Nonlinear Generation of Zonal Fields by the Beta-Induced Alfvén Eigenmode in Tokamak

The zonal fields effect on the beta-induced Alfvén eigenmode (BAE) destabilized by the energetic particles in toroidal plasmas is studied through the gyrokinetic particle simulations. It is found that the localized zonal fields with a negative value around the mode rational surface are generated by the nonlinear BAE. In the weakly driven case, the zonal fields with a strong geodesic acoustic mode (GAM) component have weak effects on the nonlinear BAE evolution. In the strongly driven case, the zonal fields are dominated by a more significant zero frequency component and have stronger effects on the nonlinear BAE evolution.     

Turbulence-Driven Tearing Modes in Inhomogeneous Magnetized Plasma

The effects of density inhomogeneity in the nonlinear growth of tearing modes in the presence of background density, electrostatic and magnetic fluctuations are investigated. The nonlinear interaction is assumed to occur in the inner layer of the tearing mode, where the fields and their variations are greatest. Our results demonstrate that turbulence-generated dissipative effects replace the collisional resistivity as the driving force of the tearing mode. The inhomogeneity introduces a real frequency to the nonlinear tearing mode, as well as new unstable tearing-mode–related drift waves.     

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 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 53 083011).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 tu...     

Transition from fishbone mode to β-induced Alfvén eigenmode on HL-2A tokamak

In the presence of energetic particles(EPs) from auxiliary heating and burning plasmas, fishbone instability and Alfvén modes can be excited and their transition can take place in certain overlapping regimes. Using the hybrid kinetic-magnetohydrodynamic model in the NIMROD code, we have identified such a transition between the fishbone instability and the β-induced Alfvén eigenmode(BAE) for the NBI heated plasmas on HL-2 A. When the safety factor at magnetic axis is well below one, typical kink-fishbone transition occurs as the EP fraction increases. When q0 is raised to approaching one, the fishbone mode is replaced with BAE for sufficient amount of EPs. When q0 is slightly above one, the toroidicity-induced Alfvén eigenmode dominates at lower EP pressure, whereas BAE dominates at higher EP pressure.     

Flow Shear Stabilization of Ion Temperature Gradient Modes in an Internal Transport Barrier

Ion temperature gradient(ITG) driven instability is studied with gyro-kinetic theory in an internal transport barrier(ITB) of tokamak plasmas.The stabilization effects of a parallel velocity shear on the modes are investigated.It is found that the mode structures and stability properties,as well as the effects of a velocity shear,in an ITB are significantly different from that in off-ITB regions.     

Some nonlinear problems in transport theory

The integro-differential Boltzmann equation governing the diffusion of the particles of a mixture is formulated by incorporating the nonlinear effects due to the collisions of a same kind of particles between themselves. For the case of - cross sections the integral version of the original Boltzmann equation is derived, and the general features of the associated nonlinear evolution problem are discussed. A simple application of the theory is developed with regard to the problem of the heating of a plasma.     

Effects of resonant magnetic perturbations on radial electric fields in DIII-D tokamak

Gyrokinetic simulations of DIII-D tokamak equilibrium find that resonant magnetic perturbation (RMP) drives a neoclassical non-ambipolar electron particle flux, which causes a rapid change of equilibrium radial electric fields consistent with experimental observations during the suppression of the edge localized mode (ELM). The simulation results provide a support for the conjecture that RMP-induced changes of radial electric fields lead to the enhanced turbulent transport at the pedestal top during the ELM suppression (Taimourzadeh et al 2019 Nucl. Fusion 59 046005). Furthermore, gyrokinetic simulations of collisionless damping of zonal flows show that resonant responses to the RMP decrease the residual level of the zonal flows and damp the geodesic acoustic mode.     

Effects of resonant magnetic perturbations on radial electric fields in DⅢ-D tokamak

Gyrokinetic simulations of DⅢ-D tokamak equilibrium find that resonant magnetic perturbation(RMP) drives a neoclassical non-ambipolar electron particle flux,which causes a rapid change of equilibrium radial electric fields consistent with experimental observations during the suppression of the edge localized mode (ELM).The simulation results provide a support for the conjecture that RMP-induced changes of radial electric fields lead to the enhanced turbulent transport at the pedestal top during the ELM suppression (Taimourzadeh et a12019 Nucl.Fusion 59046005).Furthermore,gyrokinetic simulations of collisionless damping of zonal flows show that resonant responses to the RMP decrease the residual level of the zonal flows and damp the geodesic acoustic mode.     

