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An adaptive moving mesh finite difference scheme for tokamak magneto-hydrodynamic simulations
2024-11-08
聚变理论与模拟中心
An adaptive moving mesh finite difference scheme for tokamak magneto-hydrodynamic simulations J. Wang a , J.M. Duan b , Z.W. Ma a,* , W. Zhang a a：Institute for Fusion Theory and Simulation, Zhejiang University, Hangzhou 310027, Chinab：Ecole ´ Polytechnique F´ed´erale de Lausanne, 1015 Lausanne, SwitzerlandAn adaptive moving mesh finite difference scheme is developed for tokamak magneto-hydrodynamic (MHD) simulations, based on the CLT code (S. Wang and Z.W. Ma, Phys. Plasmas, 2015). Our numerical scheme is built on the MHD equations in curvilinear coordinates, based on a coordinate transformation from the physical domain to a computational domain. The scheme is constructed on a uniform Cartesian computational mesh that is obtained from a non-uniform adaptive moving mesh in the physical domain through the coordinate transformation. Mesh points in the physical domain in general move and concentrate in the vicinity of solutions with rapid variations by solving an adaptive mesh equation, whilst total number of mesh points remains unchanged. The local resolution can be significantly increased and computational resource is largely reduced. Comparison between results obtained with the original uniform mesh and the new adaptive moving mesh is carried out by simulation of the linear and nonlinear 2/1 tearing mode, linear and nonlinear 1/1 resistive internal kink mode. It is found that the adaptive moving mesh scheme possesses better numerical stability and convergence.
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Development of a gyrokinetic-MHD energetic particle simulation code. II. Linear simulations of Alfven eigenmodes driven by energetic particles
2024-11-08
聚变理论与模拟中心
Development of a gyrokinetic-MHD energetic particle simulation code. II. Linear simulations of Alfvén eigenmodes driven by energetic particles Z. Y. Liu ; P. Y. Jiang ; S. Y. Liu ; L. L. Zhang ; G. Y. Fu ABSTRACT We have developed a hybrid code GMEC: Gyro-kinetic Magnetohydrodynamics (MHD) Energetic-particle Code that can numerically simulate energetic particle-driven Alfvén eigenmodes and energetic particle transport in tokamak plasmas. In order to resolve the Alfvén eigenmodes with high toroidal numbers effectively, the field-aligned coordinates and meshes are adopted. The extended MHD equations are solved with the five-point finite difference method and the fourth-order Runge–Kutta method. The gyrokinetic equations are solved by particle-in-cell method for the perturbed energetic particle pressures that are coupled into the MHD equations. Up to now, a simplified version of the hybrid code has been completed with several successful verifications, including linear simulations of toroidal Alfvén eigenmodes and reversed shear Alfvén eigenmodes.
