Presence Of Resonant Magnetic Perturbations Research Articles

Effects of resonant magnetic perturbations on turbulence and flows in the edge of HL-2A plasmas

The influence of resonant magnetic perturbations (RMPs) on the dynamics of turbulence and flows at the edge of the HL-2A tokamak is analyzed utilizing transfer entropy technique. The results have shown that the RMP damps the poloidal flows as well as the E × B shearing rate, whereas enhances the toroidal flows and leads to a broadened particle spectrum with increased small scale turbulence transport. The causality analysis indicates that the regulation impact of poloidal flow on turbulent fluctuations and particle flux is weakened, while that of the toroidal rotation on the latter is strengthened by the RMP field. The impact of the changes in poloidal flow dominates over that of the modified toroidal flow on turbulent transport in the edge. The magnetic perturbation and the flows generally show predator–prey oscillations, where the causal effect between the former and the toroidal flow transits to a synchronization relation in the presence of RMP. In addition, the RMP field will weaken the causal effect on poloidal Reynolds stress while strengthening the parallel-radial component simultaneously. The present findings provide a possible explanation on the effects of external fields on the edge transport, which is suggested to be dominated by the complex interactions among external perturbations, flows, and ambient microturbulence.

Quasi-mode evolution in a stochastic magnetic field

We present a multi-scale model of quasi-mode evolution in a stochastic magnetic field. The similarity between a quasi-mode and a ballooning mode enables us to address the challenges arising from the disparate geometries in the theories of ballooning modes in the presence of resonant magnetic perturbations. We obtain useful insights into our understanding of ballooning mode dynamics in a stochastic background. To maintain quasi-neutrality at all scales, the beat between the quasi-mode and the stochastic magnetic field drives microturbulence, which drives the turbulent background that promotes mixing and damps the quasi-mode. As a result of the broad mode structure of the quasi-mode, the turbulent viscosity and the turbulent diffusivity produced by the microturbulence are larger than those in our related study on resistive interchange modes. The stochastic magnetic field can also enhance the effective plasma inertia and reduce the effective drive, thereby slowing the mode growth. A nontrivial correlation between the microturbulence and the magnetic perturbations is shown to develop. This could account for the reduction in the Jensen–Shannon complexity of pedestal turbulence in the Resonant Magnetic Perturbation Edge-Localized Mode suppression phase observed in recent experiments. Directions for future experimental and theoretical studies are suggested.

Neoclassical transport of impurities in tokamaks with non-axisymmetric perturbations

The effect of resonant magnetic perturbations (RMPs) on neoclassical transport of impurities is calculated in DIII-D and NSTX. The neoclassical fluxes are evaluated using the NEO code with nonlinear one-fluid nonaxisymmetric equilibrium calculated using M3D-C1. Neoclassical fluxes of impurities show significant changes with RMPs if the impurity resides in low-collisionality regime, but are weakly affected by RMPs in the Pfirsch–Schlüter (P–S) regime. Charge number (Z) of the impurity affects the collisionality of impurity species, which then determines the effect of 3D fields on neoclassical impurity transport. This suggests that RMPs can be possibly used for exhaust of low-Z impurities in these facilities, but have little effect for impurities with charge number greater than 10 or so. Additionally, it is shown that it is the change in the convective fluxes which is a main contributor in modifying the neoclassical impurity fluxes in the presence of RMPs.

Transition in particle transport under resonant magnetic perturbations in a tokamak

Nonlinear 3D MHD simulations and validations reveal that the hybrid particle-MHD transport is a key process for driving the pump-out in the presence of Resonant Magnetic Perturbations (RMPs) in the KSTAR tokamak. Particle transport and the resulting density pump-out by RMPs are shown to be composed of not only the classical flow convection near magnetic islands due to polarization but also the neoclassical ion diffusion across perturbed magnetic surfaces. The latter is known as the Neoclassical Toroidal Viscosity (NTV) and is integrated into nonlinear MHD simulations here for the first time, revealing that the two-stage pump-outs observed in KSTAR experiments are reproduced only with such integrated nonlinear MHD and transport evolution. Near-resonant responses, which have received less attention than the resonant response, play distinct roles in the pump-out along with the island formation. In addition, this modeling is used to investigate the pump-outs in double-null-like plasmas and numerically capture the effect of the double-null shape on the pump-outs, which may explain the difficulty of Edge Localized Mode (ELM) suppression access in double-like plasmas. This reveals new aspects of the impact toroidal geometry and mode coupling have on 3D physics and reveals the importance of near-resonant components in suppressing ELMs.

