ITER-recommended hardware. Combined, these two areas of focus help determine design of the ECE system.

The radio frequency current condensation effect reported in Reiman and Fisch (2018 Phys. Rev. Lett. 121 225001) is modeled in the nonlinear resistive magnetohydrodynamic code. A series of numerical investigations have been performed to investigate the enhancement of electron cyclotron current drive (ECCD) by the current condensation effect during the control of neoclassical tearing mode (NTM) in tokamak plasmas. In the numerical model, both the parallel transport and the perpendicular transport of electron temperature are considered. The EC driven current and driven perturbed electron temperature can nonlinearly evolve within the given magnetic configuration and eventually reach saturation states. The input power threshold of ECCD and the fold bifurcation phenomenon are numerically verified via nonlinear simulations. The numerical results show good agreements with the analytical results. Moreover, spatial distributions of EC current for the two solutions at different condensed level are displayed. The control effectiveness of ECCD for large NTM islands has been evaluated while considering the current condensation effect. While taking into account current condensation effect, for a sufficiently large input power, a larger island can be more effectively stabilized than a smaller one, which suggests a reassessment of the previous idea that the ECCD should always be turned on as early as possible. The potential physics mechanism behind the ECCD control have all been discussed in detail. Furthermore, the condensation effect is found to have favorable effects on the radial misalignment of ECCD. In the consideration of the situation for extremely localized control needs, a highly peaked heating profile is adopted to verify that the fold bifurcation phenomenon still exists and the current condensation effect can still take effect in this extreme condition.

A nonlinear 4-dimensional drift island theory derived in (Imada et al 2019 Nucl. Fusion 59 046016 and references therein) provides qualitative predictions of the plasma response to a stationary neoclassical tearing mode (NTM) magnetic island in a low beta, large aspect ratio tokamak plasma. (Dudkovskaia et al 2021 Plasma Phys. Control. Fusion 63 054001) refines a model for the magnetic drift frequency and exploits the limit of rare collisions, reducing this theory to 3-dimensional and thus providing a more accurate treatment of the trapped-passing boundary layer. The drift island theory is further improved in (Dudkovskaia et al 2023 Nucl. Fusion 63 016020) by introducing plasma shaping and finite beta effects. In the present paper, an improved model is adopted to resolve the drift island separatrix boundary layer, allowing one to investigate the polarisation current contribution that exists around the magnetic island separatrix, including in the presence of the background electric field. In particular, different magnetic topologies from both sides of the separatrix generate a radial discontinuity in the distribution function gradient there, when collisions are neglected. Allowing for collisional dissipation in the leading order distribution function around the separatrix resolves this discontinuity, smoothing the density distribution. The overall effect of the polarisation current on the NTM threshold is then combined from the outer contributions that exist outside the layer, as well as the separatrix layer piece, and self-consistently accounts for the electrostatic potential reconstructed from plasma quasi-neutrality. The corresponding NTM threshold is quantified and compared with previous predictions of (Dudkovskaia et al 2021 Plasma Phys. Control. Fusion 63 054001, Dudkovskaia et al 2023 Nucl. Fusion 63 016020).

In (Imada et al 2019 Nucl. Fusion 59 046016 and references therein) a new 4D drift kinetic nonlinear theory, valid in the limit of a low beta, small inverse aspect ratio, circular cross section, toroidal geometry, to describe the plasma response to the neoclassical tearing mode (NTM) magnetic perturbation is derived. In (Dudkovskaia et al 2021 Plasma Phys. Control. Fusion 63 054001) this theory is reduced in a low collisionality limit, which allows a dimensionality reduction to a 3D problem to efficiently resolve the collisional dissipation layer in the vicinity of the trapped-passing boundary. (Dudkovskaia et al 2021 Plasma Phys. Control. Fusion 63 054001) adopts an improved model for the magnetic drift frequency, which reduces the threshold magnetic island half-width from $8.73\rho_{b i}$ , where $\rho_{b i}$ is the trapped ion banana orbit width, to $1.46 \rho_{b i}$ , making it in closer agreement with experimental observations for the large aspect ratio tokamak equilibrium. In the present paper, the theory is extended to a high beta, arbitrary tokamak geometry to capture the plasma shaping effects on the NTM threshold physics with the focus on the non-zero triangularity discharges that are known to have a strong impact on the plasma MHD stability. First, it is found that the higher triangularity plasma is more prone to NTMs which is in agreement with the $2/1$ tearing mode onset relative frequency measurements in DIII-D. Second, the NTM threshold dependence on the tokamak inverse aspect ratio obtained in (Dudkovskaia et al 2021 Plasma Phys. Control. Fusion 63 054001) is refined and extended to a finite aspect ratio limit. Third, the NTM threshold dependence on poloidal beta is obtained and benchmarked against the EAST threshold island width measurements.

