Frequency multiplication with toroidal mode number of kink/fishbone modes on a static HL-2A-like tokamak

In the presence of energetic particles (EPs), the long-lived mode (LLM) frequency multiplication with n = 1, 2, 3, or higher is often observed on HL-2A, where n is the toroidal mode number. Hybrid kinetic-MHD model simulations of the energetic particle (EP) driven kink/fishbone modes on a static HL-2A-like tokamak using NIMROD code find that when the background plasma pressure is relatively high, and the EP pressure and the beam energy are relatively low, the mode frequency increases almost linearly with EP pressure, and the frequency is proportional to n ('frequency multiplication'), even in the absence of any equilibrium plasma rotation. In addition, the frequency multiplication persists as the safety factor at the magnetic axis q0 varies. In the absence of EPs, the growth rate of the 1/1 mode is the largest; however, as the EP pressure increases, the growth rate of 2/2 modes or 3/3 modes becomes dominant, suggesting that higher-n modes are more vulnerable to EPs. These results may shed light on the understanding of the toroidal mode number dependence of kink/fishbone modes in the advanced scenarios of tokamaks with weak or reversed central magnetic shear.     

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.     

Investigation of ion fishbone stability on HL-2A using NIMROD

Numerical calculations of resistive internal kink mode with effects of energetic particles (EPs) on HL-2A have been performed using the hybrid kinetic-MHD model inplemented in the NIMROD code. The m/n=1/1 resistive internal kink mode is unstable in MHD limit. However, with kinetic effects of energetic ions, a fishbone mode is excited with mode frequency around 10 kHz. We calculate the impact of resistivity on the growth rate and frequency of ion fishbone mode, and the results are in good agreement with the analytic solutions, which are obtained by solving the fishbone dispertion relation including resistivity effect. The effects of β_frac and cut off velocity of EP on fishbone mode are calculated in detail, where β_frac is the ratio of EP pressure to background plasma pressure. This work presents a clear explanation of the stabilizing effect of ECRH on ion fishbone, which is first observed on HL-2A.     

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 ...     

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。     

Nonlinear phase dynamics of ideal kink mode in the presence of shear flow

We investigate nonlinear phase dynamics of an ideal kink mode, induced by E × B flow. Here the phase is the cross phase(θ_c) between perturbed stream function of velocity■ and magnetic field ■, i.e. θ_c= θ_φ-θ_ψ. A dimensionless parameter, analogous to the Richardson number,■(γ_(kink): the normalized growth rate of the pure kink mode; ■: normalized E × B shearing rate) is defined to measure the competition between phase pinning by the current density and phase detuning by the flow shear. When R_i 1, θ_c is locked to a fixed value,corresponding to the conventional eigenmode solution. When R_i≤1, θ_c enters a phase slipping or oscillating state, corresponding to a nonmodal solution. The nonlinear phase dynamics method provides a more intuitive explanation of the complex dynamical behavior of the kink mode in the presence of E × B shear flow.     

Experimental observation of reverse- sheared Alfvén eigenmodes (RSAEs) in ELMy H-mode plasma on the EAST tokamak

Reverse-sheared Alfvén eigenmodes (RSAEs) have been observed by using an interferometer and ECE diagnostics in NBI heated ELMy H-mode plasma on EAST tokamak. A typical feature of these modes is a fast frequency sweeping upward from ∼80 kHz to ∼110 kHz in hundred milliseconds during which the plasma temperature, density and rotation keeps no change. Only core channels of the interferometer can observe these modes, implying a core localized mode. The ECE measurement further showed that these modes located at about ρ=0.37–0.46, just around the position of q_min with ρ∼0.4. These core localized modes are very weak in the magnetic fluctuations measured by mirnov probes mounted at the machine vacuum vessel. A multiple frequency fluctuation component, seemingly the so-called ‘grand cascades’, was also clearly observed on the ECE signal at ρ=0.46. During the phase, a transient internal transport barrier (ITB) in ion temperature and toroidal rotation was observed and the ITB foot was just close to the position of q_min . A modulation of RSAE frequency by ELM event was observed and this modulation could be attributed to rotation decrease orq_min increase due to ELM. Further study of these modes in EAST can provide valuable constraints for the q profile measurement and will be important for the long pulse operation.     

Internal Kink Instability in Shaped Tokamaks

A criterion of an ideal internal kink mode is derved for a shaped tokamak configuration in which q-profile is very flat in the core region.A combining criterion is obtained including the necessary criterion of Mercier and the sufficient criterion of Lortz.The new criterion makes progress compared with the necessary criterion of Mercier.In the elongated plasma.a polidal beta can cause instability,while the triangularity has a stabilizing effect.The result is applicable for DⅢ-D and SUNIST.     

