Structure-preserving algorithms for guiding center dynamics based on the slow manifold of classical Pauli particle

The classical Pauli particle(CPP) serves as a slow manifold, substituting the conventional guiding center dynamics. Based on the CPP, we utilize the averaged vector field(AVF) method in the computations of drift orbits. Demonstrating significantly higher efficiency, this advanced method is capable of accomplishing the simulation in less than one-third of the time of directly computing the guiding center motion. In contrast to the CPP-based Boris algorithm, this approach inherits the advantages of the AVF method, yielding stable trajectories even achieved with a tenfold time step and reducing the energy error by two orders of magnitude. By comparing these two CPP algorithms with the traditional RK4 method, the numerical results indicate a remarkable performance in terms of both the computational efficiency and error elimination. Moreover, we verify the properties of slow manifold integrators and successfully observe the bounce on both sides of the limiting slow manifold with deliberately chosen perturbed initial conditions. To evaluate the practical value of the methods, we conduct simulations in non-axisymmetric perturbation magnetic fields as part of the experiments,demonstrating that our CPP-based AVF method can handle simulations under complex magnetic field configurations with high accuracy, which the CPP-based Boris algorithm lacks. Through numerical experiments, we demonstrate that the CPP can replace guiding center dynamics in using energy-preserving algorithms for computations, providing a new, efficient, as well as stable approach for applying structure-preserving algorithms in plasma simulations.

Simulation of charge-exchange induced NBI losses on EAST

The neutral beam injection is widely adopted in tokamaks as a key heating tool,playing a crucial role in generating burning plasmas.However,the loss of beam ions can damage the first wall and reduce the heating efficiency,resulting in failure to maintain steady-state conditions.In this work,the effect of neutral particles in the edge on fast ions generated by NBI in the Experimental Advanced Superconducting Tokamak(EAST)device is studied using the particle tracer code(PTC).The poloidal distribution of neutral particles is calculated by edge plasma simulation code SOLPS-ITER.In this simulation,four beam lines in EAST are considered:co-current tangential(co-tang),co-current perpendicular(co-perp),counter-current tangential(ctr-tang)and counter-current perpendicular(ctr-perp).It is shown that,in the absence of neutral particles,the loss fraction of ctr-injection is considerably higher than that of the co-injection.When considering the neutral particles,it is found that the ctr-perp injection demonstrates a significant variation in particles loss fraction(ranging from 18.56%to 25.42%)compared to the other three injection configurations.In terms of the loss fraction induced by neutral particles,ctr-injection exceeds co-injection,and perpendicular configuration exceeds tangential configuration.Furthermore,the difference of charge exchange ratios of three different energy(full energy,half energy,one third energy)of the four injections can be attributed to variations in the poloidal trajectories associated with each of these injections.Moreover,approximately half of fast ions which undergo neutralization directly lose to the first wall while the rest re-enter the bulk plasma and re-ionize.Except for the ctr-tang injection,the reionization ions from the other three injections exhibit effective confinement.

Effects of sawtooth heat pulses on edge flows and turbulence in a tokamak plasma

Enhancements of edge zonal flows,radial electric fields,and turbulence are observed in electron cyclotron resonance heating-heated plasmas(Zhao et al 2013 Nucl.Fusion 53083011).In this paper,the effects of sawtooth heat pulses on flows and turbulence are presented.These experiments are performed using multiple Langmuir probe arrays in the edge plasmas of the HL-2A tokamak.The edge zonal flows,radial electric fields,and turbulence are all enhanced by sawteeth.Propagation of the zonal flow and turbulence intensities is also observed.The delay time of the maximal intensity of the electric fields,zonal flows,and turbulence with respect to the sawtooth crashes is estimated as~1 ms and comparable to that of the sawtooth-triggered intermediate phases.Not only the zonal flows but also the radial electric fields lag behind the turbulence.Furthermore,the intensities of both the zonal flows and electric fields nearly linearly increase/decrease with the increase/decrease of the turbulence intensity.A double-source predator-prey model analysis suggests that a relatively strong turbulence source may contribute to the dominant zonal flow formation during sawtooth cycles.

