Neoclassical Transport Research Articles

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.

Energy transport analysis of NSTX plasmas with the TGLF turbulent and NEO neoclassical transport models

This work presents a study of plasma transport at low aspect ratio on the National Spherical Torus Experiment tokamak, where the turbulent and neoclassical energy fluxes calculated by the quasilinear Trapped Gyro Landau Fluid (TGLF) model and the multi species drift-kinetic Neoclassical solver (NEO) are validated against experimental data. The turbulent energy transport of two plasma discharges, one in the L-mode confinement regime and another in the H-mode regime, is dominated by electrostatic drift-wave instabilities, while the ion heat transport has a significant neoclassical contribution. The data analysis workflow is described in detail to understand how the variations of mapping and fitting of experimental data affect the power balance solution and subsequent flux-matching plasma profile predictions with the TGYRO solver. On average, the predicted plasma profiles are consistent with experimental data. However, the solutions are sensitive to various input parameters, including boundary conditions, and the electron-ion coupling. Linear gyrokinetic stability analysis demonstrates close agreement of the real frequencies of unstable modes between TGLF and CGYRO gyrokinetic simulations, but higher growth rates are predicted by TGLF, especially for the H-mode case. Estimates of the low-k modes’ contributions to the total flux are consistent with linear stability analysis and the E × B suppression of turbulence in TGLF simulations with the SAT1 saturation model, while the SAT2 saturation model over-predicts the low-k modes’ contribution in the H-mode case. Moreover, the results with SAT1 model are consistent with power balance analysis, which indicates only neoclassical ion energy fluxes inside ρ < 0.4 in the L-mode case and ρ⩽0.7 in the H-mode case. The presence of multi-scale turbulence and ion-scale driven zonal flow mixing effects are also observed in TGLF scans of the electron turbulent heat flux over a range of temperature gradients and the electron-ion temperature ratio, which could explain the strong model sensitivity to variations of input parameters.

Constructing precisely quasi-isodynamic magnetic fields

We present a novel method for numerically finding quasi-isodynamic stellarator magnetic fields with excellent fast-particle confinement and extremely small neoclassical transport. The method works particularly well in configurations with only one field period. We examine the properties of these newfound quasi-isodynamic configurations, including their transport coefficients, particle confinement and available energy for trapped-electron-instability-driven turbulence, as well as the degree to which they change when a finite pressure profile is added. We finally discuss the differences between the magnetic axes of the optimized solutions and their respective initial conditions, and conclude with the prospects for future quasi-isodynamic optimization.

Algebraic and numerical studies on the roles of momentum conservation and self-adjointness in moment-based neoclassical particle fluxes

Algebraic and numerical studies on the roles of momentum conservation and self-adjointness in moment-based neoclassical particle fluxes

Self-consistent gyrokinetic modeling of turbulent and neoclassical tungsten transport in toroidally rotating plasmas

The effect of toroidal rotation on both turbulent and neoclassical transport of tungsten (W) in tokamaks is investigated using the flux-driven, global, nonlinear 5D gyrokinetic code GYSELA. Nonlinear simulations are carried out with different levels of momentum injection that drive W into the supersonic regime, while the toroidal velocity of the main ions remains in the subsonic regime. The numerical simulations demonstrate that toroidal rotation induces centrifugal forces that cause W to accumulate in the outboard region, generating an in–out poloidal asymmetry. This asymmetry enhances neoclassical inward convection, which can lead to central accumulation of W in cases of strong plasma rotation. The core accumulation of W is mainly driven by inward neoclassical convection. However, as momentum injection continues, roto-diffusion, proportional to the radial gradient of the toroidal velocity, becomes significant and generates outward turbulent flux in the case of ion temperature gradient turbulence. Overall, the numerical results from nonlinear GYSELA simulations are in qualitative agreement with the theoretical predictions for impurity transport.

