离子温度梯度模湍流扩散特性的量化描述

采用回旋动理学模型对无剪切平板位形中离子温度梯度模(ITG)湍流扩散的物理特性进行了数值模拟研究。提出了湍流有效扩散距离的描述方法,定量地讨论了湍流扩散性质对磁场位形因子和离子温度梯度特征长度的依赖关系。结果显示,随着极向磁场的减小,湍流扩散增强;随着离子温度梯度特征长度的增加,湍流扩散减弱。更重要的是,通过对比ITG和ETG湍流以及不同碰撞阻尼下的ITG湍流中的湍流扩散特征,论证了带状流对ITG湍流扩散的影响。模拟结果表明,在此模型下,带状流对湍流扩散具有明显的抑制作用。

Nonlinear dynamics of the reversed shear Alfvén eigenmode in burning plasmas

In a tokamak fusion reactor operated at steady state,the equilibrium magnetic field is likely to have reversed shear in the core region,as the noninductive bootstrap current profile generally peaks off-axis.The reversed shear Alfvén eigenmode(RSAE)as a unique branch of the shear Alfvén wave in this equilibrium,can exist with a broad spectrum in wavenumber and frequency,and be resonantly driven unstable by energetic particles(EP).After briefly discussing the RSAE linear properties in burning plasma condition,we review several key topics of the nonlinear dynamics for the RSAE through both wave-EP resonance and wave-wave coupling channels,and illustrate their potentially important role in reactor-scale fusion plasmas.By means of simplified hybrid MHD-kinetic simulations,the RSAEs are shown to have typically broad phase space resonance structure with both circulating and trapped EP,as results of weak/vanishing magnetic shear and relatively low frequency.Through the route of wave-EP nonlinearity,the dominant saturation mechanism is mainly due to the transported resonant EP radially decoupling with the localized RSAE mode structure,and the resultant EP transport generally has a convective feature.The saturated RSAEs also undergo various nonlinear couplings with other collective oscillations.Two typical routes as parametric decay and modulational instability are studied using nonlinear gyrokinetic theory,and applied to the scenario of spontaneous excitation by a finite amplitude pump RSAE.Multiple RSAEs could naturally couple and induce the spectral energy cascade into a low frequency Alfvénic mode,which may effectively transfer the EP energy to fuel ions via collisionless Landau damping.Moreover,zero frequency zonal field structure could be spontaneously excited by modulation of the pump RSAE envelope,and may also lead to saturation of the pump RSAE by both scattering into stable domain and local distortion of the continuum structure.

Gyrokinetic simulations of the kinetic electron effects on the electrostatic instabilities on the ITER baseline scenario

The linear and nonlinear simulations are carried out using the gyrokinetic code NLT for the electrostatic instabilities in the core region of a deuterium plasma based on the International Thermonuclear Experimental Reactor(ITER)baseline scenario.The kinetic electron effects on the linear frequency and nonlinear transport are studied by adopting the adiabatic electron model and the fully drift-kinetic electron model in the NLT code,respectively.The linear simulations focus on the dependence of linear frequency on the plasma parameters,such as the ion and electron temperature gradientsκ_(Ti,e)≡R=L_(Ti,e),the density gradientκ_(n)≡R/L_(n)and the ion-electron temperature ratioτ=T_(e)=T_(i).Here,is the major radius,and T_(e)and T_(i)denote the electron and ion temperatures,respectively.L_(A)=-(δ_(r)lnA)^(-1)is the gradient scale length,with denoting the density,the ion and electron temperatures,respectively.In the kinetic electron model,the ion temperature gradient(ITG)instability and the trapped electron mode(TEM)dominate in the small and large k_(θ)region,respectively,wherek_(θ)is the poloidal wavenumber.The TEMdominant region becomes wider by increasing(decreasing)κ_(T_(e))(κ_(T_(i)))or by decreasingκ_(n).For the nominal parameters of the ITER baseline scenario,the maximum growth rate of dominant ITG instability in the kinetic electron model is about three times larger than that in the adiabatic electron model.The normalized linear frequency depends on the value ofτ,rather than the value of T_(e)or T_(i),in both the adiabatic and kinetic electron models.The nonlinear simulation results show that the ion heat diffusivity in the kinetic electron model is quite a lot larger than that in the adiabatic electron model,the radial structure is finer and the time oscillation is more rapid.In addition,the magnitude of the fluctuated potential at the saturated stage peaks in the ITGdominated region,and contributions from the TEM(dominating in the higher k_(θ)region)to the nonlinear transport can be neglected.In the adiabatic electron model,the zonal radial electric field is found to be mainly driven by the turbulent energy flux,and the contribution of turbulent poloidal Reynolds stress is quite small due to the toroidal shielding effect.However,in the kinetic electron model,the turbulent energy flux is not strong enough to drive the zonal radial electric field in the nonlinear saturated stage.The kinetic electron effects on the mechanism of the turbulence-driven zonal radial electric field should be further investigated.