Role of the zonal flow in multi-scale multi-mode turbulence with small-scale shear flow in tokamak plasmas

The structural characteristics of zonal flows and their roles in the nonlinear interaction of multi-scale multi-mode turbulence are investigated numerically via a self-consistent Landau-fluid model.The multi-mode turbulence here is composed of a shorter wavelength electromagnetic(EM)ion temperature gradient(ITG)mode and a Kelvin-Helmholtz(KH)instability with long wavelengths excited by externally imposed small-scale shear flows.For strong shear flow,a prominent periodic intermittency of fluctuation intensity except for dominant ITG component is revealed in turbulence evolution,which onset time depends on the ion temperature gradient and the shear flow amplitudes corresponding to different KH instabilities.It is identified that the intermittency phenomenon results from the zonal flow dynamics,which is mainly generated by the KH mode and back-reacts on it.It is demonstrated that the odd symmetric components of zonal flow(same symmetry as the external flow)make the radial parity of the KH mode alteration through adjusting the drift velocities at two sides of the resonant surface so that the KH mode becomes bursty first.Afterwards,the ITG intermittency follows due to nonlinear mode coupling.Parametric dependences of the features of the intermittency are elaborated.Finally,associated turbulent heat transport is evaluated.

Application of Galerkin spectral method for tearing mode instability

Magnetic reconnection and tearing mode instability play a critical role in many physical processes.The application of Galerkin spectral method for tearing mode instability in two-dimensional geometry is investigated in this paper.A resistive magnetohydrodynamic code is developed,by the Galerkin spectral method both in the periodic and aperiodic directions.Spectral schemes are provided for global modes and local modes.Mode structures,resistivity scaling,convergence and stability of tearing modes are discussed.The effectiveness of the code is demonstrated,and the computational results are compared with the results using Galerkin spectral method only in the periodic direction.The numerical results show that the code using Galerkin spectral method individually allows larger time step in global and local modes simulations,and has better convergence in global modes simulations.

Interaction between energetic-ions and internal kink modes in a weak shear tokamak plasma

Based on the conventional tokamak HL-2 A-like parameters and profiles,the linear properties and the nonlinear dynamics of non-resonant kink mode(NRK)and non-resonant fishbone instability(NRFB)in reversed shear tokamak plasmas are investigated by using the global hybrid kinetic-magnetohydrodynamic nonlinear code M3 D-K.This work mainly focuses on the effect of passing energetic-ions on the NRK and NRFB instabilities,which is different from the previous works.It is demonstrated that the NRFB can be destabilized by the passing energeticions when the energetic-ion betaβ;exceeds a critical value.The transition from NRK to NRFB occurs when the energetic-ion betaβ;increases to above a critical value.The resonance condition responsible for the excitation of NRFB is interestingly found to be satisfied atω;+ω;≈ω,whereω;is the toroidal motion frequency,ω;is the poloidal motion frequency andωis the mode frequency.The nonlinear evolutions of NRFB’s mode structures and Poincaréplots are also analyzed in this work and it is found that the NRFB can induce evident energeticion loss/redistribution,which can degrade the performance of the plasmas.These findings are conducive to understanding the mechanisms of NRFB induced energetic-ion loss/redistribution through nonlinear wave-particle interaction.

Analysis of anomalous transport based on radial fractional diffusion equation

Anomalous transport in magnetically confined plasmas is investigated by radial fractional transport equations.It is shown that for fractional transport models,hollow density profiles are formed and uphill transports can be observed regardless of whether the fractional diffusion coefficients(FDCs)are radially dependent or not.When a radially dependent FDC<D_(α)(r)1 is imposed,compared with the case under=D_(α)(r)1.0,it is observed that the position of the peak of the density profile is closer to the core.Further,it is found that when FDCs at the positions of source injections increase,the peak values of density profiles decrease.The non-local effect becomes significant as the order of fractional derivative a 1 and causes the uphill transport.However,as a 2,the fractional diffusion model returns to the standard model governed by Fick’s law.

