Neoclassical Toroidal Viscosity Research Articles

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.

Tungsten transport due to the neoclassical toroidal viscosity induced by resonant magnetic perturbation in the EAST tokamak

The impact of neoclassical toroidal viscosity (NTV) induced by resonant magnetic perturbations (RMPs) on tungsten has been studied in EAST. Modeling results from NTVTOK show that the NTV effect on low charge state tungsten ions is greater than that on high charge state tungsten ions, and the effective transport coefficient of W20+ is only on the order of 10−4–10−3 m2/s, while the effective transport coefficient of W1+ can reach 0.1–1 m2/s, which is close to the 2D neoclassical diffusion coefficient of W1+. The flux of W1+ exhibits a clear phase dependence on the RMP spectrum, and the W1+ flux obtained from NTVTOK is higher at low toroidal mode numbers compared to high toroidal mode numbers of RMPs, which is qualitatively consistent with EAST experiments.

Studies on EU-DEMO 3D coils requirements and conceptual design for error field correction and plasma control

This work presents the initial studies on the requirements for the design of 3D coils on EU-DEMO. The use of 3D coils in present machines includes two main purposes: the first one is the Error Field Correction (EFC). The EFC aims at minimizing the intrinsic non-axisymmetric fields in the machine. Fulfilling the requirements is evaluated with the minimization of residual error fields, both in vacuum and with plasma response. The second purpose relates to the application of 3D fields to control the plasma. The first of these control functions includes the manipulation of the locked neoclassical tearing modes (NTMs) phase, and their positioning in front of the electron cyclotron antennae, for optimum stabilization. A second function is the application of 3D perturbation of the plasma edge to suppress ELMs. As the fastest required time constant of the applied 3D fields is comparable or longer with respect to that of the vacuum vessel, ex-vessel coils can be considered. Another constraint considered is that the 3D fields applied do not generate 3D power exhaust effects, such as divertor lobes, that jeopardize the protection of the machine divertor/wall. This constriant is met in the finding of this work, in the case considered of the ELMs suppression. The aim of this study is to assess if one set of coils could be designed that fulfills all these purposes/functions. The results show that, by using ITER tolerances for the TF, CS and PF coils, all these functions on EFC (using the overlap criterion assumption, which includes the plasma response), NTM phase control and ELMs suppression can be met with the proposed design of one row of ex vessel coils. An additional activity has started to study if the non-resonant perturbations generated by this set of coils could lead to detrimental effects via neoclassical toroidal viscosity (NTV) torque. Preliminary considerations on the coil technology, are also presented, with no showstopper found in this preliminary phase.

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.

Modeling of toroidal momentum transport induced by neoclassical toroidal viscosity torque for ITER scenarios

Neoclassical toroidal viscosity (NTV) torque caused by resonant magnetic perturbation (RMP) and the induced toroidal momentum transport are investigated for International Thermonuclear Experimental Reactor (ITER) scenarios through numerical modeling. The NTV torque is calculated using the NTVTOK code including the bounce-drift resonant effect, and the toroidal rotation evolution is modeled by solving a toroidal momentum transport equation that couples momentum source (NTV torque) and the momentum diffusion effect. The variation of RMP coil phasing (defined as toroidal phase difference between different rows of RMP coils) results in different types of plasma response and hence different features of NTV torque and toroidal momentum transport. The bounce-drift resonant effect enhances NTV torque and induces more significant toroidal rotation variation than simulations that adopt the bounce-averaged NTV model. With the initial rotation of the ITER design, plasma rotation is braked by NTV torque, but it may be sustained at moderate amplitude due to electron contributions to NTV torque. It is also found that initially static or slowly rotating plasma can be accelerated by NTV torque either toward co- Ip or counter- Ip ( Ip indicates plasma current) direction, indicating that NTV torque can be regarded as a momentum source for plasma with low torque injection; for instance, radio-frequency heated plasma.