Development of compact tokamak fusion reactor use cases to inform future transport studies

The OMFIT STEP (Meneghini et al., Nucl. Fusion, vol. 10, 2020, p. 1088) workflow has been used to develop inductive and steady-state H-mode core plasma scenario use cases for a $B_0 = 8 \, {\rm T}$ , $R_0 = 4 \, {\rm m}$ machine to help guide and inform future higher-fidelity studies of core transport and confinement in compact tokamak reactors. Both use cases are designed to produce 200 MW or more of net electric power in an up-down symmetric plasma with minor radius $a = 1.4 \, {\rm m}$ , elongation $\kappa = 2.0$ , triangularity $\delta = 0.5$ and effective charge $Z_{{\rm eff}} \simeq 2$ . Additional considerations based on the need for compatibility of the core with reactor-relevant power exhaust solutions and external actuators were used to guide and constrain the use case development. An extensive characterization of core transport in both scenarios is presented, the most important feature of which is the extreme sensitivity of the results to the quantitative stiffness level of the transport model used as well as the predicted critical gradients. This sensitivity is shown to arise from different levels of transport stiffness exhibited by the models, combined with the gyroBohm-normalized fluxes of the predictions being an order of magnitude larger than other H-mode plasmas. Additionally, it is shown that although heating in both plasmas is predominantly to the electrons and collisionality is low, the plasmas remain sufficiently well coupled for the ions to carry a significant fraction of the thermal transport. As neoclassical transport is negligible in these conditions, this situation inherently requires long-wavelength ion gyroradius-scale turbulence to be the dominant transport mechanism in both plasmas. These results are combined with other basic considerations to propose a simple heuristic model of transport in reactor-relevant plasmas, along with simple metrics to quantify coupling and core transport properties across burning and non-burning plasmas.

Poloidal impurity asymmetries, flow and neoclassical transport in pedestals in the plateau and banana regimes

Charge exchange recombination spectroscopy (CXRS) measures the radial electric field in the pedestal by measuring the impurity density, temperature and flow. Combined outboard and inboard CXRS measurements allow poloidal variations that arise due to the poloidal variation of the magnetic field to be determined. At present, impurity neoclassical pedestal models avoid the complications of treating finite poloidal gyroradius effects by assuming the impurity charge number is large compared with the main ion charge number. These models are extended slightly by retaining the impurity radial pressure gradient to demonstrate that no substantial effect occurs due to impurity diamagnetic effects. More importantly, the neoclassical model is significantly extended to obtain a more comprehensive treatment of the main ions in the plateau and banana regimes. A parallel impurity momentum equation is derived that is consistent with previous results in the banana regime and reduces to the proper large aspect ratio form required in the plateau regime. The implications for interpreting the CXRS measurements are discussed by writing all results in terms of the gradient drive and poloidal flow.

Gyrokinetic simulations of neoclassical electron transport and bootstrap current generation in tokamak plasmas in the TRIMEG code

For magnetic confinement fusion in tokamak plasmas, some of the limitations to the particle and energy confinement times are caused by turbulence and collisions between particles in toroidal geometry, which determine the “anomalous” and the neoclassical transport, respectively. Neoclassical effects are also responsible for the intrinsically generated bootstrap current, and only the self-consistent modeling of neoclassical and turbulent processes can ultimately give accurate predictive results. In this work, we focus on the implementation of neoclassical physics in the gyrokinetic code TRIMEG, which is a TRIangular MEsh-based Gyrokinetic code that can handle both the closed and open field line geometries of a divertor tokamak. We report on the implementation of a simplified Lorentz collision operator in TRIMEG. For comparison with neoclassical theory, the calculation of flux surface averages is necessary. Since the code uses an unstructured mesh, a procedure for calculating the flux surface averages of particle and energy fluxes and the bootstrap current is derived without relying on the poloidal coordinate, which is useful also for other simulations in unstructured meshes. With the newly implemented collision operator, we study electron transport and bootstrap current generation in a plasma with a finite density gradient but uniform temperature for various simplified and realistic geometries. Compared with neoclassical theory, good agreement is obtained for the large aspect ratio case regarding the particle and energy fluxes as well as the bootstrap current. However, some discrepancies are observed at moderate aspect ratio and for a case with the realistic geometry of the ASDEX Upgrade tokamak. These deviations can be explained by different treatments and approximations in theory and simulation. In this paper, we demonstrate the capability to calculate the electron transport and bootstrap current generation in TRIMEG, which will allow for the self-consistent inclusion of neoclassical effects in gyrokinetic simulations in the future.

