Non-axisymmetric Magnetic Perturbations Research Articles

Investigation of intrinsic error fields in MAST-U device

In magnetic fusion devices, undesired non-axisymmetric magnetic field perturbations, typically called error fields (EF), have been observed to have a detrimental effect on plasma stability and confinement and can lead to brute plasma terminations, i.e. plasma disruption events. The main strategies that can be adopted to minimize the effect of EFs on the plasma dynamics consist in a careful alignment of the coils, when assembling the fusion device, and, most commonly, in the use of EF correction coils which counteract the non-axisymmetric fields by prescribing properly designed correction currents. In this work, an assessment of the n=1 EF source in MAST-U is presented. When constructing the MAST-U device, an optimization of poloidal and divertor coil positions has been adopted to reduce the n=1 EF source. This optimization consisted in the application of coil shifts and tilts, of the order of mms and mrads, respectively. To investigate the presence of a residual n=1 EF dedicated studies have been performed during the first MAST-U campaign. The compass scan method was employed to identify the n=1 EF, relying on the detection of the locked mode (LM) onset, which proved to be a challenging task. Therefore, a methodology based on Transfer Functions (TFs) among each coil and the n=1 radial magnetic field has been developed which allows the detection of LM formation. Such method is described here, complemented with the experimental results achieved, which suggest that the intrinsic n=1 EF source on MAST-U is relatively small with respect to MAST. Indeed, the empirical correction currents for n=1 EF minimization are smaller, about 0.2 kA, than the ones used in MAST, 1 kA range. This proves that the optimal coil alignment for n=1 EF minimization has been a successful strategy in MAST-U.

Acceleration of plasma toroidal rotation driven by non-axisymmetric magnetic perturbation fields in the EAST tokamak

Plasma toroidal rotation acceleration in the co-current direction introduced by the n = 1 (toroidal mode number) static resonant magnetic perturbation (RMP) has been observed in the EAST tokamak. It strongly depends on the RMP coil configuration, which is manifested by its dependence on δϕUL (phase difference between upper and lower coils) and RMP current. Modeling results from NTVTOK based on the linear plasma response modeled by MARS-F shows that the Neoclassical Toroidal Viscosity (NTV) torque is in the co-current direction because of the dominant contribution from electrons with the condition that the electron normalized collisionality is much lower than that of ions in this experiment. The modeled dependence of core integrated NTV torque modulated by the magnitude of core magnetic perturbation on δϕUL is consistent with the experimental observations. Threshold condition related to normalized collisionality to achieve the transition from rotation braking to acceleration is obtained in the NTV modeling and agrees well with experimental observations. It is shown in the modeling that the discharges with rotation acceleration are located at the regime that electron contribution to NTV is dominant and the torque is in co-current direction, while others with rotation braking are located at the regime that ion contribution to NTV torque is dominant and the torque is in countercurrent direction. Though the modeling results are in qualitative agreement with the experimental results, there is quantity difference between the modeled NTV torque based on linear plasma response and the experimental values. Possible reason is that the 3D fields are underestimated by linear modeling, particularly in the case of RMP field penetration, as demonstrated by the RMP current threshold for the rotation acceleration observed in the experiments.

Effects of electron viscosity on resonant layer responses to non-axisymmetric magnetic perturbations

The resonant field penetration to magnetic islands is the central MHD mechanism of non-axisymmetric plasma responses in a tokamak such as disruptive locking or favorable ELM stabilization. The resonant field penetration can be induced by any non-ideal processes as manifested in the delicate balance under the generalized Ohm's law. Here, we show that the viscous effects by electrons are not ignorable in the field penetration unlike previous presumption, even if the electron viscosity is as small as the square root of its mass compared to the ions. It is clear that its effects become only bigger if the electron viscosity becomes anomalously large. The work strictly follows the three-field model in the linear regime targeting the prediction of the onset of the field penetration and successfully extending it with electron viscosity and identifying new regimes. The results also indicate that the error field thresholds become more strongly dependent on plasma density than ones predicted in the linear regimes without the electron viscosity, which is consistent with experimental observations and thus a significant implication.