We present localized measurements of interactions between neoclassical tearing modes (NTMs) and turbulent electron temperature fluctuations (T~e) in the expected kθρs=0-0.5 wave-number range of the ion temperature gradient (ITG) instability measured via correlation electron cyclotron emission (kθ and ρs are the poloidal wave-number and ion-sound Larmor radius, respectively). Comparison to GENE gyrokinetic simulations, shows qualitative agreement with Te being reduced (increased) inside (outside) of the islands due to modified local gradients, and Te being higher (lower) in the region outside the island where lower (higher) flow shear is expected due to radially asymmetric island shape. These results are consistent with previously reported modifications of long and intermediate wavelength turbulent density fluctuations and cross-field electron thermal diffusivity reduction at the O-point of magnetic islands. Interestingly, a 30% increase of Te is detected at the NTM rational surface when the island width is a few times ρs, which is replicated by GENE through zonal flow damping due to the destroyed magnetic field topology of the NTM rational surface. [ABSTRACT FROM AUTHOR]

• Real-time tracking of NTMs position using ECE in the quasi-in-line configuration. • Experimental proof of principle of NTMs detection and tracking. • A closed loop control scheme for NTM instabilities control with ECCD. An important goal of the control system in a tokamak is the suppression of magneto-hydrodynamic (MHD) instabilities with low m, n (poloidal and toroidal mode numbers), which can influence the confinement time of energy and particles and possibly lead to plasma disruption. These instabilities, which appear as rotating magnetic islands, can be reduced or completely suppressed by a current driven by electron cyclotron waves (ECW) accurately located within the island. A fundamental requisite for this control technique is the ability to identify the island parameters (amplitude and radial position) and to vary accordingly the ECW deposition location. Here we describe a control scheme of the steering mirror of the ECW source based on the real-time tracking of the island radial position realized using only the electron cyclotron emission (ECE) diagnostics in quasi-in-line configuration, i.e. with toroidal anti-parallel propagation of the ECW and ECE beams. The successful experimental proof of principle of this scheme, tested on the TCV tokamak, is here reported. [ABSTRACT FROM AUTHOR]

BackgroundTokamak is a possible implementation of controlled nuclear fusion whilst the particle transportation plays an important role in maintaining the progress of nuclear fusion reactions.PurposeThis study aims to investigate the effects of ripple field and neoclassical tearing mode (NTM) on the migration of deuterium ions in Tokamak by numerical simulation. and provide a reference for the confinement of high energy particles.MethodsThe guiding center orbit code ORBIT was employed for numerical simulation. Effects of NTM and ripple field on particles with different positions, pitch angles and energies, were studied in details.Results & ConclusionsSimulation results show that the particle loss rate is high under the condition of high magnetic surface and low pitch angle. NTM mainly causes the loss of passing particles, while the loss of trapped particles is mainly caused by ripple field. When both perturbations are considered, the loss of particles is approximately the sum of losses by two perturbations acting alone. Ripple field will significantly increase toroidal angular momentum diffusion of trapped particles without affecting the passing particles, whilst NTM mainly influences toroidal angular momentum diffusion of passing particles. The particle loss situation basically keeps the original characteristics regardless of NTM frequency varition, while the momentum diffusion condition of particle loss changes with the increase of NTM frequency.

Tokamak plasmas with high fusion performances are prone to magnetohydrodynamic (MHD) low m,n instabilities which may affect the energy and particle confinement time and possibly lead to disruptive plasma termination. In presently operating tokamaks high space resolution (∼2 cm) and high time resolution (0.01–0.1 ms) electron cyclotron emission (ECE) diagnostics are embedded in the control loop finalized to MHD control, often in synergy with pick-up coils sensitive to the magnetic fluctuations. Microwave diagnostics have plasma facing components (antennas) that are electrically passive, have metal body and are mechanically fixed. Such characteristics of robustness and reliability are a promising feature but the diagnostic performances in term of achievable space resolution and profile coverage for prompt detection of instabilities in the high temperature and density conditions of the DEMO reactor need to be assessed. The results of such assessment based on the EU-DEMO1-2015 scenario show that extraordinary mode ECE in 2nd harmonics seems to have enough space resolution in the region interested by 3/2 and 2/1 NTMs. [ABSTRACT FROM AUTHOR]

