Hybrid simulations of beta-induced Alfvén eigenmode with reversed safety factor profile

Nuclear Fusion ◽

10.1088/1741-4326/ac3f4d ◽

2021 ◽

Author(s):

Sizhe Duan ◽

Guoyong Fu ◽

Huishan Cai

Keyword(s):

Nonlinear Dynamics ◽

Rational Surface ◽

Injection Velocity ◽

Nonlinear Simulation ◽

Energetic Ions ◽

Radial Gradient ◽

Nonlinear Phase ◽

Simulation Results ◽

Reversed Shear ◽

Hybrid Simulations

Abstract Based on the experimental parameters in HL-2A tokamak, hybrid simulations have been carried out to investigate the linear stability and nonlinear dynamics of BAE. It is found that the (m/n=3/2) beta-incuced Alfvén eigenmode (BAE) is excited by co-passing energetic ions with qmin=1.5 in linear simulation, and the mode frequency is consistent with experimental meuasurement. The simulation results show that the energetic ions βh, the injection velocity v0 and orbit width parameter ρh of energetic ions are important parameters determining the drive of BAE. Furthermore, the effect of qmin (with fixed shape of q profile) is studied, and it is found that: when qmin ≤ 1.50, the excited modes are BAEs, which are located near q=1.50 rational surfaces; when qmin > 1.50, the excited modes are simillar to the reversed-shear Alfvén eigenmodes (RSAEs), which are mainly localized around q=qmin surfaces. Nonlinear simulation results show that the nonlinear dynamics of BAE is sensitive to the EP drive. For strongly driven case, firstly, redistribution and transport of engetic ions are trigged by (m/n=3/2) BAE, which raised the radial gradient of energetic ions distribution function near q=2 rational surface, and then an EPM (m/n=4/2) is driven in nonlinear phase. Finally, these two instabilities triggered significant redistribution of energetic ions, which results in the twice-repeated and mostly-downward frequency chirping of (m/n=3/2) BAE. For weakly driven case, there are no (m/n=4/2) EPM being driven and twice-repeated chirping in nonlinear phase, since the radial gradient near q=2 rational surface is small and almost unchanged.

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

Plasma Science and Technology ◽

10.1088/2058-6272/ac41be ◽

2021 ◽

Author(s):

Xiaolong Zhu ◽

Feng Wang ◽

Wei Chen ◽

Zhengxiong Wang

Keyword(s):

Nonlinear Dynamics ◽

Resonance Condition ◽

Particle Interaction ◽

Critical Value ◽

Mode Frequency ◽

Tokamak Plasma ◽

Tokamak Plasmas ◽

Energetic Ions ◽

Kink Mode ◽

Reversed Shear

Abstract Based on the conventional tokamak HL-2A-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 (MHD) nonlinear code M3D-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 energetic-ions when the energetic-ion beta $\beta_h$ exceeds a critical value. The transition from NRK to NRFB occurs when the energetic-ion beta $\beta_h$ increases to above a critical value. The resonance condition responsible for the excitation of NRFB is interestingly found to be satisfied at $\omega_t+\omega_p\approx\omega$, where $\omega_t$ is the toroidal motion frequency, $\omega_p$ is the poloidal motion frequency and $\omega$ is the mode frequency. The nonlinear evolutions of NRFB's mode structures and Poincar\'{e} plots are also analyzed in this work and it is found that the NRFB can induce evident energetic-ion 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.

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Influence of trapped energetic ions on low-frequency magnetohydrodynamic instabilities with reversed shear profile

Physics of Plasmas ◽

10.1063/5.0034690 ◽

2021 ◽

Vol 28 (1) ◽

pp. 012104

Author(s):

Baofeng Gao ◽

Huishan Cai ◽

Feng Wang ◽

Xiang Gao ◽

Yuanxi Wan

Keyword(s):

Low Frequency ◽

Energetic Ions ◽

Reversed Shear

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Plasma instabilities driven by pickup ions of ring-beam velocity distributions in the outer heliosheath

10.5194/egusphere-egu21-9329 ◽

2021 ◽

Author(s):

Ameneh Mousavi ◽

Kaijun Liu ◽

Sina Sadeghzadeh

Keyword(s):