Toroidal modeling of plasma flow damping and density pump-out by RMP during ELM mitigation in HL-2A

Reduction of both the plasma density and toroidal flow speed, due to application of the predominantly n = 1 (n is the toroidal mode number) resonant magnetic perturbation (RMP) for controlling the edge localized mode in the HL-2A tokamak, is numerically investigated utilizing the quasi-linear initial-value code MARS-Q (Liu et al 2013 Phys. Plasmas 20 042503). Simulation results reveal that the neoclassical toroidal viscosity (NTV) due to three dimensional fields plays the key role in modifying the plasma momentum and particle transport in the HL-2A discharge. By comparing the modeling results with the measured density pump-out in the experiment, the electron NTV particle flux model, in combination with the free-boundary condition for the axisymmetric change of the density at the plasma edge, is found to yield the best agreement in terms of both the pump-out level and the overall time scale. Further sensitivity studies show that the simulated density pump-out level is reasonably robust against variations in the model assumptions, including the particle diffusion model and the non-ambipolar versus ambipolar NTV particle flux. The latter however affects the time scale for reaching the steady state solution. Finally, it is found that the plasma edge-peeling response, the NTV torque, as well as the plasma momentum and particle transport, all are sensitive to the toroidal phase difference between the upper and lower rows of the RMP coil currents in HL-2A, with the 30∘ coil phasing producing the minimal side effects on the plasma.

Resonant mode effects on rotation braking induced by n = 1 resonant magnetic perturbations in the EAST tokamak

The spectrum effects on toroidal rotation braking, induced by n = 1 resonant magnetic perturbations (RMPs) in the discharges with and , are studied in the EAST tokamak. Here n is the toroidal mode number, RMP spectrum is varied by scanning , the phase difference between the upper and lower rows of RMP coils. The toroidal rotation changes periodically with the periodic scanning and such an effect is stronger in the discharge with lower . The spectrum dependence of the neoclassical toroidal viscosity (NTV) torque, modeled by NTVTOK based on the magnetic perturbation obtained from MARS-F calculation, agrees well with that of the experimentally observed braking torques in both discharges. The modeled NTV torque is stronger in the discharge with lower q 95, which also agrees with the observations. The comparisons between the spectrum dependence of the NTV and magnetic perturbations show that the resonant mode of magnetic perturbations near the plasma edge mainly contribute the NTV torque. These agreements between modeling and experiments highlight the capability of NTV theory in explaining the experimental observation in the EAST tokamak.

The effect of plasma beta on error-field penetration in radio-frequency wave heated plasmas in EAST

The plasma-beta effect on the n = 1 resonant magnetic perturbation (RMP) field penetration in purely radio-frequency (RF) wave heated discharges has been investigated in EAST. The experimental results show that the dependence of the threshold RMP coil current for field penetration, , on the total absorbed power P tot scales as approximately , indicating that the error-field tolerance is improved with increasing RF power. This is benefited by the increased electron perpendicular flow dominated by a counter-current electron diamagnetic flow with increasing RF power. However, theoretical scaling in cylindrical geometry overestimates the power index. Assuming an additional term for the normalized beta in the scaling, it is shown that the fitted from the experimental observation is around −1, indicating a degradation effect of plasma beta. To clarify the underlying physics of the plasma-beta effect that was not included in the theoretical scaling in cylindrical geometry, the MARS-Q code with full toroidal geometry is employed for simulation of nonlinear field penetration (Liu et al 2013 Phys. Plasmas 20 042503). The MARS-Q simulation results reproduce the dependence well, and hence the P tot scaling of the threshold current in experimental observations. The main reason for this is that the net total torque, which is mainly contributed by the neoclassical toroidal viscosity (NTV), increases with increasing plasma . The results demonstrate that the nonlinear toroidal coupling effect via NTV torque plays an important role in determining field penetration, even in cases with relatively low , which is far less than the no-wall beta limit.

Threshold density for toroidal rotation reversal bifurcation induced by symmetry breaking

Threshold density for intrinsic toroidal rotation reversal is studied using a newly proposed model [Li et al., Nucl. Fusion 61, 104002 (2021)] based on the neoclassical toroidal plasma viscosity (NTV) effect induced by symmetry breaking due to the existence of internal kink mode. In this model, rotation reversal happens when the NTV steady state flow jumps between “electron root” and “ion root,” which depends on plasma collisionality regimes. To make it convenient for cross machine comparisons or extrapolation to the future device, a scaling of threshold density for rotation reversal is proposed based on the physics of transition between the 1/ν and superbanana plateau regimes, i.e., the normalized collisionality over the particle toroidal precessional frequency rather than over the particle bounce frequency that is frequently used in neoclassical theory. The theoretical scaling of the threshold density on electron temperature and magnetic field strength is well verified by the NTVTOK modeling. Other effects, such as boundary condition, temperature gradient, and temperature ratio, which cannot be included in the theoretical scaling, are also investigated by using the NTVTOK modeling.