Implementation and verification of a model linearized multi-species collision operator in the COGENT code

We implement the multi-species linearized model collision operator, based on the approach proposed by Kolesnikov [1], in the full-f continuum gyrokinetic code COGENT [2]. We describe the operator and use it in several COGENT simulations of highly collisional plasmas. We analyze simulation results with the Braginskii fluid model [3] to illustrate that COGENT recovers both friction and thermal forces. Finally, we simulate the neoclassical transport of heavy impurities with COGENT and illustrate agreement with previously published [4] theoretical results.

Neoclassical transport in strong gradient regions of large aspect ratio tokamaks

We present a new neoclassical transport model for large aspect ratio tokamaks where the gradient scale lengths are of the size of the ion poloidal gyroradius. Previous work on neoclassical transport across transport barriers assumed large density and potential gradients but a small temperature gradient, or neglected the gradient of the mean parallel flow. Using large aspect ratio and low collisionality expansions, we relax these restrictive assumptions. We define a new set of variables based on conserved quantities, which simplifies the drift kinetic equation whilst keeping strong gradients, and derive equations describing the transport of particles, parallel momentum and energy by ions in the banana regime. The poloidally varying parts of density and electric potential are included. Studying contributions from both passing and trapped particles, we show that the resulting transport is dominated by trapped particles. We find that a non-zero neoclassical particle flux requires parallel momentum input which could be provided through interaction with turbulence or impurities. We derive upper and lower bounds for the energy flux across a transport barrier in both temperature and density and present example profiles and fluxes.

First-principles based plasma profile predictions for optimized stellarators

In the present Letter, first-of-its-kind computer simulations predicting plasma profiles for modern optimized stellarators—while self-consistently retaining neoclassical transport, turbulent transport with 3D effects, and external physical sources—are presented. These simulations exploit a newly developed coupling framework involving the global gyrokinetic turbulence code GENE-3D, the neoclassical transport code KNOSOS, and the 1D transport solver TANGO. This framework is used to analyze the recently observed degradation of energy confinement in electron-heated plasmas in the Wendelstein 7-X stellarator, where the central ion temperature was ‘clamped’ to keV regardless of the external heating power. By performing first-principles based simulations, we provide key evidence to understand this effect, namely the inefficient thermal coupling between electrons and ions in a turbulence-dominated regime, which is exacerbated by the large ratios, and show that a more efficient ion heat source, such as direct ion heating, will increase the on-axis ion temperature. This work paves the way towards the use of high-fidelity models for the development of the next generation of stellarators, in which neoclassical and turbulent transport are optimized simultaneously.

ON THE PHYSICAL PARAMETERS OF THE STELLARATOR – SOURCE OF NEUTRONS WITH NEOCLASSICAL LOSSES, TAKING INTO ACCOUNT RECYCLING AND BOHM LOSSES

The results of calculations of the physical parameters of the stellarator used as a neutron source for initiating nuclear reactions in a blanket of a hybrid reactor are presented. The calculations were carried out assuming the implementation of neoclassical transport processes, taking into account recycling and Bohm losses. The crushing effect of Bohm diffusion on the results of neutron yields is shown.