Magnetic Field ◽

Maximum Growth ◽

Dispersion Analysis ◽

Maximum Growth Rate ◽

Injection Velocity ◽

Plasma Instabilities ◽

Pickup Ions ◽

Beam Velocity ◽

Background Magnetic Field ◽

Hybrid Simulations

The stability of the pickup ions in the outer heliosheath has been studied by many researchers because of its relevance to the energetic neutral atom (ENA) ribbon observed by the Interstellar Boundary EXplorer. However, previous studies are primarily limited to pickup ions of near 90&#176; pickup angles, the angle between the pickup ion injection velocity and the background, local interstellar magnetic field. Investigations on pickup ions of smaller pickup angles are still lacking. In this paper, linear kinetic dispersion analysis and hybrid simulations are carried out to examine the plasma instabilities driven by pickup ions of ring-beam velocity distributions at various pickup angles between zero and 90&#176;. Parallel propagating waves are studied in the parameter regime where the parallel thermal spread of the pickup ions falls into the Alfv&#233;n cyclotron stability gap. The linear analysis results and hybrid simulations both show that the fastest growing modes are the right-hand helicity waves propagating in the direction of the background magnetic field, and the maximum growth rate occurs at the pickup angle of 82&#176;. The simulation results further reveal that the saturation level of the fluctuating magnetic fields for pickup angles below 45&#176; is higher than that for pickup angles above 45&#176;. So, the scattering of pickup ions at near zero pickup angles is likely more pronounced than that at near 90&#176; pickup angles .

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Effect of the electron redistribution on the nonlinear saturation of Alfvén eigenmodes and the excitation of zonal flows

Journal of Plasma Physics ◽

10.1017/s0022377820000550 ◽

2020 ◽

Vol 86 (3) ◽

Cited By ~ 1

Author(s):

A. Biancalani ◽

A. Bottino ◽

P. Lauber ◽

A. Mishchenko ◽

F. Vannini

Keyword(s):

Magnetic Field ◽

Zonal Flow ◽

Large Aspect Ratio ◽

Nonlinear Saturation ◽

Energetic Ions ◽

Electron Population ◽

Zonal Flows ◽

Particle In Cell ◽

Alfven Eigenmodes ◽

Reversed Shear

Numerical simulations of Alfvén modes driven by energetic particles are performed with the gyrokinetic (GK) global particle-in-cell code ORB5. A reversed shear equilibrium magnetic field is adopted. A simplified configuration with circular flux surfaces and large aspect ratio is considered. The nonlinear saturation of beta-induced Alfvén eigenmodes (BAE) is investigated. The roles of the wave–particle nonlinearity of the different species, i.e. thermal ions, electrons and energetic ions are described, in particular for their role in the saturation of the BAE and the generation of zonal flows. The nonlinear redistribution of the electron population is found to be important in increasing the BAE saturation level and the zonal flow amplitude.

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Transport barriers with magnetic shear in a tokamak

Journal of Plasma Physics ◽

10.1017/s0022377806004727 ◽

2007 ◽

Vol 73 (4) ◽

pp. 439-453 ◽

Cited By ~ 4

Author(s):

M. EL MOUDEN ◽

D. SAIFAOUI ◽

A. DEZAIRI ◽

B. ZINE ◽

M. EDDAHBY

Keyword(s):

Anomalous Transport ◽

Particle Diffusion ◽

Magnetic Shear ◽

Transport Barriers ◽

Simulation Results ◽

Reversed Shear

AbstractThe reversed magnetic shear is the most important factor in the study of the plasmas of a tokamak. In this paper we focus our research, as a first stage, on the control of the improved confinement regimes by studying the influence of the reversed shear on its quality in the plasma of a tokamak and especially in reducing the anomalous transport in ITER. Then we study the influence of the perturbation modes on the particle diffusion. At the end, a comparison between simulation results obtained using ITER and TEXT parameters is carried out.