Machine learning of turbulent transport in fusion plasmas with neural network

Turbulent transport resulting from drift waves,typically,the ion temperature gradient(ITG)mode and trapped electron mode(TEM),is of great significance in magnetic confinement fusion.It is also well known that turbulence simulation is a challenging issue in both the complex physical model and huge CPU cost as well as long computation time.In this work,a credible turbulence transport prediction model,extended fluid code(ExFC-NN),based on a neural network(NN)approach is established using simulation data by performing an ExFC,in which multi-scale multi-mode fluctuations,such as ITG and TEM turbulence are involved.Results show that the characteristics of turbulent transport can be successfully predicted including the type of dominant turbulence and the radial averaged fluxes under any set of local gradient parameters.Furthermore,a global NN model can well reproduce the radial profiles of turbulence perturbation intensities and fluxes much faster than existing codes.A large number of comparative predictions show that the newly constructed NN model can realize rapid experimental analysis and provide reference data for experimental parameter design in the future.

Magnetic-island-induced ion temperature gradient mode： Landau damping, equilibrium magnetic shear and pressure flattening effects

Characteristics of the magnetic-island-induced ion temperature gradient （MITG） mode are studied through gyrofluid simulations in the slab geometry, focusing on the effects of Landau damping, equilibrium magnetic shear （EMS）, and pressure flattening. It is shown that the magnetic island may enhance the Landau damping of the system by inducing the radial magnetic field. Moreover, the radial eigenmode numbers of most MITG poloidal harmonics are increased by the magnetic island so that the MITG mode is destabilized in the low EMS regime. In addition, the pressure profile flattening effect inside a magnetic island hardly affects the growth of the whole MITG mode, while it has different local effects near the O-point and the X-point regions. In comparison with the non-zero-order perturbations, only the quasi-linear flattening effect due to the zonal pressure is the effective component to impact the growth rate of the mode.

Effects of plasma radiation on the nonlinear evolution of neo-classical tearing modes in tokamak plasmas

The effects of plasma radiation on the nonlinear evolution of neo-classical tearing modes are investigated based on a set of reduced magnetohydrodynamic equations.It is found that the radiation can reduce the pressure near the rational surface.During the nonlinear evolution,the magnitude of perturbed bootstrap current is drastically enhanced in the presence of the radiation.Besides,the radiation can increase the growth rate of the magnetic islands by diminishing the pressure,such that the magnetic islands do not saturate compared with that without radiation.On the other hand,with the increase of the ratio of parallel to perpendicular transport coefficientχ‖/χ⊥,the reduction of pressure can further increase the growth rate of magnetic islands in the presence of plasma radiation.Finally,the mechanisms of the destabilizing effects driven by the radiation are discussed in detail as well.

A brief review:effects of resonant magnetic perturbation on classical and neoclassical tearing modes in tokamaks

This paper reviews the effects of resonant magnetic perturbation(RMP)on classical tearing modes(TMs)and neoclassical tearing modes(NTMs)from the theory,experimental discovery and numerical results with a focus on four major aspects:(i)mode mitigation,where the TM/NTM is totally suppressed or partly mitigated by the use of RMP;(ii)mode penetration,which means a linearly stable TM/NTM triggered by the externally applied RMP;(iii)mode locking,namely an existing rotating magnetic island braked and finally stopped by the RMP;(iv)mode unlocking,as the name suggests,it is the reverse of the mode locking process.The key mechanism and physical picture of above phenomena are revealed and summarized.

Influence of toroidal rotation on the tearing mode in tokamak plasmas

The stabilizing mechanism of toroidal rotation on the tearing mode is studied using the 3 D toroidal resistive magnetohydrodynamic code M3 D.It is found that the dominating mechanism,either the centrifugal effect or the Coriolis effect, depends on the specific pressure β and rotation frequency Ω.On the premise that Ω is sufficiently large, when β is greater than a critical value,the effect of the centrifugal force is dominant, and the stabilizing effect mainly comes from the modification of equilibrium induced by the centrifugal force;when β is less than a critical value,the stabilizing effect from the Coriolis force overcomes that from the centrifugal force.However,if Ω is small, then the effect of equilibrium modification due to the centrifugal force is not significant even if β is large.Finally, the results showed that toroidal rotation shear enhances the stabilizing effect.