The symplectic Hamiltonian guiding centre code which enables efficient calculation of charged particle trajectories and diffusion coefficients has been applied to fast ion motion in magnetically perturbed tokamak plasmas. Particularly fusion born alpha particle drift motion, in constant of motion space, is examined in the presence of low mode-number neoclassical tearing mode (NTM) perturbation in a toroidally rippled tokamak. The main focus of this study is to investigate the dependence of the radial diffusion coefficient of energetic ions on the perturbation strength and on the localization of the perturbation. The resonance between bounce motion and toroidal field ripples plays a significant role in this context. The presence of NTMs results in substantial enhancement of radial diffusion coefficient for passing particles. Depending on the strength and localization of the NTM it can cause enhancement or degradation of the radial ripple diffusion coefficient of trapped particles. [ABSTRACT FROM AUTHOR]

An integrated numerical system is established to model time-dependent behavior of the neoclassical tearing mode (NTM) in a tokamak which solves the modified Rutherford equation (MRE) by coupling with plasma transport, equilibrium, heating and current drive. The MRE is formulated in a simple form to be well-suited for time-dependent simulations including a predictive purpose for the feedback controller design by coupling the electron cyclotron effect self-consistently. In particular the electron cyclotron heating (ECH) effect is newly included to the MRE in addition to the electron cyclotron current drive (ECCD) effect to investigate their impact to stabilize the NTM. The integrated numerical system is applied to experiments for benchmarking in which NTMs are stabilized by ECCD and by ECH at ASDEX Upgrade and TCV, respectively. The impact of ECCD and ECH on stabilizing NTMs is identified in the simulations. [ABSTRACT FROM AUTHOR]

The tearing mode (TM) plasma instability was observed in low confinement (L-mode) plasmas when non-axisymmetric magnetic perturbation (MP) was applied using external coils during 2011 campaign of KSTAR. Based on the collected information of the magnetic island location in a plasma, a discharge was designed for suppression of a (2,1) TM mode by adjusting electron cyclotron (EC) launcher angles to the estimated island position. Here, the (m,n) notation describes the poloidal mode number and the toroidal mode number of the TM, respectively. The discharge is analysed with experimental observations and numerical simulations. Mirnov coil (MC) arrays and electron cyclotron emission (ECE) are used for analysis of the island width and the location as well as the mode number. The EC deposition and its alignment with the island are estimated by X-ray imaging crystal spectroscopy (XICS) and ECE measurements. An integrated numerical system is employed for modelling of this discharge to analyse a temporal evolution of the mode activity by integrating plasma equilibrium, transport, heating and current drive, and the magnetic island evolution, in a self-consistent way. The effect of EC current drive is discussed by comparing with another TM discharge but without ECCD. Some possibilities for classifying this mode to neoclassical tearing mode (NTM) and stabilisation effect of ECCD are suggested based on the experimental observation and the simulation results. [ABSTRACT FROM AUTHOR]

Highlights: [•] Two algorithms have been developed which use the NTM amplitude to control ECCD deposition and stabilise NTMs. [•] Both algorithms were tested and tuned in a simulation of the full feedback loop including an MRE. [•] Both algorithms have been successfully deployed in ASDEX Upgrade experiments. [•] Use of the NTM amplitude adds considerable robustness, which is necessary when trying to target ECCD to within 1cm of the island location. [•] This is part of ongoing work to reliably and quickly stabilise NTMs in any plasma scenario. [ABSTRACT FROM AUTHOR]

Highlights: [•] Calculation of real-time tokamak magnetic equilibrium with constraints from magnetic probes. [•] Parallel equilibrium calculation including the Motional Stark Effect diagnostic as additional constraints. [•] Feedback control of mirror for pre-emptive ECCD stabilization of neo-classical tearing modes. [•] Probe calibration by individual poloidal field coil currents. [•] Optimized parameters for poloidal field coil location, integrator gains and the location and orientation of magnetic probes. [ABSTRACT FROM AUTHOR]