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Leader-Based Consensus of Heterogeneous Nonlinear Multiagent Systems

Mathematical Problems in Engineering ◽

10.1155/2014/519524 ◽

2014 ◽

Vol 2014 ◽

pp. 1-6 ◽

Cited By ~ 1

Author(s):

Tairen Sun ◽

Yongping Pan ◽

Haoyong Yu

Keyword(s):

Nonlinear Dynamics ◽

Multiagent Systems ◽

Uncertain Systems ◽

Formal Proof ◽

Multiple Agents ◽

Distributed Consensus ◽

Distributed Controllers ◽

Nonlinear Uncertain Systems ◽

Simulation Results

This paper considers the leader-based consensus of heterogeneous multiple agents with nonlinear uncertain systems. Based on the information obtained from the following agents’ neighbors, leader observers are designed by the following agents to estimate the leader’s states and nonlinear dynamics. Then, to achieve leader-based consensus, adaptive distributed controllers are designed for the following agents to track the designed corresponding leader observers. The effectiveness of the leader observers and distributed consensus controllers are illustrated by formal proof and simulation results.

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Impact-Based Modeling of Backlash in Gear Driven Systems

ASME 2011 Dynamic Systems and Control Conference and Bath/ASME Symposium on Fluid Power and Motion Control, Volume 1 ◽

10.1115/dscc2011-6087 ◽

2011 ◽

Author(s):

Hari Vasudevan ◽

John Morrell

Keyword(s):

Nonlinear Dynamics ◽

Mechanical Systems ◽

Coefficient Of Restitution ◽

Impact Behavior ◽

Feedback Controllers ◽

Driven Systems ◽

Modeling Approach ◽

Piecewise Model ◽

Simulation Results

Backlash in gears creates nonlinear dynamics in mechanical systems and has been analyzed using a variety of methods and models. In this paper, we present a nonlinear, piecewise model for backlash dynamics that incorporates a coefficient of restitution to account for impact behavior during limit cycling. We analyze the energy absorbed by the collisions and derive a constraint for feedback controllers. We conclude with simulation results using this modeling approach.

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Simulation study of energetic-particle driven off-axis fishbone instabilities in tokamak plasmas

Nuclear Fusion ◽

10.1088/1741-4326/ac3e85 ◽

2021 ◽

Author(s):

Hanzheng Li ◽

Y Todo ◽

Hao Wang ◽

Malik Idouakass ◽

Jialei Wang

Keyword(s):

Distribution Function ◽

Resonance Frequency ◽

Linear Growth ◽

Particle Interaction ◽

Primary Resonance ◽

Tokamak Plasmas ◽

Spatial Profile ◽

Energetic Ions ◽

Nonlinear Phase ◽

Drift Frequency

Abstract Kinetic-magnetohydrodynamic hybrid simulations were performed to investigate the linear growth and the nonlinear evolution of off-axis fishbone mode (OFM) destabilized by trapped energetic ions in tokamak plasmas. The spatial profile of OFM is mainly composed of m/n = 2/1 mode inside the q = 2 magnetic flux surface while the m/n = 3/1 mode is predominant outside the q = 2 surface, where m and n are the poloidal and toroidal mode numbers, respectively, and q is the safety factor. The spatial profile of the OFM is a strongly shearing shape on the poloidal plane, suggesting the nonperturbative effect of the interaction with energetic ions. The frequency of the OFM in the linear growth phase is in good agreement with the precession drift frequency of trapped energetic ions, and the frequency chirps down in the nonlinear phase. Two types of resonance conditions between trapped energetic ions and OFM are found. For the first type of resonance, the precession drift frequency matches the OFM frequency, while for the second type, the sum of the precession drift frequency and the bounce frequency matches the OFM frequency. The first type of resonance is the primary resonance for the destabilization of OFM. The resonance frequency which is defined based on precession drift frequency and bounce frequency of the nonlinear orbit for each resonant particle is analyzed to understand the frequency chirping. The resonance frequency of the particles that transfer energy to the OFM chirps down, which may result in the chirping down of the OFM frequency. A detailed analysis of the energetic ion distribution function in phase space shows that the gradient of the distribution function along the E′ = const. line drives or stabilizes the instability, where E′ is a combination of energy and toroidal canonical momentum and conserved during the wave-particle interaction. The distribution function is flattened along the E′ = const. line in the nonlinear phase leading to the saturation of the instability.

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