Interaction between the core and the edge for ion cyclotron resonance heating based on artificial absorption plasma model

In numerical simulations of the ion cyclotron range of frequencies(ICRF)wave heating scheme,core solvers usually focus on wave propagation and absorption mechanisms within the core plasma region.However,the realistic scrape-off layer(SOL)plasma is usually simplified,making it difficult to have deeper understanding of wave propagation and absorption within the SOL.In this work,we employ a cold plasma assumption and an artificial absorption mechanism based on the approach of reference(Zhang et al 2022 Nucl.Fusion 62076032),to study wave propagation and absorption in the realistic SOL plasma of the EAST.During the exponential decay of the total coupled power with respect to the toroidal mode numbers,several fluctuations are observed in the case of low collisional frequencies.The fluctuations may be caused by the cavity modes associated with specific toroidal mode numbers.Due to the presence of cut-off densities,the edge power losses and the total coupled power exhibit different behaviors before and after the cut-off layer is“open”.Furthermore,the simulation results obtained from the kinetic model in reference(Zhang et al 2022 Nucl.Fusion 62076032)is discussed.This suggests that both the core-edge combined model and the artificial mechanism are capable of simulating wave propagation and absorption.

Loss of energetic particles due to feedback control of resistive wall mode in HL-3

Effects of three-dimensional(3D)magnetic field perturbations due to feedback control of an unstable n=1(n is toroidal mode number)resistive wall mode(RWM)on the energetic particle(EP)losses are systematically investigated for the HL-3 tokamak.The MARS-F(Liu et al 2000 Phys.Plasmas 73681)code,facilitated by the test particle guiding center tracing module REORBIT,is utilized for the study.The RWM is found to generally produce no EP loss for cocurrent particles in HL-3.Assuming the same perturbation level at the sensor location for the close-loop system,feedback produces nearly the same loss of counter-current EPs compared to the open-loop case.Assuming however that the sensor signal is ten times smaller in the close-loop system than the open-loop counter part(reflecting the fact that the RWM is more stable with feedback),the counter-current EP loss is found significantly reduced in the former.Most of EP losses occur only for particles launched close to the plasma edge,while particles launched further away from the plasma boundary experience much less loss.The strike points of lost EPs on the HL-3 limiting surface become more scattered for particles launched closer to the plasma boundary.Taking into account the full gyro-orbit of particles while approaching the limiting surface,REORBIT finds slightly enhanced loss fraction.

Recent advances in high-β_(N) experiments and magnetohydrodynamic instabilities with hybrid scenarios in the HL-2A Tokamak

Over the past several years,high-β_(N) experiments have been carried out on HL-2A.The high-β_(N) is realized using double transport barriers(DTBs)with hybrid scenarios.A stationary high-β_(N) (>2)scenario was obtained by pure neutral-beam injection(NBI)heating.Transient high performance was also achieved,corresponding to β_(N)≥3,ne/ne_(G)∼0.6,H_(98)∼1.5,f_(bs)∼30%,q_(95)∼4.0,and𝐺∼0.4.The high-β_(N) scenario was successfully modeled using integrated simulation codes,that is,the one modeling framework for integrated tasks(OMFIT).In high-𝛽𝑁plasmas,magnetohydrodynamic(MHD)instabilities are abundant,including low-frequency global MHD oscilla-tion with n=1,high-frequency coherent mode(HCM)at the edge,and neoclassical tearing mode(NTM)and Alfvénic modes in the core.In some high-β_(N) discharges,it is observed that the NTMs with m/n=3/2 limit the growth of the plasma energy and decrease β_(N).The low-n global MHD oscillation is consistent with the coupling of destabilized internal(m/n=1/1)and external(m/n=3/1 or 4/1)modes,and plays a crucial role in triggering the onset of ELMs.Achieving high-β_(N) on HL-2A suggests that core-edge interplay is key to the plasma confinement enhancement mechanism.Experiments to enhance β_(N) will contribute to future plasma operation,such as international thermonuclear experimental reactor.