Neoclassical toroidal plasma viscosity in bounce-transit and drift resonance regimes in tokamaks

Neoclassical toroidal plasma viscosity in the bounce-transit and drift resonance regimes is calculated using a version of the drift kinetic equation that encompasses the physics of the nonlinear trapping and quasilinear plateau regimes in tokamaks. It is demonstrated that the mirror-force like term controls the transition between these two regimes. When the effective collision frequency is larger than the mirroring or the nonlinear bounce frequency, the quasilinear regime prevails; otherwise, the nonlinear trapping regime reigns. The demonstration is accomplished by using the Eulerian approach and is beyond the grasp of the method of the integration along the unperturbed orbit in solving the drift kinetic equation. The neoclassical toroidal plasma viscosity in the quasilinear plateau regime is calculated. Approximate analytic expressions for the neoclassical toroidal plasma viscosity that include the asymptotic limits of the nonlinear trapping and quasilinear regimes are presented to facilitate thermal and energetic alpha particle transport modeling in tokamaks.

Toroidal modeling of 3D perturbations generated by current filaments in scrape-off layer in tokamak with biased divertor targets

The divertor biasing technique offers a promising alternative to control the edge localized mode (ELM) as well as the divertor heat load in tokamaks, as compared to the resonant magnetic perturbation (RMP) generated by magnetic coils. The linear resistive MHD code MARS-F (Liu et al 2000 Phys. Plasmas 7 3681) is employed to study the plasma response to the n = 2 (n is the toroidal mode number) field perturbation in HL-2A, produced by the divertor biasing current filaments flowing in the scrape-off layer region. The response field due to biasing currents is compared with the RMP field utilized for ELM control in HL-2A. The strength of the radial resonant field perturbation, produced by the biasing currents of 100 A level, is found to be comparable with RMP generated by several kA of ELM control coil currents for the reference plasma. The plasma normal displacement near the X-point and the associated neoclassical toroidal viscosity torque are also computed to be similar between these two techniques. The modeling results thus strongly suggest that the biasing technique can be applied to control ELMs. Moreover, the biasing currents produce field perturbations, including the plasma response, that are localized more near the plasma edge (compared to the RMP counterpart), thus reducing the chance of mode locking associated with core perturbations. Particle orbit tracing also reveals that the biasing current produced magnetic perturbation tends to widen the heat deposition region and induce the strike point splitting of the ion saturation flow on the outer divertor surface, consistent with experimental observations in HL-2A. These toroidal modeling results confirm the possibility of ELM control and plasma exhaust solution by the divertor biasing technique.

Verification of neoclassical toroidal viscosity induced by energetic particles

The thermal particles contributed neoclassical toroidal viscosity (NTV) have been successfully developed and explored by many impressive works such as the study by Shaing et al. [Phys. Plasmas 10, 1443 (2003)] and Zhu et al. [Phys. Rev. Lett. 96, 225002 (2006)]. In this work, the scope of the NTV study is extended to explore the contribution of energetic particles (EPs) through both theory and experiments. In theory, the existence of the NTV torque due to the precessional drift resonance of trapped EPs is identified based on the equivalence between the NTV torque and the perturbed drift kinetic energy [J. Park, Phys. Plasmas 18, 110702 (2011)]. Toroidal modeling with the Magneto Resistive Spectrum - drift Kinetic code [Y. Liu, Phys. Plasmas 15, 112503 (2008)], based on this equivalence, indicates that trapped EPs can contribute a significant amount of the NTV torque. Meanwhile, this work also focuses on developing the dedicated DIII-D experiments in the presence of the n = 2 external magnetic perturbation to verify the EP induced NTV (EP-NTV) by measuring the change of the NTV torque while varying the angle and the voltage of the neutral beam injection. However, the developed experiments have been unable to create conditions necessary to clearly demonstrate the presence of EP-NTV. The main challenge is separating the resonant and non-resonant momentum transport responses in the plasma. The experience, gained from this study, can help the further exploration of EP-NTV in the future experiments.