Helical mode localization and mode locking of ideal MHD instabilities in magnetically perturbed tokamak plasmas

In H-mode tokamak plasmas, the achievable pressure-gradient is limited by type-I Edge Localized Modes (ELMs), which are projected to cause severe damage to future fusion devices. There are several approaches aiming to mitigate/suppress the occurrence of ELMs, such as the application of an external non-axisymmetric magnetic perturbation field, which breaks the axisymmetry of the tokamak plasma. In this work we use the CASTOR3D code to investigate helical localization and mode locking of edge-localized ideal MHD instabilities in rotating and flow-free magnetically perturbed tokamak plasmas with periodicity. Helically localized instabilities are separated into two classes: quasi-locked and strictly locked. In a non-rotating plasma, the localization of quasi-locked modes is determined by an envelope while their precise location under the envelope is arbitrary, whereas strictly locked modes can only occur at a single helical position. Strictly locked modes only rotate if the toroidal plasma rotation exceeds a critical threshold; above the threshold the forced rotation of the strictly locked modes is non-uniform. For quasi-locked modes, no such critical threshold exists; they rotate uniformly beneath their envelope in the case of finite plasma rotation. The helical localization of both quasi-locked and strictly locked instabilities is determined by the energetic decomposition of the instabilities close to the most unstable flux-surface; for example, strongly current-density driven instabilities are aligned with regions of augmented parallel equilibrium current-density. Finally, we compare the computationally determined localization of MHD instabilities to experimental observations. The determined MHD instability is located at the same position as the experimentally measured modes with respect to the equilibrium corrugation, verifying that ideal MHD can describe the experimentally observed instabilities.

Account of non-standard orbits in computations of neoclassical toroidal viscous torque in the resonant plateau regime of a tokamak

This article extends theoretical details based on a short paper originally submitted to the 2022 EPS conference in plasma physics [1]. The quasilinear theory of resonant transport regimes in a tokamak is developed for the general case of orbits forming various classes separated in phase space by homoclinic orbits with infinite bounce time. Beyond standard orbits (banana and passing orbits) also all types of non-standard orbits (e.g. “potato” orbits) are taken into account. In case of a weak radial electric field, such orbits are usually present only near the magnetic axis. If the radial electric field cannot be treated as weak, there can be arbitrary many classes, located elsewhere. The present approach covers all such cases and is demonstrated on a specific example of a radial electric field profile. The resulting quasilinear kinetic equation is applicable to compute neoclassical toroidal viscous (NTV) torque in a tokamak with non-axisymmetric magnetic field perturbations. A fully non-local approach to NTV computation has been realized in the upgraded version of the code NEO-RT. Based on a generalization of magnetic flux surfaces to drift surfaces, the notion of a local thermodynamic equilibrium is extended for our purpose. We obtain an expression for the integral toroidal torque within a chosen flux surface and dicuss means to compute such integrals taking singularities in bounce and precession frequencies into account.

Dependence of the L–H power threshold on the alignment of external non-axisymmetric magnetic perturbations in ASDEX Upgrade

Experiments at ASDEX Upgrade have been conducted to study the impact of the alignment of external magnetic perturbations (MPs) with n = 2 toroidal mode symmetry on the power threshold of the transition from L- to H-mode (PLH). This is interesting for ITER, since its operation will rely on an MP field configuration that securely suppresses edge localized modes (ELMs) while avoiding an increase in the L–H power threshold. PLH can increase up to ≈80% when the external MP field is aligned to maximize the associated plasma response at the edge. This alignment deviates from the equilibrium field pitch and is similar to the one that is required to suppress ELMs by MPs in H-mode. The relative radial magnetic field perturbation δBr/BT has to exceed a critical value, roughly 1.7−2×10−4 (at the q = 5 surface), to cause an increase in PLH. This value is above the one that is required to sustain ELM suppression at ASDEX Upgrade. Combining plasma response calculations with a critical value of δBr/BT captures well the measured dependencies of PLH on the alignment of the applied MP field. The increase in PLH is accompanied by a change in the E×B flow velocity (vE×B) profile. The application of MPs in L-mode flattens and reverses the edge vE×B profile when at least δBr/BT≈1.9×10−4 is applied. This is the same value above which PLH increases. More heating power is needed to roughly achieve the same shear in the vE×B profile at the transition to H-mode as without MPs but with an vE×B profile that is shifted into the ion diamagnetic direction.