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On nonlinear scattering of drift wave by toroidal Alfvén eigenmode in tokamak plasmas
2024-11-08
聚变理论与模拟中心
On nonlinear scattering of drift wave by toroidal Alfvén eigenmode in tokamak plasmas Liu Chen1,2,3, Zhiyong Qiu1,3,∗ and Fulvio Zonca1,31 Institute for Fusion Theory and Simulation, School of Physics, Zhejiang University, Hangzhou, China 2 Department of Physics and Astronomy, University of California, Irvine, CA 92697-4575, United States of America 3 Center for Nonlinear Plasma Science and C.R. ENEA Frascati, C.P. 65, 00044 Frascati, Italy E-mail: zqiu@zju.edu.cn Received 19 March 2023, revised 1 August 2023 Accepted for publication 21 August 2023 Published 7 September 2023Abstract:Using electron drift wave (eDW) as a paradigm model, we have investigated analytically direct wave–wave interactions between a test DW and ambient toroidal Alfvén eigenmodes (TAEs) in toroidal plasmas, and their effects on the stability of the eDW. The nonlinear effects enter via scatterings to short-wavelength electron Landau damped kinetic Alfvén waves (KAWs). Specifically, it is found that scatterings to upper-sideband KAW lead to stimulated absorption of eDW. Scatterings to the lower-sideband KAW, on the contrary, lead to its spontaneous emission. As a consequence, for typical parameters and fluctuation intensity, nonlinear scatterings by TAEs have negligible net effects on the eDW stability; in contrast to the ‘reverse’ process investigated in Chen et al (2022 Nucl. Fusion 62 094001), where it is shown that nonlinear scattering by ambient eDWs may lead to significant damping of TAE.Keywords: toroidal Alfvén eigenmode, burning plasma, drift wave, nonlinear mode coupling, gyrokinetic theory (Some figures may appear in colour only in the online journal)
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巨脉冲和快射电暴的圆偏振机制
2024-10-14
聚变理论与模拟中心
北宋时期的司天监于1054年记录了一次超新星爆发，这一事件形成了一颗半径约10公里的中子星和包裹它的蟹状星云。巧合的是，该中子星的磁轴恰好对准了6500光年外的地球。通过高速自转，中子星沿着磁轴发出的电磁辐射每秒扫过地球30次。1968年，科学家首次探测到来自这颗中子星的巨脉冲（giant pulse）无线电波。2003年，Hankins的观测结果显示这些巨脉冲由众多仅1纳秒宽的子脉冲堆积而成，并且这些子脉冲具有极高的圆偏振度。左图：蟹状星云；右图：中子星辐射示意图2007年，Lorimer首次报道了快射电暴（fast radio burst），可以说快射电暴是近年来天文领域最重要的意外发现。2020年，人们观测到银河系内一颗磁星（磁场更强的中子星）爆发了快射电暴。与巨脉冲相似，部分快射电暴也展现出高度的圆偏振。然而，巨脉冲和快射电暴的圆偏振机制至今尚不明确。等间隔双线分布的巨脉冲信号本研究首次在蟹状星云中子星的一个巨脉冲中发现了等间隔成对分布的子脉冲。每对脉冲中，第一个为左旋圆偏振，第二个为右旋圆偏振。上图展示了9对子脉冲的配对情况，成对子脉冲的时间间隔均在21微秒左右，不确定度仅为0.8微秒。理论上，法拉第效应可以用于解释这一现象。然而，中子星磁层内的等离子体由电子和正电子组成，沿磁场方向观测，它们的回旋运动对左右圆偏振是对称的，因此法拉第效应不起作用。我们大胆假设中子星磁层内的正负电子等离子体存在高度不对称性，即正负电荷没有完全中和，或正负电子能量存在显著差异。在这种不对称等离子体中，法拉第效应会将一个线偏振波分裂成前后延迟的左右圆偏振模式。在磁层参数允许的范围内，只有考虑巨脉冲的相对论强场效应，我们才能计算出符合观测结果的一对圆偏振射电脉冲。该理论还成功解释了巨脉冲的反常色散和随机偏振角等特异现象。此外，已有观测表明某些快射电暴也包含纳秒量级的子脉冲，其圆偏振可以用类似的机制进行解释。鉴于广泛认为中子星磁场方向上存在电场，这些电场可以加速正负电子，并可能诱发所假设的等离子体不对称性。此外，部分磁层粒子模拟结果也显示出不对称等离子体的迹象。关于巨脉冲和快射电暴的产生机制，学术界尚无定论，根本原因在于我们对中子星磁层的认识不足。通过观察中子星的电磁辐射，难以推断出更多有用的磁层信息。本研究发现的纳秒级成对巨脉冲可作为一种诊断磁层的新工具，有望帮助确定中子星磁层的等离子体参数。该研究由浙江大学物理学院武慧春教授完成，近日发表在《Astrophysical Journal Letters》。论文链接：https://doi.org/10.3847/2041-8213/ad8154
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Fluid simulations of resistive drift-wave turbulence with diamagnetic flow in ZPED experiments
2024-05-22
聚变理论与模拟中心
