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

Plasma Science and Technology 2023年第2期25卷 11-19页

作者：钟奇肖湧 Institute for Fusion Theory and Simulation Department of PhysicsZhejiang UniversityHangzhou 310027People's Republic of China

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.

关键词： gyrokinetics Poisson solver slowing-down distribution

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A Gyrokinetic simulation model for low frequency electromagnetic fluctuations in magnetized plasmas

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Science China(Physics,Mechanics & Astronomy) 2021年第4期64卷 90-95页

作者： Liu Chen HaoTian Chen Fulvio Zonca Yu Lin Institute for Fusion Theory and Simulation and Department of Physics Zhejiang UniversityHangzhou 310027China Department of Physics and Astronomy University of CaliforniaIrvineCalifornia 92697USA Institute of Space Science and Technology Nanchang UniversityNanchang 330031China Center for Nonlinear Plasma Science and C.R.ENEA Frascati-C.P.65 Frascati 00044Italy Physics Department Auburn UniversityAuburn AL 36849USA

We present a new model for simulating the electromagnetic fluctuations with frequencies much lower than the ion cyclotron frequency in plasmas confined in general magnetic configurations.This novel model(termed as GK-E&B)employs nonlinear gyrokinetic equations formulated in terms of electromagnetic fields along with momentum balance equations for solving fields.It,thus,not only includes kinetic effects,such as wave-particle interaction and microscopic(ion Larmor radius scale)physics;but also is computationally more efficient than the conventional formulation described in terms of potentials.As a benchmark,we perform linear as well as nonlinear simulations of the kinetic Alfvén wave;demonstrating physics in agreement with the analytical theories.

关键词： plasma kinetic equations gyrokinetics Gyrokinetic simulations particle orbit and trajectory

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Cyclokinetic models and simulations for high-frequency turbulence in fusion plasmas

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Frontiers of physics 2016年第5期11卷 23-56页

作者：赵登 R. E. Waltz 王晓钢 Institute of Fluid Physics China Academy of Engineering Physics P.O. Box 919-108 Mianyang 621900 China State Key Laboratory of Nuclear Physics and Technology School of Physics Peking University Beijing 100871 China General Atomics P.O. Box 85608 San Diego CA 92186-5608 USA Department of Physics Harbin Institute of Technology Harbin 150001 China

Cyrokinetics is widely applied in plasma physics. However, this framework is limited to weak turbulence levels and low drift-wave frequencies because high-frequency gyro-motion is reduced by the gyro-phase averaging. In order to test where gyrokinetics breaks down, Waltz and Zhao developed a new theory, called cyclokinetics [R. E. Waltz and Zhao Deng, Phys. Plasmas 20, 012507 （2013）]. Cyclokinetics dynamically follows the high-frequency ion gyro-motion which is nonlineaxly coupled to the low-frequency drift-waves interrupting and suppressing gyro-averaging. Cyclokinetics is valid in the high-frequency （ion cyclotron frequency） regime or for high turbulence levels. The ratio of the cyclokinetic perturbed distribution function over equilibrium distribution function δf/F can approach 1. This work presents, for the first time, a numerical simulation of nonlinear cyclokinetic theory for ions, and describes the first attempt to completely solve the ion gyro-phase motion in a nonlinear turbulence system. Simulations are performed [Zhao Deng and R. E. Waltz, Phys. Plasmas 22（5）, 056101 （2015）] in a local flux-tube geometry with the parallel motion and variation suppressed by using a newly developed code named rCYCLO, which is executed in parallel by using an implicit time-advanced Eulerian （or continuum） scheme [Zhao Deng and R. E. Waltz, Comp. Phys. Comm. 195, 23 （2015）]. A novel numerical treatment of the magnetic moment velocity space derivative operator guarantee saccurate conservation of incremental entropy. By comparing the more fundamental cyclokinetic simulations with the corresponding gyrokinetic simulations, the gyrokinetics breakdown condition is quantitatively tested. Gyrokinetic transport and turbulence level recover those of cyclokinetics at high relative ion cyclotron frequencies and low turbulence levels, as required. Cyclokinetic transport and turbulence level are found to be lower than those of gyrokinetics at high turbulence levels and low-Ω＊ values with stable ion cyclotron modes. The gyrokinetic ap

关键词： turbulence cyclokinetics gyrokinetics drift waves ion cyclotron modes

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Electromagnetic High Frequency Gyrokinetic Particle-in-Cell Simulation

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Communications in Computational Physics 2008年第8期4卷 575-591页

作者： R.A.Kolesnikov W.W.Lee H.Qin Plasma Physics Laboratory Princeton UniversityP.O.Box 451PrincetonNew Jersey 08543USA

Using the gyrocenter-gauge kinetic theory,an electromagnetic version of the high frequency gyrokinetic numerical algorithm for particle-in-cell simulation has been developed.The new algorithm,being an alternative to a direct Lorentz-force simulation,offers an efficient way to simulate the dynamics of plasma heating and current drive with radio frequency waves.Gyrokinetic formalism enables separation of gyrocenter and gyrophase motions of a particle in a strong magnetic field.From this point of view,a particlemay be viewed as a combination of a slow gyrocenter and a quickly changing Kruskal ring.In this approach,the nonlinear dynamics of high frequency waves is described by the evolution of Kruskal rings based on first principles physics.The efficiency of the algorithm is due to the fact that the simulation particles are advanced along the slow gyrocenter orbits,while the Kruskal rings capture fast gyrophase physics.Moreover,the gyrokinetic formalism allows separation of the cold response from kinetic effects in the current,which allows one to use much smaller number of particles than what is required by a direct Lorentz-force simulation.Also,the new algorithm offers the possibility to have particle refinement together with mesh refinement,when necessary.To illustrate the new algorithm,a simulation of the electromagnetic low-hybrid wave propagating in inhomogeneous magnetic field is presented.

关键词： gyrokinetics magnetized plasmas plasma kinetic equations

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Self-consistent kinetic theory with nonlinear wave-particle resonances

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Plasma Science and Technology 2019年第12期21卷 6-12页

作者： Liu CHEN Fulvio ZONCA Institute for Fusion Theory and Simulation and Department of Physics Zhejiang UniversityHangzhou 310027People's Republic of China Department of Physics and Astronomy University of CaliforniaIrvineCA 92697-4575United States of America ENEA C.R.FrascatiVia E.Fermi 45I-00044 Frascati(Rome)Italy

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.

关键词： gyrokinetics nonlinear phenomena:waves wave propagation and other interactions(including parametric effects,mode coupling,ponderomotive) fusion products effects(e.g.alpha-particles,etc) fast particle effects particle orbit and trajectory perturbative methods

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