Understanding of neoclassical offset rotation based on DIII-D experiments

Neoclassical offset rotation induced by non-axisymmetric magnetic perturbations in tokamaks is investigated using NTVTOK model based on plasma profiles in one DIII-D discharge. The calculated counter-Ip (Ip indicates plasma current) ion root of neoclassical offset rotation is found to be consistent with DIII-D experimental observations. The modeling results predict that this DIII-D plasma regime is close to the marginal condition for the co-Ip electron root to exist. The importance of bounce–drift resonance is highlighted in the calculation, which affects the neoclassical offset rotation, especially the electron root. The ion root usually exists for various parameter regimes, while the electron root is only possible in low collisionality (e.g., high temperature and/or low density) regimes. The magnetic perturbation spectrum is found to influence the existence of electron roots when electrons are closer to resonant superbanana plateau regime than ions. By adjusting the plasma collisionality and tuning the spectrum of magnetic perturbations, it is possible to control the plasma rotation and hence to optimize the plasma confinement.

Quasisymmetric Optimization of Nonaxisymmetry in Tokamaks.

Predictive 3D optimization reveals a novel approach to modify a nonaxisymmetric magnetic perturbation to be entirely harmless for tokamaks, by essentially restoring quasisymmetry in perturbed particle orbits as much as possible. Such a quasisymmetric magnetic perturbation (QSMP) has been designed and successfully tested in the KSTAR and DIII-D tokamaks, demonstrating no performance degradation despite the large overall amplitudes of nonaxisymmetric fields and strong response otherwise expected in the tested plasmas. The results indicate that a quasisymmetric optimization is a robust path of error field correction across the resonant and nonresonant field spectrum in a tokamak, leveraging the prevailing concept of quasisymmetry for general 3D plasma confinement systems such as stellarators. The optimization becomes, in fact, a simple eigenvalue problem to the so-called torque response matrices if a perturbed equilibrium is calculated consistent with nonaxisymmetric neoclassical transport.

Observations of heteroclinic bifurcations in resistive magnetohydrodynamic simulations of the plasma response to resonant magnetic perturbations.

A class of topological magnetic island bifurcations that has not previously been observed in toroidal plasmas is described. Increasing an externally applied three-dimensional magnetic field in resistive magnetohydrodynamic simulations results in the asymmetric elongation of resonant island flux surfaces followed by a sequence of heteroclinic bifurcations. These bifurcations produce new sets of hyperbolic-elliptic fixed points as predicted by the Poincaré-Birkoff fixed point theorem. Field line calculations verify that the new fixed points do not connect to those of the prebifurcated islands as required for heteroclinic bifurcations on a torus with winding numbers composed of common integer factors.

Efficient estimation of drift orbit island width for passing ions in a shaped tokamak plasma with a static magnetic perturbation

Non-axisymmetric magnetic perturbations contribute to the transport of fast ions in tokamaks. While knowledge of the perturbed magnetic topology suffices for characterizing the displacement of thermal particles (few keV), the trajectories of fast particles (0.1–few keV) vary depending on their charge, mass, kinetic energy and velocity pitch. The computational effort needed to follow the drift orbits for a large number of phase space samples (as done in Monte Carlo simulations) is too high for scenario simulators, so it is necessary to develop computationally efficient reduced models. In this paper, we present a method that allows to estimate the locations, widths and overlaps of resonant drift orbit islands in the guiding center phase space of passing fast ions with small computational effort. The new method constitutes a significant improvement over the method presented in our previous work (Shinohara K. et al 2018 Nucl. Fusion 58 082026), both in performance and in accuracy. This is achieved by deriving an expression for the drift orbit island width from the perturbed guiding center velocity in the straight-orbit coordinates of the unperturbed drift surfaces and eliminating the need for computationally expensive Poincaré maps. When applied to resonant magnetic perturbation fields in a KSTAR tokamak plasma, our new estimates for the island widths are shown to agree with Poincaré maps from orbit-following simulations to within 15%. The island positions and the chaotic regions caused by island overlaps also agree well.