Fluid simulations of resistive drift-wave turbulencewith diamagnetic flow in ZPED experimentsCite as: Phys. Plasmas 31, 052108 (2024); Submitted: 3 December 2023 . Accepted: 23 April 2024 .Published Online: 7 May 2024H. J. Zhao, Y. Mao, Z. Y. Wang, W. W. Xiao,a) and Y. Xiaoa)AFFILIATIONSInstitute for Fusion Theory and Simulation, School of Physics, Zhejiang University, Hangzhou 310027, Chinaa)Authors to whom correspondence should be addressed: wwxiao@zju.edu.cn and yxiao@zju.edu.cnABSTRACTWe derive a diamagnetic resistive fluid model (DRF) and develop an associated two-dimensional fluid simulation code (DRF-2D) to explore the dynamics of resistive drift modes within the plasmas of the Zheda Plasma Experiment Device (ZPED). The validation of the linear dispersion relation for the DRF-2D code revealed a harmonious agreement between analytical theory and linear numerical simulations. Leveraging plasma parameters obtained from the ZPED experiments, we conducted a comprehensive series of nonlinear simulations using the DRF-2D code. Our simulations successfully replicate the nonlinear trends in turbulent fluctuations and transport observed in the ZPED experiments, particularly demonstrating a remarkably accurate alignment of the turning point in the magnetic field. Notably, the DRF model sheds light on the observed frequency sign reversal from the electron diamagnetic direction to the ion diamagnetic direction in the ZPED experiments. This is demonstrated through well-matched turning points in the confining magnetic field between the nonlinear simulations and ZPED experiments. The fidelity of our model in capturing these phenomena underscores its efficacy in providing valuable insights and predictive capabilities for the intricate dynamics observed in the ZPED plasmas. FIG. 4. Density mode structures obtained from nonlinear simulations. The m-spectra are presented in (a)–(c), respectively. Corresponding 2D mode structures are depicted in (d)–(f).Fluid simulations of resistive drift-wave turbulence with diamagnetic flow in ZPED experiments.pdf
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A simple model for internal transport barrier induced by fishbone in tokamak plasmas
2024-05-22
聚变理论与模拟中心
J. Plasma Phys. (2023), vol. 89, 905890612 A simple model for internal transport barrierinduced by fishbone in tokamak plasmasZhaoyang Liu 1 and Guoyong Fu 1,†1Institute for Fusion Theory and Simulation and School of Physics, Zhejiang University,Hangzhou 310027, PR China(Received 17 July 2023; revised 24 November 2023; accepted 24 November 2023)Fishbone bursts have been observed to strongly correlate to internal transport barrier (ITB)formation in a number of tokamak devices. A simple model incorporating the fishbonedynamics and ion pressure gradient evolution is proposed in order to investigate the keyphysics parameters assisting the triggering of ITB. The time evolution of fishbone isdescribed by the well-known predator–prey model. For each burst cycle, the energeticparticles (EPs) resonantly interact with fishbone and are radially expelled from innerregion leading to a radial current. A compensating bulk plasma return current and, hence,poloidal flow can be induced if the fishbone cycle frequency is greater than the poloidalflow damping rate. When the shear of the poloidal flow exceeds a critical value, theturbulent fluctuations are suppressed and the bulk ion pressure gradient transits to thehigh-confinement state. It is shown that this process is only sensitive to the depositionrate of the trapped EPs within the q = 1 surface, but not sensitive to other parameters. Aquantitative formula for the shearing rate of poloidal flow induced by fishbone bursts isderived and verified numerically. FIGURE 2. Poloidal flow (a) and flow shear (b) driven by a single burst of fishbone (dashed line) and multiple bursts of fishbone (solid line). A simple model for internal transport barrier induced by fishbone in tokamak plasmas.pdf