Enhancement of neoclassical impurity density up/down asymmetry and Pfirsch–Schlüter transport due to the plasma elongation in the tokamak plasmas

The standard neoclassical theory of the impurity transport in tokamak plasma is improved by including the plasma elongation effect. The neoclassical up/down asymmetry of the impurity density is largely enhanced by the plasma elongation and is under-predicted by the neoclassical theory with the circular cross section assumption. Accordingly, the impurity Pfirsch–Schlüter neoclassical transport is also enhanced by the plasma elongation.

Analytical model for the combined effects of rotation and collisionality on neoclassical impurity transport

The influence of rotation, collisionality and trapped particle fraction on the magnitude and direction of neoclassical impurity transport in tokamaks is analyzed using an extensive database of drift-kinetic simulations with the NEO code. It is shown that an operational window opens at sufficiently high Mach number and low collisionality, where the magnitude of the temperature screening of impurities increases with higher rotation. If the collisionality increases, this effect is quickly lost and the temperature gradient then drives an inward impurity flux when rotation is present. The boundary between these two regimes is calculated as a function of the trapped particle fraction, and it is shown that plasma parameters achieved in recent JET experiments allow them to access the new beneficial regime, in accordance with observations of reduced tungsten accumulation. Applications to ASDEX Upgrade experiments where these effects become relevant are also presented, and the implications for ITER are discussed. A method for extracting the physically distinct Pfirsch–Schlüter (PS) and banana-plateau (BP) neoclassical flux components from the NEO output is introduced and employed to construct a model that describes them analytically at arbitrary rotation and collisionality. The beneficial behavior of the screening with rotation is found to be a BP effect, in contrast to the known detrimental role of rotation in the PS component. The new analytical model is able to reproduce the results of NEO when modeling radial profiles of transport coefficients from experimental kinetic profiles, with the added feature of isolating the BP and PS components for additional physical analysis, while remaining well suited for fast applications.

Isotope mass dependence of pedestal transport in JET H-mode plasmas

We present a comparative transport analysis of the isotope mass dependence in the pedestal of two pairs of deuterium/hydrogen type I ELMy H-mode discharges in JET with ITER-like wall, one characterized by the same input power, the other one by the same stored energy. The investigation, carried out using the gyrokinetic code GENE, focuses on the steep profile region of the pedestal. While large wavenumber modes mainly contribute to the electron heat flux and are scarcely influenced by the main gas isotope, an effect of the ion mass in agreement with the experimental (so called anti-gyro-Bohm) scaling is revealed in the low wavenumber range. In this context, the major role played by the shear in regulating the ion-temperature-gradient turbulence is analyzed in some detail. The competing level of turbulent and neoclassical transport is quantified to shed light on the experimental features of the pedestal profiles at different ion mass, with the particle transport found to be consistent with a higher pedestal top density for increasing isotope masses, and the heat transport shown to match the roughly unaltered observed temperature profiles.

Effects of bootstrap current on magnetic configuration in Chinese first quasi-axisymmetric stellarator

Neoclassical properties in quasi-axisymmetric (QA) stellarators are analogous to these in tokamaks. Consequently, a substantial bootstrap current could significantly modify the MHD equilibrium properties of a QA stellarator, which is an important characteristic in this type of stellarator. This paper is dedicated to systemically investigate the effects of bootstrap current on the magnetic configuration in Chinese first quasi-axisymmetric stellarator (CFQS). For the first time, self-consistent bootstrap currents in free-boundary equilibria are calculated with an accurate Fokker–Planck neoclassical numerical mode in CFQS. Several important results are achieved: (a) as the bootstrap current grows with increasing volume-averaged normalized pressure , magnetic shear develops in the bulk plasma and meanwhile, a deep magnetic well is robustly sustained, which leads to improved stabilization of interchange modes up to . (b) In the analysis of global ideal MHD instability, as the bootstrap current rises to 39 kA (), external kink modes become destabilized and the unstable mode with m/n = 2/1 is dominant. (c) From to 1.5%, the bootstrap current hardly changes the QA property and a low neoclassical transport is maintained. However, as is enhanced beyond 2.0%, the substantial bootstrap current gives rise to an increase of non-QA magnetic field components, which weakens the neoclassical transport properties. (d) An increase of the negative magnetic shear at the core region by the bootstrap currents has a favorable effect on the properties of J (second adiabatic invariant). The maximum-J region can be extended by raising bootstrap currents.