Simulation on the transition of electrostatic instabilities in EAST steady-state scenario

The parameter dependence of transition between electrostatic instabilities is studied using gyrokinetic simulation based on a real discharge of steady-state scenario in the Experimental Advanced Superconducting Tokamak.The scan of radial locations shows that trapped electron mode(TEM)dominates around the core while the ion temperature gradient mode(ITG)simultaneously dominates outside.The maximum growth rate of TEM appears aroundρ=0.24,where the maximum electron temperature gradient R/LTelocates,ρis the normalized poloidal flux.Effects of the parameters on the transition between TEM and ITG instability are studied atρ=0.24.It is found that TEM dominates in the scanning with individually changing R/LTe from 2.50 to 25.02 or the density gradient R/L_(n)from 1.38 to 13.76.Meanwhile,the electron-ion temperature ratio T_(e)/T_(i)is found to destabilize TEM,the effect of Teis more sensitive than that of T_(i).The dominant instability diagrams in the(R/L_(Te),R/L_(Ti))plane at different T_(e)/T_(i)and R/Lnare numerically obtained,which clearly show the parameter range of the dominant TEM or dominant ITG instability region.It is found that the dominant TEM region becomes narrower in the plane by decreasing R/L_(n)when T_(e)/T_(i)>0.5.

Gyrokinetic simulation of low-n Alfvénic modes in tokamak HL-2A plasmas

The turbulence characteristics of plasmas with internal transport barriers in the HL-2A tokamak are analyzed by means of linear gyrokinetic simulations. It is found that turbulence is dominated by the ion temperature gradient(ITG)mode together with large-scale modes characterized by high-frequency electromagnetic fluctuation, which are destabilized by the steep ion temperature gradient in the weak magnetic shear regime. Comparison with solutions of analytical dispersion relations shows that their linear features match well with the beta-induced Alfvén eigenmode branch of the shear Alfvénic spectrum. It is further clarified that the large population of fast ions in these plasmas plays a stabilization role through the dilution mechanism in high-n ITG mode regimes.

Solving Poisson equation with slowing-down equilibrium distribution for global gyrokinetic simulation

Fusion-born alpha particles in burning plasmas are usually regarded as have a slowing-down distribution,which differs significantly from the Maxwellian distribution of thermal particles in velocity space.A generalized multi-point average method has been developed for gyrokinetic Poisson equation with slowing-down equilibrium distribution using optimization in Fourier space.Its accuracy is verified in both long and short wavelength limits.The influence of changing equilibrium distribution from Maxwellian to slowing-down on gyrokinetic Poisson equation is analyzed to illustrate the significance of the new method.The effect of critical speed in the slowingdown distribution on the field solver is also presented.This method forms an important basis for global gyrokinetic simulation of low-frequency drift Alfvénic turbulence in burning plasmas.

反磁剪切托卡马克等离子体中低频剪切阿尔芬波的理论研究

位于动理学热离子带隙附近的低频阿尔芬扰动因可以与高能量粒子或背景热粒子发生相互作用而引起了广泛的关注.本文在一般鱼骨模色散关系的理论框架下,针对反磁剪切托卡马克等离子体中观测到的由高能量粒子或者背景热粒子激发的低频剪切阿尔芬波的线性特性进行了一系列的理论研究.由于这些低频剪切阿尔芬波与2019年DⅢ-D开展的专门研究高能量离子驱动低频不稳定的实验密切相关,因此本文通过采用DⅢ-D具有代表性实验的平衡参数,证明了实验上观测的低频模和比压阿尔芬本征模分别是以阿尔芬极化为主的反应型和耗散型不稳定模,因此,将前者称为低频阿尔芬模更准确.由于受逆磁和捕获粒子动理学效应的影响,低频阿尔芬模既可以在低频区(频率小于热离子的渡越或反弹频率)与比压阿尔芬声模耦合,又可以在高频区(频率大于或近似等于热离子的渡越频率)与比压阿尔芬本征模耦合,此外,由于受到不同激发机制的影响,与局域在安全因子最小值有理面附近的低频阿尔芬模相比,驱动比压阿尔芬本征模的高能量离子的压强梯度在偏离安全因子最小值的有理面时达到最大值,相应的比压阿尔芬本征模的本征函数在高能量离子驱动最大的径向位置处出现峰值.通过改变安全因子最小值理论上重现了实验上观测的比压阿尔芬本征模和低频阿尔芬模的上升频谱特征.研究还表明,比压阿尔芬声模由于受到强烈的朗道阻尼,因而很难被高能量粒子激发,这与基于第一性原理的理论预测和模拟结果一致.本文证明了一般鱼骨模色散关系在解释和预测实验和数值模拟结果方面的强大能力.