A brief review: experimental investigation of zonal flows and geodesic acoustic modes in fusion plasmas

Zonal flows self-generated by turbulence play an important role in regulating turbulence, reducing transport level, and thus improve plasma confinement in fusion plasmas. The zonal flows and geodesic acoustic modes have been identified in various devices. The related issues, such as the poloidal and toroidal symmetries, coupling to turbulence, effects on turbulence and transport, nonlinear energy transfer between turbulence and zonal flows, dependence of the plasma parameters, roles in the confinement regime transitions etc are overviewed briefly in this paper. The interaction between zonal flows and magnetic islands is emphasized.     

Sawtooth-like oscillations and steady states caused by the m/n = 2/1 double tearing mode

The sawtooth-like oscillations resulting from thedouble tearing mode (DTM) are numerically investigated through the three-dimensional, toroidal, nonlinear resistive-MHD code (CLT). We find that the nonlinear evolution of theDTM can lead to sawtooth-like oscillations, which are similar to those driven by the kink mode. The perpendicular thermal conductivity and the external heating rate can significantly alter the behaviors of the DTM driven sawtooth-like oscillations. With a high perpendicular thermal conductivity, the system quickly evolves into a steady state withmagnetic islands and helical flow. However, with a low perpendicular thermal conductivity, the system tends to exhibit sawtooth-like oscillations. With a sufficiently high or low heating rate, the system exhibits sawtooth-like oscillations, while with an intermediate heating rate, the system quickly evolves into a steady state. At the steady state, there exist the non-axisymmetric magnetic field and strong radial flow, and both are with helicity ofLike the steady state withradial flow, which is beneficial for preventing the helium ash accumulation in the core, the steady state withradial flow might also be a good candidate for the advanced steady state operations in future fusion reactors. We also find that the behaviors of the sawtooth-like oscillations are almost independent of tokamak geometry, which implies that the steady state with saturatedislands might exist in different tokamaks.     

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 coefficient ${\chi }_{\parallel }/{\chi }_{\perp },$ 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.     

Kinetic Theories of Geodesic Acoustic Modes: Radial Structure,Linear Excitation by Energetic Particles and Nonlinear Saturation

Geodesic Acoustic Modes (GAMs) are oscillating zonal mode structures unique to toroidal plasmas and are capable of regulating microscopic turbulence and associated transports. In this paper, we investigate three important aspects of GAM dynamics: (1) GAM continuous spectrum and its mode conversion to kinetic GAM (KGAM); (2) linear excitation of energetic particle induced GAM (EGAM) and its coupling to the GAM continuum, and (3) nonlinear saturation of EGAM via wave particle trapping. The analogy between the GAM-EGAM dynamics and the well known beam-plasma instability is also discussed.     

Impact of the mass isotope on plasma confinement and transport properties in the HL-2A tokamak

The impact of the mass isotope on plasma confinement and transport properties has been investigated in Ohmically-heated hydrogen and deuterium plasmas in the HL-2A tokamak. Experimental results show that under similar discharge parameters the deuterium plasma has better confinement and lower turbulent transport than the hydrogen one, and concomitantly, it is found that the magnitude of geodesic acoustic mode zonal flows, the tilting angle of the Reynolds stress tensor and the turbulence correlation lengths are all larger in the edge region of the deuterium plasma. The results provide direct experimental evidence on the importance of the nonlinear energy coupling between ambient turbulence and zonal flows for governing the isotope effects in fusion plasmas.     

Tokamak Plasma Flows Induced by Local RF Forces

The tokamak plasma flows induced by the local radio frequency(RF) forces in the core region are analyzed. The effective components of local RF forces are composed of the momentum absorption term and the resonant parallel momentum transport term(i.e. the parallel component of the resonant ponderomotive forces). Different momentum balance relations are employed to calculate the plasma flows depending on different assumptions of momentum transport.With the RF fields solved from RF simulation codes, the toroidal and poloidal flows by these forces under the lower hybrid current drive and the mode conversion ion cyclotron resonance heating on EAST-like plasmas are evaluated.     