Turbulent transport of fast ions in tokamak plasmas in the presence of resonant magnetic perturbations

The effects of resonant magnetic perturbations on the turbulent transport of fast ions in tokamak devices are investigated using a theoretical transport model of test-particle type. The direct numerical simulation method is used to compute, via the transport model, the diffusion coefficients. The numerical results are in good agreement with other, analytically derived, estimations. It is found that finite Larmor radius effects algebraically decrease the transport, while the amplitude of magnetic perturbations has an opposite effect. In the presence of stochastic dynamics, the asymmetric toroidal magnetic field induces a small, radial, outward pinch. A synergistic mechanism of non-linear coupling between the effects of turbulence and those of magnetic perturbations enhances the radial diffusion. General scaling laws are proposed for the transport coefficients.

Numerical simulations of NBI fast ion loss with RMPs on the EAST tokamak

Fast ion losses in the presence of resonant magnetic perturbations (RMPs) on the EAST tokamak have been simulated by using the Monte Carlo orbit-following code GYCAVA (Xu et al 2019 Comput. Phys. Comm. 244 40). Fast ions produced by the co-current tangential neutral beam injection (NBI) were considered. The initial distribution of NBI fast ions was numerically computed by the TGCO code and the n = 1 vacuum and response RMP fields were numerically computed by the MHD code MARS-F (Liu et al 2000 Phys. Plasmas 7 3681). It is found that fast ion losses increase almost linearly with the RMP coil current. Poincaré plots show that fast ion losses in the presence of RMPs on EAST are mainly due to the orbit stochasticity induced by RMPs. The collision effect, including the slowing down and the pitch angle scattering, on fast ion losses have also been numerically studied. The synergy effect of RMPs and collision-induced pitch angle scattering can enhance the particle loss of fast ions. The collision effect, including the effective ion charge number effect, on the power loss of fast ions is weak. Fast ion losses increase with the effective ion charge number increasing, which is related to the pitch angle scattering effect. The plasma response to RMPs can enhance or reduce fast ion losses. The plasma response effect on fast ion losses depends on the RMP coil phasing, that is, the phase difference between the upper and lower coils. The heat loads on the outer wall clearly follow the n = 1 periodicity of the RMP coil configuration. Positions of maximum heat loads are closely related to the coil phasing of RMPs. These mean that the magnetic topology of RMPs is responsible for the toroidal distribution of heat loads.

Gyrokinetic study of collisional resonant magnetic perturbation (RMP)-driven plasma density and heat transport in tokamak edge plasma using a magnetohydrodynamic screened RMP field

The total-f gyrokinetic particle-in-cell code XGC is applied to study various aspects of collisional transport in the tokamak edge pedestal in the presence of resonant magnetic perturbations (RMPs) calculated with M3D-C1. Simulations including the separatrix and scrape-off layer are exercised for a model DIII-D H-mode plasma. Neutral particle recycling is modeled by means of ionization and charge exchange with the plasma. A fully nonlinear Fokker–Planck collision operator is utilized to account for non-Maxwellian edge plasma. The study yields kinetic evidence that (i) neglecting the non-axisymmetric component of the RMP-generated electrostatic potential perturbation could yield a fictitiously high particle pump-out rate in the edge pedestal; that (ii) the experimental level of particle pump-out from the pedestal cannot be provided by collisional transport across Kolmogorov–Arnold–Moser surfaces except across the magnetic separatrix where stochastic magnetic field lines exist; that (iii) the H-mode type electron heat barrier is retained in the steep slope area under the M3D-C1 calculated RMPs; and that (iv) the stochastic electron heat-transport rate around the magnetic separatrix surface is much lower than the prediction by Rechester–Rosenbluth (1978 Phys. Rev. Lett. 40 38–41) and is qualitatively consistent with the experimentally observed rate. Detailed kinetic physics analysis on how the transport fluxes, electrostatic potential perturbation, and -well structure respond to onset of RMPs is also reported.