ITB formation in gyrokinetic flux-driven ITG/TEM turbulence

The formation mechanism of internal transport barriers (ITBs) in flux-driven turbulence is studied by means of the full-f gyrokinetic code GKNET. In the adiabatic electron case with a weak magnetic shear configuration, toroidal momentum injection can change the radial mean electric field through radial force balance, leading to a kind of driven ITB formation in which the ion thermal diffusivity by ion temperature gradient (ITG) turbulence decreases to the neoclassical transport level. Only cocurrent toroidal rotation in the outer core region can benefit the ITB formation, and this mechanism is identified to originate from a positive feedback loop between the radial shear and resultant momentum flux. On the other hand, in the kinetic electron case with a reversed magnetic shear configuration, robust co-intrinsic rotation is driven near the surface in ITG turbulence and sustains the shear through the radial force balance, leading to the spontaneous reduction of ion turbulent thermal diffusivity, while this is not observed in the adiabatic electron case. In the presence of electron heating, counter-intrinsic rotation by trapped electron mode turbulence is selectively driven in the negative magnetic shear region, which provides steeper shear formation and a resultant larger reduction of ion turbulent thermal diffusivity. This indicates that the co-existence of different modes can trigger the ‘discontinuity’ of mode structure, intrinsic rotation, and resultant mean near , leading to spontaneous ITB formation.

NON-AXISYMMETRIC NEOCLASSICAL TRANSPORT FROM MIS-ALIGNMENT OF EQUIPOTENTIAL AND MAGNETIC SURFACES

Coefficients of neoclassical transport in tokamaks and stellarators with non-axisymmetric equipotential surfaces mis-aligned with magnetic flux surfaces are derived for the 1/ν regime. In the general case, they are given by integral expressions including field line integrals similar to those defining the effective helical ripple [V.V. Nemov et al. // Phys. Plasmas. 1999, v. 6, p. 4622]. For small mis-alignments in a tokamak with a simplified geometry, they are reduced to simple analytical expressions.

How to evaluate neoclassical transport coefficients by a single δf simulation

The δf method is extended to calculate all possible components of neoclassical transport matrices, including non-diagonal components and interspecies components of any species combinations in an arbitrary magnetic field configuration, by a single simulation. The method is implemented in a global neoclassical code FORTEC-3D and applied to cases of multi-ion species plasmas in a tokamak and a helical configuration, respectively. The results are benchmarked against analytic solutions and local simulation results. It is found that the results obtained with the newly developed method provide reliable solutions that satisfy the Onsager symmetry relation as well as the intrinsic ambipolarity in a tokamak configuration.

Plasma Instability During ITBs Formation with Pellet Injection in Tokamak

JET H-mode plasma discharge 53212 simulation during the pellet fueling operation in the presence of an internal transport barrier is carried out using the 1.5D BALDUR integrated predictive modelling code. The plasma instability during ITB formation with pellet injection in a tokamak is investigated. These simulations use a neoclassical transport model and an anomalous transport model (either multimode or mixed Bohm/gyro-Bohm core transport model). The boundary condition is described at the top of the pedestal, which is calculated theoretically based on a combination of magnetic and flow shear stabilization pedestal width scaling and an infinite-n ballooning pressure gradient model. The toroidal flow calculation is based on the neoclassical viscosity toroidal velocity model. It was found that the shallower pellet does not destroy the ITB, which locating mainly between r/a = 0.8 and 0.9. Moreover, in the plasma center region (0.4&lt;r/a&lt;0.6) the effective electron thermal diffusivities do not change during the ablation time. However, the effective electron thermal diffusivities decrease after pellet ablation, which means a shallower pellet can improve the internal transport barrier.