Error field correction strategies in preparation to MAST-U operation

Abstract In magnetic fusion devices, unwanted non-axisymmetric magnetic field perturbations, known as error fields (EF), can have detrimental effects on plasma stability and confinement. Such EFs may originate from several sources, such as axi-symmetric coil misalignments, coil feeds, 3D structures in the wall surrounding the plasma, presence of ferromagnetic materials near the plasma surface, blanket materials in future devices. To minimize their impact on plasma performance and on the available operational space, it is important to identify the EF sources and develop EF control strategies. MAST Upgrade (MAST-U) is a spherical tokamak which will operate in the near future after a series of enhancements from the previous MAST experiment (Morris A.W. et al., MAST accomplishments and upgrade for fusion next-steps. IEEE Transactions on Plasma Science, April 2014). To deliver a machine with EF amplitude low enough to allow a high quality experimental programme, systematic analysis of the intrinsic EF sources has been carried out for poloidal field (P) and divertor (D) coils. To deliver a machine with EF amplitude low enough to allow a high quality experimental programme, systematic analysis of the intrinsic EF sources has been carried out for poloidal field (P) and divertor (D) coils, whose magnetic field measurements were available when writing this paper. Such measurements reveal that P and D coils are 3D deformed and thus are responsible for intrinsic EFs, with mainly n = 1 and n = 2 toroidal mode numbers. In preparation to MAST-U operation, both passive and active EF control strategies have been adopted for n = 1 and n = 2 EFs compensation. Passive EF control consisted of installing finely each D and P coil within MAST-U device so as to minimize the intrinsic n = 1 EF amplitude. The optimal coil alignment has been determined based on magnetic field measurements and the corresponding 3D electro-magnetic modelling, and envisaged coil shift and tilt of 3.2 mm and 0.7 mrad, respectively, in the case of P coil named P4. Conversely, active control will be use during MAST-U operation to reduce the n = 2 EF which is associated mainly with P4 and P5, as well (Kirk A. et al. 2014 Plasma Phys. Control. Fusion 56, 104003). Since these coils have been re-used from the MAST device, studies attempting n = 2 EF control, based on MAST plasmas, have been modelled utilizing the MARS-F code (Liu Y.Q. et al. 2000 Phys. Plasmas 7, 3681) to interpret experimental results in MAST and to give hints for future n = 2 EF control studies in MAST-U. A model-based control set for n = 2 EF control has been identified which would allow for the minimization of rotation braking, of the resonant magnetic field at th=agand of the plasma displacement in MAST-U, simultaneously.

Real-time pedestal optimization and ELM control with 3D fields and gas flows on DIII-D

The capabilities of the DIII-D tokamak’s plasma control system (PCS) were expanded to allow for pedestal optimization and edge localized mode (ELM) control. Three proof of principle control schemes are presented that were successfully implemented and tested. These use multiple inputs from real-time (RT) diagnostics like a based ELM monitor and edge profile measurements from Thomson scattering (TS) as well as 3D, i.e. non-axisymmetric, magnetic fields and gas puffs as actuators to regulate the density pedestal.The first scheme targets to optimize the access of ELM suppression induced by non-axisymmetric magnetic perturbations (MPs). The conducted set of experiments identifies a path dependence of plasma confinement on the applied MP amplitude. The controller aims to transition into ELM suppression at the minimum 3D field amplitude and reduces it further afterwards, allowing for partial confinement recovery. Another pedestal control scheme is deployed to compensate the density ‘pump-out’ in MP ELM suppression by regulating the gas puff. This uses RT TS diagnostic data, extracting the pedestal height from the electron density () profiles and enables studies of the transition into and out of MP ELM suppression at constant density. A limit cycle behavior of edge rotation and MP amplitude persists under these conditions. The third control scheme combines MPs and gas puffs as actuators to perform pedestal density trajectory control to access Super high confinement mode (H-mode) and furthermore, allowing the integration of a radiative divertor in this regime. While MPs mainly impact the pedestal top density, the control scheme allows to loosen the tight coupling of pedestal top and separatrix density evolution.With respect to ITER, the achieved results emphasize the need for an advanced control system to keep MP amplitude close to but above the ELM suppression threshold at all times, enabling high confinement and, respectively, at high fusion energy gain factor (Q). Furthermore, pedestal control enables detailed physics studies in present-day tokamaks and allows the exploration of core-edge integrated plasma scenarios.