Monte Carlo orbit-following simulations including the finite Larmor radius effect based on a phase-space coordinate transform method

Monte Carlo orbit-following simulations based on a phase-space coordinate transform method are presented in this paper. Guiding-center orbits are computed by using this method, that is, using the phase-space coordinate transform and solving the gyrokinetic equations of motion. This method has been adopted in a Monte Carlo orbit-following code GYCAVA for studying the behavior of fast ions in a tokamak. The finite Larmor radius effect can be included in the guiding-center orbit computation. The cylindrical coordinates are used for avoiding singularity of the safety factor at X points of the divertor configuration. An n-point discrete sum method is used to compute the gyro-average, which is related to the finite Larmor radius effect. The GYCAVA code has been integrated with other equilibrium, magnetohydrodynamic and neutral beam injection codes for studying losses and wall loads of fast ions in the presence of perturbation fields. The GYCAVA code has been verified by tests of the orbit computation and the Monte Carlo Coulomb collision. Simulations of fast ion losses in the presence of resonant magnetic perturbations in the EAST tokamak have been performed.

Specific Features of Charged Particle Confinement in the T-15 Tokamak in the Presence of Magnetic Perturbations

Charged particle motion in the regions of magnetic islands and near-separatrix ergodicity of magnetic field lines in the Т-15 tokamak is studied numerically. The trajectories are calculated by integration of exact three-dimensional equations of motion for trapped and passing charged particles starting at different pitch angles. It is shown that the presence of resonant magnetic perturbations qualitatively affects the trajectories of passing particles. In the region of magnetic islands, the orbits of passing particles acquire an island structure, while in the region of the near-separatrix ergodicity of magnetic field lines, the orbits are stochastized. It is shown that magnetic perturbations insignificantly affect trapped particle motion. Even in the absence of magnetic surfaces, the trajectories of trapped particles are regular and their cross sections have the shape of a standard banana orbit. The possibility of charged particles to pass between regions with different magnetic topologies is analyzed.

Overview of new MAST physics in anticipation of first results from MAST Upgrade

The mega amp spherical tokamak (MAST) was a low aspect ratio device (R/a = 0.85/0.65 ~ 1.3) with similar poloidal cross-section to other medium-size tokamaks. The physics programme concentrates on addressing key physics issues for the operation of ITER, design of DEMO and future spherical tokamaks by utilising high resolution diagnostic measurements closely coupled with theory and modelling to significantly advance our understanding. An empirical scaling of the energy confinement time that favours higher power, lower collisionality devices is consistent with gyrokinetic modelling of electron scale turbulence. Measurements of ion scale turbulence with beam emission spectroscopy and gyrokinetic modelling in up-down symmetric plasmas find that the symmetry of the turbulence is broken by flow shear. Near the non-linear stability threshold, flow shear tilts the density fluctuation correlation function and skews the fluctuation amplitude distribution. Results from fast particle physics studies include the observation that sawteeth are found to redistribute passing and trapped fast particles injected from neutral beam injectors in equal measure, suggesting that resonances between the m = 1 perturbation and the fast ion orbits may be playing a dominant role in the fast ion transport. Measured D–D fusion products from a neutron camera and a charged fusion product detector are 40% lower than predictions from TRANSP/NUBEAM, highlighting possible deficiencies in the guiding centre approximation. Modelling of fast ion losses in the presence of resonant magnetic perturbations (RMPs) can reproduce trends observed in experiments when the plasma response and charge-exchange losses are accounted for. Measurements with a neutral particle analyser during merging-compression start-up indicate the acceleration of ions and electrons. Transport at the plasma edge has been improved through reciprocating probe measurements that have characterised a geodesic acoustic mode at the edge of an ohmic L-mode plasma and particle-in-cell modelling has improved the interpretation of plasma potential estimates from ball-pen probes. The application of RMPs leads to a reduction in particle confinement in L-mode and H-mode and an increase in the core ionization source. The ejection of secondary filaments following type-I ELMs correlates with interactions with surfaces near the X-point. Simulations of the interaction between pairs of filaments in the scrape-off layer suggest this results in modest changes to their velocity, and in most cases can be treated as moving independently. A stochastic model of scrape-off layer profile formation based on the superposition of non-interacting filaments is in good agreement with measured time-average profiles. Transport in the divertor has been improved through fast camera imaging, indicating the presence of a quiescent region devoid of filament near the X-point, extending from the separatrix to ψn ~ 1.02. Simulations of turbulent transport in the divertor show that the angle between the divertor leg on the curvature vector strongly influences transport into the private flux region via the interchange mechanism. Coherence imaging measurements show counter-streaming flows of impurities due to gas puffing increasing the pressure on field lines where the gas is ionised. MAST Upgrade is based on the original MAST device, with substantially improved capabilities to operate with a Super-X divertor to test extended divertor leg concepts. SOLPS-ITER modelling predicts the detachment threshold will be reduced by more than a factor of 2, in terms of upstream density, in the Super-X compared with a conventional configuration and that the radiation front movement is passively stabilised before it reaches the X-point. 1D fluid modelling reveals the key role of momentum and power loss mechanisms in governing detachment onset and evolution. Analytic modelling indicates that long legs placed at large major radius, or equivalently low at the target compared with the X-point are more amenable to external control. With MAST Upgrade experiments expected in 2019, a thorough characterisation of the sources of the intrinsic error field has been carried out and a mitigation strategy developed.