Abstract: Neoclassical Tearing Modes (NTMs) are a class of MHD instability in high beta tokamak plasmas which significantly increase radial transport, thus capping the performance of fusion plasmas. More importantly, NTMs can lead to disruptions which compromise the lifetime of structural components. Several tokamaks have demonstrated that Electron Cyclotron Resonant Heating (ECRH) can stabilise NTMs if the power deposition is aligned with the mode location. The deposition location depends on the toroidal magnetic field, flux and density profiles, and can be controlled by tilting the mirror in the ECRH launcher. Until recently, the mirror angle was set by feedforward control at ASDEX Upgrade. In order to adapt automatically to different discharge scenarios, the system at ASDEX Upgrade has been extended to steer the mirror using feedback control. The mirror must react on the current diffusion time scale, on the order of 100ms. This is within the capabilities of the mechanical subsystem and real-time plasma diagnostics, but requires careful interfacing between these components. For example, asynchronous data transfer and non-linearities make it difficult to design an analytically optimal controller. Therefore a simulation has been used to test and tune different controller architectures. This simulation is the subject of the current contribution. Performing the optimisation process offline saves valuable experiment time and allows risk-free experimentation with novel designs. Settings which were optimised in the simulation led to considerable improvement of the system performance. [Copyright &y& Elsevier]

A Hamiltonian guiding centre drift orbit code based on a symplectic integration algorithm, which enables the efficient calculation of particle trajectories and diffusion coefficients, is applied to fast alpha particle motion in magnetically perturbed tokamak plasmas. In particular, fast ion drift motion is examined in the presence of a stationary, low mode-number MHD magnetic perturbation in a toroidally rippled tokamak with circular flux surface. The main focus of our study is to investigate the dependence of the radial diffusion coefficient of energetic ions on their energy, on the perturbation strength and the localization of the perturbation. As expected, the resonance between bounce motion and toroidal field ripples plays a significant role in this context. For an ensemble of fast ions uniformly distributed in toroidal angle but with a given poloidal starting position their radial transport coefficient takes on higher values in the neighbourhood of resonance speeds and can exhibit there local minima, i.e. it shows an M-shaped speed dependence around resonances for sufficiently strong ripple perturbations. Expectedly, the addition of a modelled low-mode number neoclassical tearing mode perturbation will modify the pure ripple resonance structure of the radial diffusion coefficient. Depending on the strength and localization of the MHD mode it can cause enhancement or degradation of the radial ripple diffusion coefficient. [ABSTRACT FROM AUTHOR]

An Electron Cyclotron Wave (ECW) system will be used in the European DEMO for the stabilization of Neoclassical Tearing Modes (NTMs). In order to avoid movable mirrors in the harsh environment close to the plasma and to simplify the NTM launcher integration, the tuning of the ECW deposition location can be achieved by launching frequency-tunable ECWs from fixed mirrors while the frequency is tuned in discrete steps of 2–3GHz. An overview of the frequency step-tunable ECW system for NTM stabilization is presented. The design considerations are discussed based on the current DEMO baseline parameters and the status of technologies. A simulation of NTM stabilization with an idealized frequency tunable ECW system on an analytical NTM model is shown. The simulation takes into account a realistic tuning speed based on the present technology and considers the current NTM launcher configurations in DEMO. A simple sweeping strategy is adapted for the control of frequency. Various uncertainties, which will affect the feasibility, need to be further investigated. [ABSTRACT FROM AUTHOR]

A model of neoclassical tearing mode (NTM) induced by resonant magnetic perturbation (RMP) in the presence of the bootstrap current in tokamak plasmas is established based on the full magnetohydrodynamic equations. The model is solved numerically by using a finite difference method and the numerical results are obtained. It is found that, the NTM can be induced by the given stable equilibrium, added the perturbed bootstrap current in ohm equation, and the applied RMP. Moreover, with the increasing amplitude of the static RMP, locked mode occurs, which is determined by the plasma flow and fraction of bootstrap current. The mode locking threshold increases with the increasing of plasma rotation frequency and decreasing of fraction of bootstrap current. Furthermore, the dynamic RMP is investigated, results show that the mode locking threshold is lower compared to the static RMP applied, which provides a better way of adjusting the NTM to the frequency of dynamic RMP and slightly suppressing the neoclassical magnetic island. • A new MHD code, named NTM2D, is used to numerically simulate the NTMs induced by RMPs in tokamak plasmas. • The mode locking threshold is further investigated with the RMP applied in the whole charge period. • It is found that the mode locking threshold with the dynamic RMP is lower than the threshold with the static RMP. [ABSTRACT FROM AUTHOR]