径向电场对离子温度梯度模稳定性的影响

为了理解托卡马克装置中给定径向电场对离子温度梯度模(ITG)稳定性的影响,基于非线性回旋动理学理论和气球模表象推导了环位形下包含径向电场引起的极向流和密度扰动影响的ITG的本征模方程,并分别在长/短波长极限下研究了高能量粒子诱发测地声模(EGAM)所伴随的径向电场对ITG的本征频率、增长率和平行模结构的影响.不仅对该本征模方程进行了理论研究,还使用本征矩阵法对其进行数值求解,以便对理论结果进行验证.研究发现EGAM伴随的电场引起的极向转动会大幅降低ITG的增长率,而极向模数m=1的密度扰动对ITG的线性稳定性影响很小.这一结果与一般认为的带状流通过极向流剪切抑制湍流的结果是一致的.除此之外,使用本文发展的一般性方法也可以研究高能量粒子激发的阿尔芬不稳定性与漂移波湍流通过阿尔芬不稳定性激发带状结构发生的间接非线性相互作用,即带状结构所伴随的径向电场通过极向转动和密度扰动影响ITG的稳定性.该间接非线性通道可以作为对主导背景等离子体输运的微观湍流和主导高能量粒子输运的阿尔芬不稳定性之间的直接相互作用通道的补充.

同轴回旋自谐振脉塞放大器的线性分析

从同轴回旋自谐振脉塞(CARM)放大器的回旋动力学理论入手,详细分析了各参量对同轴CARM放大器的线性增益的影响。通过数值模拟,发现该器件的线性增益对及对同轴波导的外半径、电子导引中心半径以及加速电压的变化非常敏感,而随波导内半径的变化不敏感。经优化,当外半径为3.805 cm,导引中心半径为1.309 cm,内半径为1.039 cm,加速电压为54.9 kV时,器件的线性增益最高为294.96 dB/m。

同轴腔CARM放大器的线性分析

从同轴腔回旋自谐振脉塞(CARM)放大器的回旋动力学理论入手,详细分析了各参量对同轴腔 CARM放大器的线性增益的影响。通过数值模拟,发现该器件的线性增益及输出功率对同轴腔的外半径和 电子导引中心半径以及加速电压的变化非常敏感,而对腔体内半径的变化并不敏感。由数值模拟可知,器件 的线性增益能达到294．96 dB／m。

磁约束聚变等离子体的大规模回旋动理学模拟

文章介绍了磁约束核聚变能源科学及其密切相关的聚变等离子体物理,以及研究磁约束聚变等离子体非线性物理所必需的大规模回旋动理学模拟的方法及其前沿进展.

Self-consistent kinetic theory with nonlinear wave-particle resonances

We have developed, based on the oscillating-center transformation, a general theoretical approach for self-consistent plasma dynamics including, explicitly, effects of nonlinear(higherorder) wave-particle resonances. A specific example is then given for low-frequency responses of trapped particles in axisymmetric tokamaks. Possible applications to transport as well as nonlinear wave growth/damping are also briefly discussed.

CARM放大器回旋动力学理论及其与实验的比较

对圆柱腔回旋自动谐振脉塞(CARM)回旋动力学理论与美国麻省理工学院的实验进行了比较研究,理论结果与实验符合。研究了磁场及电子横向速度与纵向速度比对输出功率和增益的影响,发现通过优化参数,原实验的输出功率有可能从10MW提高到14MW。

托卡马克中离散阿尔芬不稳定性的动理学分析

动理学是描述等离子体的重要方法。本文介绍了动理学的一种近似处理——回旋动理学,并在简单模型下演示了线性回旋动理学方程近似过程。结合ITER(International Thermonuclear Experimental Reactor)设计参数和模拟放电实验数据,利用线性回旋近似研究环形聚变等离子体中高能量粒子的动理学效应对离散阿尔芬本征模(αTAE)的影响。

Gyrokinetic simulations of nonlinear interactions between magnetic islands and microturbulence

A conservative scheme of kinetic electrons for gyrokinetic simulations in the presence of magnetic islands has been implemented and verified in the gyrokinetic toroidal code, where zonal and nonzonal components of all perturbed quantities are solved together. Using this new conservative scheme, linear simulation of kinetic ballooning mode has been successfully benchmarked with the electromagnetic hybrid model. Simulations of nonlinear interactions between magnetic islands and the ion temperature gradient(ITG) mode in a tokamak show that the islands rotate at the electron diamagnetic drift velocity. The linear ITG structure shifts from the island O-point toward the X-point due to the pressure flattening effect inside the islands, and the nonlinear ITG structure peaks along the magnetic island separatrix because of the increased pressure gradient there.