Non-ideal effects on ballooning mode stability in the presence of resonant magnetic perturbations

The ideal ballooning mode model in the presence of the externally applied resonant magnetic perturbation (RMP), developed by Bird and Hegna [Nucl. Fusion 53, 013004 (2013)], is extended to include the non-ideal effects, i.e., the finite resistivity and diamagnetic drift effects. Using the eigenvalue equation with the non-ideal effects, a comprehensive analysis is carried out to elucidate the impact of the RMP on ballooning mode stability. Finite resistivity is shown to reduce the line bending stabilization in low to intermediate toroidal mode number (n), resulting in the more peaked growth rate spectrum with respect to n. It is shown that the combination of finite resistivity and the RMP-induced local shear modulation have a strong influence on line bending stabilization, leading to an interesting threshold behavior of the ballooning mode stability. This signifies the importance of the RMP to the line bending stabilization coupled with finite resistivity, as well as the local shear modulation.

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.

Tomographic reconstruction for a tangentially viewing visible light imaging diagnostic on EAST

A two-dimensional tomographic reconstruction method based on the Phillips-Tikhonov regularization is proposed in this study, for a tangentially viewing visible light imaging diagnostic on EAST. Phantom tests are demonstrated to evaluate the performance of this method. The purpose of this method is to reconstruct the local emission from experimental images in various parts of the visible spectrum, which can be employed to reflect spatial distributions of certain particles (Li-II in this study) in plasmas. As a potential application of the Li-II distribution, the measurement of plasma boundary displacements in the presence of resonant magnetic perturbations is tried. Though the result of this attempt is limited by the computational precision and conditions of diagnostic system at present, it provides valuable references for further works.

Helical electric potential modulation via zonal-flow coupling to resonant magnetic perturbations

Helical modulations of the electric potential were observed in several devices during application of resonant magnetic perturbations (RMPs). To address the implication of the helical modulation on RMP-induced transport, we derive a system of 1D equations for zonal flows (ZFs) and helical potential in the presence of RMPs. As ZFs are turbulence-driven, turbulence plays a major role in this plasma self-organization towards a quasi-equilibrium with 3D helical potential. The model reveals how RMPs modify an initially given a saturated-state of coexisting turbulence and ZFs. It is shown that RMPs trigger a transport bifurcation by allowing energy-transfer out of turbulence-driven ZFs into ZF-driven helical potential.

Nonlinear simulation of ELM dynamics in the presence of resonant magnetic perturbations

We report on nonlinear simulation studies on the dynamical behaviour of ELMs under the influence of resonant magnetic perturbations (RMPs) using a two-fluid initial value electromagnetic nonlinear global code (CUTIE). To simulate ELMs we introduce a particle source in the confinement region and a particle sink in the edge region. To study ELM control using RMPs we have applied an n = 2 static external magnetic perturbation at the edge and made detailed parametric studies under varying conditions for the machine and plasma parameters typical of COMPASS-D. Our results show that ELM mitigation is possible for RMP powers beyond a specific threshold. The results also provide valuable insights into the RMP induced modifications of the complex nonlinear dynamics of the ELMs, in particular on the redistribution of mode energy and the cascading of energy to shorter scale lengths. We also observe a hysteresis in states as we increase the amplitude of RMPs and then decrease it to the same value.