Poloidally localized edge density fluctuation with applied and spontaneous 3-D fields in experimental advanced superconducting tokamak (EAST)

Poloidally localized density fluctuation with applied and spontaneous 3-D fields in high-confinement mode (H-mode) plasma is observed by using poloidally distributed multichannel interferometer diagnostics in the experimental advanced superconducting tokamak. With the application of an n = 1 rotating nonaxisymmetric magnetic perturbation (NAMP) field, a density fluctuation appears on different interferometer channels sequentially. Evidence shows that this fluctuation is located at the plasma edge. When an n = 1 static NAMP field is applied, the density fluctuation amplitude increases in parts of channels but decreases in other channels, implying a poloidal localization. This localization is enhanced with the increase in the NAMP field. In addition, when a spontaneous n = 1 external kink mode with a frequency of ∼3.5 kHz appears in the plasma edge, the amplitude of density fluctuation is modulated by the n = 1 kink. This modulation could be attributed to the localization effect on fluctuation by the 3-D fields of the spontaneous kink mode.

Overview of the recent experimental research on the J-TEXT tokamak

Recent J-TEXT research has highlighted the significance of the role that non-axisymmetric magnetic perturbations, so called three-dimensional (3D) magnetic perturbation (MP) fields, play in a fundamentally 2D concept, i.e. tokamaks. This paper presents the J-TEXT results achieved over the last two years, especially on the impacts of 3D MP fields on magnetohydrodynamic instabilities, plasma disruptions and plasma turbulence transport.On J-TEXT, the resonant MP (RMP) system, capable of providing either a static or a high frequency (up to 8 kHz) rotating RMP field, has been upgraded by adding a new set of 12 in-vessel saddle coils. The shattered pellet injection system was built in J-TEXT in the spring of 2018. The new capabilities advance J-TEXT to be at the forefront of international magnetic fusion facilities, allowing flexible study of 3D effects and disruption mitigation in a tokamak.The fast rotating RMP field has been successfully applied for avoidance of mode locking and the prevention of plasma disruption. A new control strategy, which applies pulsed RMP to the tearing mode only during the accelerating phase region, was proved by nonlinear numerical modelling to be efficient in accelerating mode rotation and even completely suppresses the mode. Remarkably, the rotating tearing mode was completely suppressed by the electrode biasing. The impacts of 3D magnetic topology on the turbulence has been investigated on J-TEXT. It is found that the fluctuations of electron density, electron temperature and plasma potential can be significantly modulated by the island structure, and a larger fluctuation level appears at the X-point of islands. The suppression of runaway electrons during disruptions is essential to the operation of ITER, and it has been reached by utilizing the 3D magnetic perturbations on J-TEXT. This may provide an alternative mechanism of runaway suppression for large-scale tokamaks and ITER.

Unified modeling of both resonant and non-resonant neoclassical transport under non-axisymmetric magnetic perturbations in tokamaks

A numerical model for neoclassical transport under nonaxisymmetric magnetic perturbations in low collisionality plasmas in tokamaks is developed. To take into account bounce-drift resonances and magnetic drift effects, a Fourier decomposition of the drift kinetic equation in new coordinates, rather than bounce average of it, is employed. A pitch angle scattering collisional operator is used to keep accuracy in the nonresonant regimes or resonant plateau regimes with resonant pitch near pitch space boundaries. Full toroidal geometry effects are also included to increase the accuracy in the modeling of neoclassical transport in the resonant regimes. Neoclassical transport in the most important collisionless regimes, including resonant super-banana plateau and bounce-drift resonances regimes, nonresonant 1/ν and ν−ν regimes, and the transitions between them, can be modeled simultaneously in this model by numerically solving the drift kinetic equation. By application to the neoclassical toroidal viscosity modeling in one discharge in the EAST tokamak, it is found that the bounce-drift resonances dominate the contributions near the plasma core where the plasma E→×B→ drift frequency is close to the bounce frequency, while the precessional resonance dominates the contribution near the edge pedestal top where the E→×B→ drift frequency is close to zero.