Implementation of field-aligned coordinates in a semi-Lagrangian gyrokinetic code for tokamak turbulence simulation

Field-aligned coordinates have been implemented in the gyrokinetic semi-Lagrangian code NLT, Ye et al （2016 J. Comput. Phys. 316 180）, to improve the computational efficiency for the numerical simulations of tokamak turbulence and transport. 4D B-spline interpolation in field- aligned coordinates is applied to solve the gyrokinetic Vlasov equation. A fast iterative algorithm is proposed for efficiently solving the quasi-neutrality equation. A pseudo transform method is used for the numerical integration of the gyro-average operator for perturbations with a high toroidal mode number. The new method is shown to result in an improved code performance for reaching a given accuracy. Some numerical tests are presented to illustrate the new methods.

EAST装置中捕获电子模线性增长率的回旋动理学模拟

基于全超导托卡马克(experimental and advanced superconducting tokamak, EAST)中以电子加热为主的放电试验,使用GTC(Gyrokinetic Toroidal Code)代码进行线性回旋动理学模拟,研究等离子体参数对捕获电子模(trapped electron mode, TEM)线性增长率(γ)的影响。结果表明,γ随电子与离子温度比( T e / T i )和归一化电子温度梯度( R / L T e )的增大而增大,但随着归一化密度梯度( R / L n )的增加而降低。安全因子( q )和磁剪切( s ∧)对TEM线性增长率的影响与归一化半径范围内(ρ<0.4) s ∧值的大小有关。当 s ∧>0.3时,γ随着 q 的增大而增大,随着 s ∧的增大而减小,与简化模型的理论分析一致。然而,当 s ∧<0.3时出现了相反的结果,即γ随 q 的增大而减小,随着 s ∧的增大而增大,其原因可能是较小的 s ∧无法抑制TEM湍流。

Global and Kinetic MHD Simulation by the Gpic-MHD Code

In order to implement large-scale and high-beta tokamak simulation, a new algorithm of the electromagnetic gyrokinetic PIC （particle-in-cell） code was proposed and installed on the Gpic-MHD code [Gyrokinetic PIC code for magnetohydrodynamic （MHD） simulation]. In the new algorithm, the vorticity equation and the generalized Ohm＇s law along the magnetic field are derived from the basic equations of the gyrokinetic Vlasov, Poisson, and Ampere system and are used to describe the spatio-temporal evolution of the field quantities of the electrostatic potential φ and the longitudinal component of the vector potential Az. The basic algorithm is equivalent to solving the reduced-MHD-type equations with kinetic corrections, in which MHD physics related to Alfven modes are well described. The estimation of perturbed electron pressure from particle dynamics is dominant, while the effects of other moments are negligible. Another advantage of the algorithm is that the longitudinal induced electric field, ETz = -δAz/δt, is explicitly estimated by the generalized Ohm＇s law and used in the equations of motion. Furthermore, the particle velocities along the magnetic field are used （vz-formulation） instead of generalized momentums （pz-formulation）, hence there is no problem of ＇cancellation＇, which would otherwise appear when Az is estimated from the Ampere＇s law in the pz-formulation. The successful simulation of the collisionless internal kink mode by the new Gpic-MHD with realistic values of the large-scale and high-beta tokamaks revealed the usefulness of the new algorithm.

Nonlinear excitation of a geodesic acoustic mode by reversed shear Alfvén eignemodes

The parametric decay process of a reversed shear Alfvén eigenmeode(RSAE)into a geodesic acoustic mode and a kinetic RSAE is investigated using nonlinear gyrokinetic theory.The excitation conditions mainly require the pump RSAE amplitude to exceed a certain threshold,which could be readily satisfied in burning plasmas operated in steady-state advanced scenario.This decay process can contribute to thermal plasma heating and confinement improvement.

GTC Simulation of Ideal Ballooning Mode in Tokamak Plasmas

In the present paper,we first derive the eigenmode equation of the ideal ballooning mode in tokamak plasmas using a gyrokinetic equation.It is shown that the gyrokinetic eigenmode equation can be reduced to the magnetohydrodynamic（MHD） form in the long wavelength limit when kinetic effects are ignored.Then,the global gyrokinetic toroidal code（GTC） is applied for simulations of the edge-localized ideal ballooning modes.The obtained mode structures are compared with the results of ideal MHD simulations.The observed scaling of the linear growth rate with the toroidal mode number is consistent with the ideal MHD theory.The simulation results verify the GTC capability of simulating MHD processes in toroidal plasmas.