Comparative studies of electrostatic turbulence induced transport in presence of resonant magnetic perturbations in RFX-mod

Three-dimensional non-axisymmetric magnetic fields are purposely applied to toroidally symmetric fusion plasmas in order to modify transport of heat and particle fluxes to the plasma-facing components (PFCs), and specifically to control and suppress edge localized modes (ELMs) in H-mode tokamak plasmas. This paper presents a comparative study between two magnetic configurations available in the RFX-mod device, namely the original reversed-field pinch configuration and the more recent low-field circular ohmic tokamak. The paper presents a detailed analysis of the modulation of electrostatic turbulence and induced transport in the presence of an externally applied magnetic perturbation, as measured in both configurations. A detailed study of the underlying magnetic topology in both configurations is given through the field line tracing code FLiT. The electrostatic turbulence induced flux is observed to be modulated by the underlying topology, with an enhancement close to the O-point and a reduction at the X-point of the induced magnetic island. The transport modification are discussed in terms of relevant frequency and wavenumber spectrum.

Drive of a long-lived vortex-flow pattern by coupling to zonal flows in presence of resonant magnetic perturbations

The working hypothesis for the origin of edge-localized-mode stabilization is that Resonant Magnetic Perturbations (RMPs) increase transport in the pedestal, thus lowering the pressure gradient below the ideal MHD threshold. Large-scale vortex-flows matching the RMP helicity were observed experimentally [N. Vianello et al., Plasma Phys. Controlled Fusion 57, 014027 (2015)]. We derive and solve numerically a 1D model for the generation of long-lived vortex-flows in presence of RMPs. We show that, in presence of RMPs, zonal flows are damped and partially transfer their energy to a resonant vortex-flow pattern. The resulting vortex-flow has a multiscale nature with a fast-varying fine-structure set by zonal flows and a slowly-varying radial envelope with a resonant character. The model predicts that the saturated vortex-flow energy E scales with RMP amplitude as E∼δBrBα with α≃1.9. This novel type of nonlinearly driven non-axisymmetric flow has a radial—streamer like—component, and is therefore a candidate for increased convective transport.

When poloidal rotation in a tokamak remains neoclassical in the presence of resonant magnetic perturbations

Plasma rotation and radial electric field in the presence of resonant magnetic perturbations (RMPs) is considered. The situation is discussed in detail where no change of poloidal rotation is observed while the radial electric field and toroidal rotation are changing self-consistently when RMPs are switched on. Recent experimental results from DIII-D are discussed in connection with this model.

Stable and unstable manifolds, and the structure of magnetic footprints

The generic analytic formulae of the stable and unstable manifolds near the separatrix and on the divertor plates in tokamaks in the presence of resonant magnetic perturbations are derived. The stable (unstable) manifolds on the divertor plates describe the form of the magnetic footprint boundaries. They are derived using the separatrix mapping. The analytical formulae depend on a few of the equilibrium plasma parameters and the magnetic perturbations.

Three-dimensional distortions of the tokamak plasma boundary: boundary displacements in the presence of resonant magnetic perturbations

The three-dimensional plasma boundary displacements induced by applied non-axisymmetric magnetic perturbations have been measured in ASDEX Upgrade, DIII-D, JET, MAST and NSTX. The displacements arising from applied resonant magnetic perturbations (RMPs) are measured up to ±5% of the minor radius in present-day machines. Good agreement can be found between different experimental measurements and a range of models—be it vacuum field line tracing, ideal three-dimensional MHD equilibrium modelling, or nonlinear plasma amplification. The agreement of the various experimental measurements with the different predictions from these models is presented, and the regions of applicability of each discussed. The measured displacement of the outboard boundary from various machines is found to correlate approximately linearly with the applied resonant field predicted by vacuum modelling (though it should be emphasized that one should not infer that vacuum modelling accurately predicts the displacement inside the plasma). The RMP-induced displacements foreseen in ITER are expected to lie within the range of those predicted by the different models, meaning less than ±1.75% (±3.5 cm) of the minor radius in the H-mode baseline and less than ±2.5% (±5 cm) in a 9 MA plasma. Whilst a displacement of 7 cm peak-to-peak in the baseline scenario is marginally acceptable from both a plasma control and heat loading perspective, it is important that ITER adopts a plasma control system which can account for a three-dimensional boundary corrugation to avoid an n = 0 correction which would otherwise locally exacerbate the displacement caused by the applied fields.