托卡马克等离子体中快粒子触发的高频鱼骨模不稳定性研究

本文考虑托卡马克等离子体中快粒子的空间密度分布剖面,在中性束及电子回旋共振加热的条件下,建立了研究鱼骨模的色散关系并对鱼骨模作了数值研究。结果表明:快粒子对内扭曲模有致稳作用,且在近轴加热条件下可激发高频鱼骨模,其频率与快粒子的环向进动频率一致。鱼骨模的增长率与快粒子的密度梯度有关,一般随密度梯度的增加而增大。在高比压区间,勉强通行快粒子可驱动鱼骨模进入第二稳定区,在该区域鱼骨模是稳定的。     

Wave-Number Spectral Characteristics of Drift Wave Micro-Turbulence with Large-Scale Structures

Wave-number spectral characteristics of drift wave micro-turbulence with large-scale structures (LSSs) including zonal flows (ZFs) and Kelvin-Holmheltz (KH) mode are investigated based on three dimensional gyrofluid simulations in a slab geometry. The focus is on the property of the wave-number spectral scaling law of the ambient turbulence under the back reaction of the self-generated LSSs. A comparison of the spectral scaling laws between ion/electron temperature gradient (ITG/ETG) driven turbulences is presented. It is shown that the spectral scaling of the ITG turbulence with robust ZFs are fitted well by an exponential-law function in and a power-law one in . However, the ETG turbulence is characterized by a mixing Kolmogorov-like power-law and exponential-law scaling for both and spectra due to the ZFs and KH mode dynamics, with and the slope index factors. The underlying physical mechanism is understood as the spectral scattering caused by the back-reaction of the LSSs on the ambient turbulence. These findings may provide helpful guideline to diagnose the plasma fluctuations and flow structures in experiments.     

Review of the experiments for energetic particle physics on HL-2A

This paper reviews the energetic particle(EP) experiments during electron cyclotron resonance heating(ECRH) and neutral beam injection in the HL-2 A tokamak.A number of important results are summarized,which relate to ITER physics,including the behavior of the multi-mode instability,the nonlinear interaction between wave–wave and wave–particles,the losses of EP induced by the instabilities,the effect of the EP instabilities on the thermal plasma confinement and the control of the EP instabilities by means of ECRH.Systematic experiments indicate that when the drive is great enough,the nonlinear effects and the multi-mode coexistence may play an important role,which affect the transport both of the EPs and the background plasma confinement,and these instabilities could be controlled.Some new phenomena about the EP induced instabilities discovered recently on the device,such as high frequency reversed shear Alfvén eigenmodes,Alfvénic ion temperature gradient modes,the geodesic acoustic mode induced by energetic electrons excited by interaction between tearing mode and beta induced Alfvén eigenmode and double e-fishbone in negative magnetic shear discharges etc,have also been presented in the paper.     

Prompt acceleration of a μ+ beam in a toroidal wakefield driven by a shaped steep-rising-front Laguerre–Gaussian laser pulse

Recent experimental data for anomalous magnetic moments strongly indicates the existence of new physics beyond the Standard Model. Energetic μ⁺ bunches are relevant to μ⁺ rare decay, spin rotation, resonance and relaxation (μSR) technology, future muon colliders, and neutrino factories. In this paper, we propose prompt μ⁺ acceleration in a nonlinear toroidal wakefield driven by a shaped steep-rising-front Laguerre–Gaussian (LG) laser pulse. An analytical model is described, which shows that a μ⁺ beam can be focused by an electron cylinder at the centerline of a toroidal bubble and accelerated by the front part of the longitudinal wakefield. A shaped LG laser with a short rise time can push plasma electrons, generating a higher-density electron sheath at the front of the bubble, which can enhance the acceleration field. The acceleration field driven by the shaped steep-rising-front LG laser pulse is about four times greater than that driven by a normal LG laser pulse. Our simulation results show that a 300 MeV μ⁺ bunch can be accelerated to 2 GeV and its transverse size is focused from an initial value of w₀ = 5 μm to w = 2 μm in the toroidal bubble driven by the shaped steep-rising-front LG laser pulse with a normalized amplitude of a = 22.     

用于预测带电粒子非线性行为的新型神经网络层

基于加速器高阶传输映射的非线性效应解析分析,具有物理图像清晰、守辛、准确的优点,但其缺点是适用范围较窄。为了扩展非线性效应解析分析的适用范围,提出一种模拟李指数运算过程的神经网络层并构建了用于预测带电粒子非线性行为的新型神经网络。经过大量粒子跟踪数据的学习,可用于预测带电粒子复杂的非线性运动行为,并从中提取线性传输矩阵与表征非线性运动的指数因子。为了验证该新型神经网络的有效性,跟踪一段由薄透镜磁铁组成的磁聚焦结构得到大量的训练数据,并对所提出的神经网络进行训练。训练后的神经网络在测试数据集上表现良好,测试数据的损失函数方均根小于8×10-4,达到了预测带电粒子非线性行为的目的。