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大尺度动理学模拟揭示对撞等离子体电磁湍流非线性演化与离子随机加热机制
2024-05-20
聚变理论与模拟中心
在天体物理中，常会出现高速等离子体的对撞，如超新星爆发的喷射物和太阳风与星际介质之间的相互作用。此类过程中等离子体速度和温度存在各项异性，宇宙中的种子磁场会在韦伯型不稳定性（Weibel-type instabilities）等作用下被放大成为电磁湍流并产生冲激波，继而产生极强的自生磁场。因此强磁场产生、无碰撞冲激波及其驱动的带电粒子加速等科学问题的研究是当前实验室天体物理领域的关注焦点，而且利用高功率激光装置（如美国的NIF，OMEGA以及中国的神光）已经成功产生了类似于天体中的对撞等离子体环境。浙江大学聚变理论与模拟中心团队，联合上海交通大学和中国科学院国家天文台相关团队，利用吴栋副教授开发的动理学模拟程序LAPINS，定量研究了磁化和非磁化碳氘与碳氢对撞等离子体系统中电磁湍流的非线性演化及其对离子动理学等过程的影响。研究表明：1）在成丝不稳定性和双流不稳定性的协同驱动下会产生电磁湍流；2）在外加横向磁场（垂直于对撞方向）作用下，等离子体自组织效应导致湍流场的剧烈放大，可以产生数十倍于外加磁场的自生磁场；3）离子在湍流场随机加速和碰撞热化的共同作用下，其分布函数会呈现超高斯分布，其中的高能离子会使得系统中氘氘聚变反应产额增加5～6倍。研究结果很好地解释了已有的实验结果。该成果以“Ion Kinetics and Neutron Generation Associated with Electromagnetic Turbulence in Laboratory-Scale Counterstreaming Plasmas” 为题于2024年4月11日发表在Physical Review Letters期刊。浙江大学物理学院博士生刘鹏为该文的第一作者，上海交通大学吴栋副教授、浙江大学聚变理论与模拟中心盛正卯教授为共同通讯作者。 文章信息P. Liu, D. Wu*， T. X. Hu , D. W. Yuan, G. Zhao, Z. M. Sheng*，X. T. He, and J. Zhang，Ion Kinetics and Neutron Generation Associated with Electromagnetic Turbulence in Laboratory-Scale Counterstreaming Plasmas，Phys. Rev. Lett. 132, 155103 (2024), PhysRevLett.132.155103 (aps.org)在激光驱动对流等离子体系统中（a），大尺度动理学模拟得到的非磁化（b）和磁化（c）对流等离子体中自生湍流磁场的空间分布。Ion Kinetics and Neutron Generation Associated with Electromagnetic Turbulence in Laboratory-Scale Counterstreaming Plasmas.pdf
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Magnetic field topology modeling under resonant magnetic perturbations on EAST
2024-03-04
聚变理论与模拟中心
Kinetic infernal mode (KIM) is an electromagnetic instability driven by thermal ions in weak magnetic shear region with a frequency similar to the kinetic ballooning mode (KBM). Gyrokinetic simulations of KIM using Gyrokinetic Toroidal Code (GTC) found that the electromagnetic instability shows a smooth transition from KBM to KIM in both frequency and growth rate when magnetic shear varies from strong to weak, which suggests that KIM and KBM may belong to the same mode physically. The mode structure analysis reveals that the mode transition is induced by the change in distance between adjacent mode rational surfaces. The magnetic shear and driving source effects are investigated in detail. The simulation results show that KIM prefers to grow on the mode rational surface nearest to the minimum magnetic shear, i.e., where the shear stabilizing effect is weakest, instead of at the maximum of density gradient or temperature gradient. However, the magnitude of the growth rate is determined by magnetic shear and temperature gradient simultaneously. These findings suggest that KIM can be effectively regulated by modifying the strength and position of magnetic shear, as well as pressure gradients.122.Linear gyrokinetic simulatioin of kinetic infernal mode.pdf
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Gyrokinetic theory of toroidal Alfvén eigenmode saturation via nonlinear wave-wave coupling
2023-07-03
聚变理论与模拟中心