Nonlinear MHD modeling of n = 1 RMP-induced pedestal transport and mode coupling effects on ELM suppression in KSTAR

Fully suppressing edge-localized modes (ELMs), e.g., with resonant magnetic perturbations (RMPs), is essential to reach and sustain high-performance steady-state H-mode plasmas because large ELMs can significantly reduce the lifetime of divertor components in future tokamak reactors. RMP-driven ELM suppression in KSTAR has been modeled by coupling the neoclassical transport code PENTRC to the nonlinear 3D MHD code JOREK. We have found that the radial transport from the combined effects of the kink-peeling, tearing response, and neoclassical toroidal viscosity can explain the pedestal degradation observed in experiments. In addition, it has been found that the RMP response can increase the inter-ELM heat flux on the lower outer divertor by redistributing the heat transport between the divertor plates. In addition to the degraded pedestal, ELM suppression is also attributable to the RMP-induced mode interactions. While the linear stability of peeling-ballooning mode (PBMs) improves owing to the degraded pedestal, the PBM and RMP interaction increases the spectral transfer between edge harmonics, preventing catastrophic growth and the crash of unstable modes. Here, it turns out that the magnetic islands near the pedestal top can play a vital role in mediating the mode interactions.

Toroidal modeling of energetic passing particle drift kinetic effects on tearing mode stability

Drift kinetic effects of the neutral beam injection induced passing energetic particles (EPs) on the linear stability of the n = 1 tearing mode (TM) (with the dominant poloidal harmonic of m = 2) are numerically investigated utilizing the MARS-K code (Liu et al 2008 Phys. Plasmas 15 112503), in a tokamak plasma with finite equilibrium pressure and anisotropic thermal transport. In the low plasma pressure regime, it is found that co- (counter-) passing EPs stabilize (destabilize) the TM, agreeing with previous studies. However, as the plasma pressure increases beyond a critical value, it is found that co-passing EPs also destabilize the mode. An in-depth analysis reveals that the net effect of co-passing EPs is a result of competition between the stabilizing contribution from the non-adiabatic drift kinetic terms and the destabilizing contribution associated with adiabatic terms, with the latter becoming more dominant at higher equilibrium pressure. Non-perturbative magnetohydrodynamic-kinetic hybrid modeling also finds that co- and counter-passing EPs modify the TM eigenfunction differently, with the counter-passing EPs enhancing the sideband harmonics. Furthermore, effects of the plasma resistivity and toroidal rotation, as well as that of the equilibrium distribution of EPs in the particle pitch angle space, are also investigated, showing asymmetric results on the TM stability between the co- and counter-passing EPs. The first order finite orbit width correction is found to be stabilizing with co-passing EPs and destabilizing with counter-passing particles. Finally, drift resonances between passing EPs and the TM induce finite frequency to the mode and generate finite net torques inside the plasma, due to the neoclassical toroidal viscosity and the Reynolds stress associated with 3D perturbations.

EUROfusion-theory and advanced simulation coordination (E-TASC): programme and the role of high performance computing

This paper is a written summary of an overview oral presentation given at the 1st Spanish Fusion High Performance Computer (HPC) Workshop that took place on the 27 November 2020 as an online event. Given that over the next few years ITER 24 24ITER (‘The Way’ in Latin) is the world’s largest tokamak under construction in the south of France: a magnetic fusion device that has been designed to prove the feasibility of fusion as a large-scale and carbon-free source of energy (https://www.iter.org/). will move to its operation phase and the European-DEMO design will be significantly advanced, the EUROfusion consortium has initiated a coordination effort in theory and advanced simulation to address some of the challenges of the fusion research in Horizon EUROPE (2021–2027), i.e. the next EU Framework Programme for Research and Technological Development. This initiative has been called E-TASC, which stands for EUROfusion-Theory and Advanced Simulation Coordination. The general and guiding principles of E-TASC are summarized in this paper. In addition, an overview of the scientific results obtained in the pilot phase (2019–2020) of E-TASC are provided while highlighting the importance of the required progress in computational methods and HPC techniques. In the initial phase, five pilot theory and simulation tasks were initiated: towards a validated predictive capability of the low to high transition and pedestal physics; runaway electrons in tokamak disruptions in the presence of massive material injection; fast code for the calculation of neoclassical toroidal viscosity in stellarators and tokamaks; development of a neutral gas kinetics modular code; European edge and boundary code for reactor-relevant devices. In this paper, we report on recent progress made by each of these projects.

Neoclassical toroidal viscosity torque prediction via deep learning

GPECnet is a densely connected neural network that has been trained on GPEC data, to predict the plasma stability, neoclassical toroidal viscosity (NTV) torque, and optimized 3D coil current distributions for desired NTV torque profiles. Using NTV torque, driven by non-axisymmetric field perturbations in a tokamak, can be vital in optimizing pedestal performance by controlling the rotation profile in both the core, to ensure tearing stability, and the edge, to avoid edge localized modes (ELMs). The generalized perturbed equilibrium code (GPEC) software package can be used to calculate the plasma stability to 3D perturbations and the NTV torque profile generated by applied 3D magnetic fields. These calculations, however, involve complex integrations over space and energy distributions, which takes time to compute. Initially, GPECnet has been trained solely on data representative of the quiescent H-mode (QH) scenario, in which neutral beams are often balanced and toroidal rotation is low across the plasma profile. This work provides the foundation for active control of the rotation shear using a combination of beams and 3D fields for robust and high performance QH mode operation.