Rotation braking with n = 1 nonaxisymmetric magnetic perturbation in the EAST tokamak

The toroidal plasma rotation braking effect during the application of n = 1 static resonant magnetic perturbation is studied by momentum transport analysis in the EAST tokamak. The braking torque shows a global profile and two peaks located near the plasma core and the edge, respectively. The effect of momentum diffusion contributes significantly to the calculated torque. Simulation results with the obtained torque and momentum diffusion coefficients well reproduce the observed plasma rotation evolution. Neoclassical toroidal viscosity (NTV) torque is modeled for comparison with the experimental torque. The total integrated NTV torque is around −0.12 Nm, which is comparable to the observed braking torque (around −0.33 Nm). In the plasma edge, there is a peak in the NTV torque profile, which agrees well in amplitude with the obvious peak in the observed torque density profile. An additional peak in the NTV torque profile due to the ion bounce resonance is also located in the core region. However, the magnitude of this peak is much smaller than the observed one near the plasma core.

Impact of n = 1 field on the non-axisymmetric magnetic perturbations associated with the edge localized mode crashes in the ASDEX Upgrade tokamak

In the ASDEX Upgrade tokamak, the growth of non-axisymmetric magnetic perturbation (NAMP) associated with the ELM crash events has been observed, and both the poloidal and toroidal phases of NAMPs, measured by a set of Mirnov coils, were highly random. By applying an n = 1 magnetic perturbation (MP) field, the phases of NAMPs were locked to the phase of the total n = 1 resonant MP (RMP) field, which takes the plasma response to the MP field into account. This observation can be explained by the resonant electromagnetic J × B torque applied by the RMP field on a magnetic island formed due to the magnetic reconnection, which is predicted to occur during the ELM crashes by several numerical modelling results.

The effects of resonant magnetic perturbations and charge-exchange reactions on fast ion confinement and neutron emission in the Mega Amp Spherical Tokamak

The application of non-axisymmetric resonant magnetic perturbations (RMPs) to low current plasmas in the Mega Amp Spherical Tokamak (MAST) was found to be correlated with substantial drops in neutron production, suggesting a significant degradation of fast ion confinement. The effects of such perturbations on fast ions in MAST have been modelled using a revised version of a non-steady-state orbit-following Monte-Carlo code, in which the parametrization of fusion reaction rates has been updated and neutron rates have been recalculated. Losses of fast ions via charge-exchange (CX) with background neutrals and the subsequent reionization of fast neutrals due to collisions with bulk plasma particles have also been taken into account. The effects of the plasma response to externally-applied RMPs have been included in the modelling. The updated results show that computed neutron rates in the presence of RMPs with the plasma response and CX reactions taken into account agree very well with the experimental data throughout the analysis target time. CX reactions play an important role in determining the neutron rates, in particular before the onset of RMPs.

Plasma Response to Resonant Magnetic Perturbations in Large Aspect Ratio Tokamaks

In this paper, a plasma response model is investigated for large aspect ratio tokamaks, on the presence of external nonaxisymmetric resonant magnetic perturbations. To control plasma confinement, the plasma is perturbed by external resonant helical windings, similar to those introduced by an ergodic magnetic limiter. The plasma response to the perturbation is modeled as an additional magnetic perturbation, created by a current sheet on the main perturbed resonant surface, vanishing the radial component of the total magnetic field in the considered resonant surface. In order to show the influence of the plasma response on the field line topology, the field line differential equations are integrated numerically, showing the reduction of magnetic island sizes and the regularization of chaotic regions around the resonant surface where the response was introduced, in agreement with results observed in sophisticated simulation codes. Finally, the connection lengths indicate that, regarding their distribution, the plasma response introduces a homogenization effect which may affect the deposition patterns at the tokamak wall.

Global kinetic simulations of neoclassical toroidal viscosity in low-collisional perturbed tokamak plasmas

The neoclassical toroidal viscosity (NTV) caused by a non-axisymmetric magnetic field perturbation is numerically studied using two global kinetic simulations with different numerical approaches. Both simulations reproduce similar collisionality ( νb*) dependencies over wide νb* ranges. It is demonstrated that resonant structures in the velocity space predicted by the conventional superbanana-plateau theory exist in the small banana width limit, while the resonances diminish when the banana width becomes large. It is also found that fine scale structures are generated in the velocity space as νb* decreases in the large banana width simulations, leading to the νb*-dependency of the NTV. From the analyses of the particle orbit, it is found that the finite k∥ mode structure along the bounce motion appears owing to the finite orbit width, and it suffers from bounce phase mixing, suggesting the generation of the fine scale structures by the similar mechanism as the parallel phase mixing of passing particles.