The investigation of quasi coherent mode on EAST using Doppler reflectometry

An electrostatic Quasi coherent mode has been observed in density fluctuations and perpendicular velocity fluctuations with the frequency range of 3–80 k Hz on the Experimental Advanced Superconducting Tokamak using multi-channel Doppler reflectometry. It appears in the edge localized mode(ELM)-free period after L-H transition or in the inter-ELM period. The mode rotates almost together with the plasma with the poloidal wave number around 0.6cm~(-1) and its frequency chirps with plasma poloidal velocity. The mode can exist in a large radial coverage(ρ?=?0.75–0.98), and peaks near the top of pedestal, suggesting that it might be excited in the steep gradient pedestal region, and spread into the core area.     

Influence of adiabatic response of passing energetic ions on high-frequency fishbone

Adiabatic response effects on high-frequency fishbone instability driven by passing energetic ions are studied. With finite orbit width effects, the adiabatic contribution $\delta {W}_{{\rm{hf}}}$ is derived analytically for purely passing energetic ions. By approximating the adiabatic contribution to the first order of the reverse aspect ratio $\varepsilon ,$ we derive one of its analytic expressions, which is expected to be more accurate than that in a previous work (Graves J P 2004 Phys. Rev. Lett. 92 185003). For high-frequency fishbone instability, nonadiabatic response is usually dominant over adiabatic response, but under certain circumstances the latter plays an important role, comparable to the former. With a more generalized distribution function by introducing Gaussian-type factors representing their pitch and radial dependences and using a slowing-down equilibrium distribution for the energy of energetic ions, numerical analysis indicates that the adiabatic contribution is conducive to stabilization of the mode and causes a decrease in mode frequency. In addition, we find that the adiabatic contribution has a weak stabilizing effect on the fishbone instability when the finite orbit width effect is taken into account. We further analyze the dependence of the adiabatic contribution on the characteristic parameters of the distribution function. When the neutral beam has either a larger deviation from the plasma axis or a larger radial profile, the adiabatic contribution has a more evident effect on the fishbone instability. When the neutral beam has a relatively small critical energy, the adiabatic contribution has a greater effect on the mode instability.     

Linear hybrid simulations of low-frequency fishbone instability driven by energetic passing particles in tokamak plasmas

A linear simulation study of energetic passing particle-driven low-frequency fishbone instability in tokamak plasmas has been carried out using the global kinetic-MHD (magnetohydrodynamics) hybrid code M3D-K. This work is focused on the interaction of energetic passing beam ions andn=1 mode with a monotonic safety factorqprofile andSpecifically, the stability and mode frequency as well as mode structure of then=1 mode are calculated for scans of parameter values of beam ion beta, beam ion injection energy, beam ion orbit width, beam ion beta profile, as well as background plasma beta. The excited modes are identified as a low-frequency fishbone with the corresponding resonance ofwhereis the beam ion toroidal transit frequency andis the beam ion poloidal transit frequency. The simulated mode frequency is approximately proportional to the beam ion injection energy and beam ion orbit width. The mode structure is similar to that of internal kink mode. These simulation results are similar to the analytic theory of Yuet al.     

Balance of Liquid-phase Turbulence Kinetic Energy Equation for Bubble-train Flow

In this paper the investigation of bubble-induced turbulence using direct numerical simulation (DNS) of bubbly two-phase flow is reported. DNS computations are performed for a bubble-driven liquid motion induced by a regular train of ellipsoidal bubbles rising through an initially stagnant liquid within a plane vertical channel. DNS data are used to evaluate balance terms in the balance equation for the liquid phase turbulence kinetic energy. The evaluation comprises single-phase-like terms (diffusion, dissipation and production) as well as the interfacial term. Special emphasis is placed on the procedure for evaluation of interfacial quantities. Quantitative analysis of the balance equation for the liquid phase turbulence kinetic energy shows the importance of the interfacial term which is the only source term. The DNS results are further used to validate closure assumptions employed in modelling of the liquid phase turbulence kinetic energy transport in gas-liquid bubbly flows. In this context, the performance of respective closure relations in the transport equation for liquid turbulence kinetic energy within the two-phase k—epsilon and the two-phase k—l model is evaluated.     

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

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 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 β_h exceeds a critical value. The transition from NRK to NRFB occurs when the energetic-ion beta β_h increases to above a critical value. The resonance condition responsible for the excitation of NRFB is interestingly found to be satisfied at ωt + ω_p ≈ ω, where ωt is the toroidal motion frequency, ω_p is the poloidal motion frequency and ω is the mode frequency. The nonlinear evolutions of NRFB's mode structures and Poincaré 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.