Acceleration of ion rotation during internal reconnection events in the versatile experiment spherical torus (VEST)

Acceleration of ion rotation is observed during internal reconnection events (IREs) in the versatile experiment spherical torus. Two IRE discharges with opposite torques, i.e. acceleration or deceleration of ohmic plasmas with intrinsic, counter-I p rotation, can be generated using different wall conditionings method. When an IRE occurs, acceleration and deceleration of impurity ion rotation as well as well-known ion heating are observed globally via ion Doppler spectroscopy with multiple channels including a single channel with a high temporal resolution of 0.2 ms. Interestingly, ion heating is observed earlier than the ion rotation acceleration, indicating that this phenomenon has a different mechanism from usual magnetic reconnection. We present several possible mechanisms for the rotation acceleration. For several reasons, the ions are thought to be accelerated by a neoclassical toroidal viscosity (NTV) torque rather than mechanisms such as the reconnection outflow and toroidal electric field induced by the current profile change. A simple 0D momentum balance model with NTV torque in the 1/ν collisionality regime agrees well with the experimental results. Furthermore, a positive correlation between ion temperature and plasma rotation is identified, whereby the NTV torque S NTV and ion temperature T i are related via .

Torque to counter-current direction driving low frequency tearing modes in JT-60U

In the JT-60U tokamak, low frequency modes (LFMs) have been reported recently when the m/n = 2/1 neoclassical tearing mode grows sufficiently. LFMs show the low mode frequencies (<20 Hz) with the rotation direction to the counter-current direction (ctr-direction) toroidally, even if strong injection power to the co-current direction (co-direction) is applied by tangential neutral beam injections. As a candidate to drive the rotation to the ctr-direction, the neoclassical toroidal viscosity (NTV) torque is investigated in this study. Indeed, when a LFM is observed, the estimated ‘offset velocity’ of the NTV torque is larger than the observed toroidal velocity around the q = 2 surface and results in the torque to the ctr-direction (ctr-torque). The torque balance between the NTV torque and the torque induced by the eddy current on the resistive wall is investigated. It is found that the rotation to the ctr-direction having the low mode frequency is obtained as the result of the ctr-torque to the offset velocity. Our investigation suggests the requirement to include the NTV torque in the modeling on the mode locking of neoclassical tearing modes in tokamaks.

Symmetry breaking driving spontaneous plasma rotation in tokamak fusion devices

Plasma rotation plays a critical role in improving plasma confinement in a magnetically confined fusion device. Spontaneous plasma rotation and its reversal of orientation without external momentum input have been observed in some tokamak fusion devices, while the underlying physics is not well understood. A new mechanism based on neoclassical toroidal plasma viscosity induced by symmetry breaking is proposed and well reproduces both spontaneous toroidal rotation and its reversals in tokamaks by considering a small non-axisymmetric displacement in the plasma center, since internal instabilities are often observed in those experiments. The nonlinear hysteresis process of plasma rotation reversals is also well reproduced in the modeling. The mechanism for driving spontaneous plasma rotation proposed in this paper may be utilized for achieving more economical operation of future tokamak fusion reactors.

Investigation of the toroidal flow damping in the edge plasma of J-TEXT tokamak with an electrode biasing

The toroidal flow damping has been investigated in the edge plasma of J-TEXT tokamaks with an electrode biasing (EB). The estimated viscosity of the toroidal flow after the bias turning off is about 67 times of the classical viscosity and four times of the neo-classical viscosity, which infers that the flow damping is anomalous in the transition phase. In the equilibrium phase, the torque densities driven by the EB, the momentum transport, and the neo-classical toroidal viscosity (NTV) under different bias conditions are calculated, which show that the NTV torques are comparable with the other terms. According to the angular momentum balance equation, the remnant damping torque densities and the effective damping coefficients have been obtained. Considering that the remnant damping is mainly contributed by the neutral particle damping, this investigation provides a method to estimate the neutral particle density (nH), which gives that the nH in the edge plasma of J-TEXT is in the range of 1–4 (×1017 m−3).