Nonlinear wave-wave coupling constitutes an important route for the turbulence spectrum evolution in both space and laboratory plasmas. For example, in a reactor relevant fusion plasma, a rich spectrum of symmetry breaking shear Alfvén wave (SAW) instabilities are expected to be excited by energetic fusion alpha particles, and self-consistently determine the anomalous alpha particle transport rate by the saturated electromagnetic perturbations. In this work, we will show that the nonlinear gyrokinetic theory is a necessary and powerful tool in qualitatively and quantitatively investigating the nonlinear wave-wave coupling processes. More specifically, one needs to employ the gyrokinetic approach in order to account for the breaking of the “pure Alfvénic state” in the short wavelength kinetic regime, due to the short wavelength structures associated with nonuniformity intrinsic to magnetically confined plasmas. Using well-known toroidal Alfvén eigenmode (TAE) as a paradigm case, three nonlinear wave-wave coupling channels expected to significantly influence the TAE nonlinear dynamics are investigated to demonstrate the strength and necessity of nonlinear gyrokinetic theory in predicting crucial processes in a future reactor burning plasma. These are: 1.the nonlinear excitation of meso-scale zonal field structures via modulational instability and TAE scattering into short-wavelength stable domain; 2. the TAE frequency cascading due to nonlinear ion induced scattering and the resulting saturated TAE spectrum; and 3. the crossscale coupling of TAE with micro-scale ambient drift wave turbulence and its effect on TAE regulation and anomalous electron heating.108.Gyrokinetic theory of toroidal Alfvén eigenmode saturation via nonlinear wave-wave coupling.pdf
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Observation of turbulence energy transfer in a cylindrical laboratory plasma
2023-07-03
聚变理论与模拟中心
We report the experimental results on the turbulence energy transfer in a cylindrical laboratory plasma based on the data obtained by a set of Quadruple Langmuir Probe (QLP) on Zheda Plasma Experiment Device (ZPED). The turbulence energy transfer is directly embodied in the alternating change of the fluctuation amplitudes between the low frequency shear flow (LFSF) at ∼ 0.2kHz and the drift wave (DW) turbulence at ∼ 1 − 2kHz. The estimation of radial electric field and bispectral analysis of the experiments suggest that the DW turbulence gains the energy from the low frequency turbulence. The energy transport due to the interaction between the LFSF ant the DW turbulence with the magnetic field increase is a possible reason to drive the turbulence energy transfer in the laboratory plasma. 107.Observation of turbulence energy transfer in a cylindrical laboratory plasma.pdf
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On Nonlinear Scattering of Drift Wave by Toroidal Alfvén Eigenmode in Tokamak Plasmas
2023-07-03
聚变理论与模拟中心
106.On Nonlinear Scattering of Drift Wave by Toroidal Alfvén Eigenmode in Tokamak Plasmas.pdf
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Studies of the electron kinetics in capacitively coupled Ar/ 𝐎𝟐 mixture plasma generated by A.C power discharge
2023-07-03
聚变理论与模拟中心
105.Studies of the electron kinetics in capacitively coupled Ar-O2 mixture plasma generated by AC power discharge.pdf
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Machine Learning to Classify Electrostatic Plasma Turbulence in Tokamaks
2022-11-30
聚变理论与模拟中心
104.Machine Learning to Classify Electrostatic Plasma Turbulence in Tokamaks.pdf
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Elongation Effect on Beta-induced Alfvén Eigenmodes
2022-11-30
聚变理论与模拟中心
103.Elongation Effect on Beta-induced Alfvén Eigenmodes.pdf
