Stability of tokamak plasmas with internal transport barriers against high n ideal magnetohydrodynamic ballooning mode

A ballooning mode equation for tokamak plasma, with the toroidicity and the Shafranov shift effects included, is derived for a shift circular flux tokamak configuration. Using this equation, the stability of the plasma configuration with an internal transport barrier （ITB） against the high n （the toroidal mode number） ideal magnetohydrodynamic （MHD） ballooning mode is analysed. It is shown that both the toroidicity and the Shaftanov shift effects are stabilizing. In the ITB region, these effects give rise to a low shear stable channel between the first and the second stability regions. Out of the ITB region towards the plasma edge, the stabilizing effect of the Shaftanov shift causes the unstable zone to be significantly narrowed.     

Global gyrokinetic stability of pressure-gradient-driven electromagnetic modes in tokamaks with regions of low shear

Tokamaks with large pressure gradients (alpha(max)) formed in regions of weak magnetic shear are shown to be susceptible to novel, low-n, global, kinetic, electromagnetic modes with a toroidal mode number n in the range 21 on the magnetic axis and alpha(max) near q(min), new, global kinetic infernal modes with a strong mode rotation omega(r) and a finite growth rate gamma<|omega(r)| are found. For equilibria with reverse shear where q(min) is off axis and alpha(max) near q(min), the existence of an unstable low-n global branch of Alfve n ion temperature gradient modes is revealed with an oscillatory gamma as a function of n. The addition of trapped electron dynamics is shown to be further destabilizing.     

Role of flow shear in the ballooning stability of tokamak transport barriers

A tokamak's confinement time is greatly increased by a transport barrier (TB), a region having a high pressure gradient and usually also a strongly sheared plasma flow. The pressure gradient in a TB can be limited by ideal magnetohydrodynamic instabilities with a high toroidal mode number n ("ballooning modes"). Previous studies in the limit n--> infinity showed that arbitrarily small (but nonzero) flow shears have a large stabilizing influence. In contrast, the more realistic finite n ballooning modes studied here are found to be insensitive to sub-Alfvénic flow shears, provided the magnetic shear s approximately 1 (typical for TBs near the plasma's edge). However, for the lower magnetic shears that are associated with internal transport barriers, significantly lower flow shears will influence ballooning mode stability, and flow shear should be retained in the analysis of their stability.     

Mechanism of stabilization of ballooning modes by toroidal rotation shear in tokamaks

A ballooning perturbation in a toroidally rotating tokamak is expanded by square-integrable eigenfunctions of an eigenvalue problem associated with ballooning modes in a static plasma. Especially a weight function is chosen such that the eigenvalue problem has only the discrete spectrum. The eigenvalues evolve in time owing to toroidal rotation shear, resulting in a countably infinite number of crossings among them. The crossings cause energy transfer from an unstable mode to the infinite number of stable modes; such transfer works as the stabilization mechanism of the ballooning mode.     

高能粒子对托卡马克气球模稳定作用的数值分析

用数值方法分析了高能捕获粒子对托卡马克气球模不稳定性的影响.利用变步长RKF积分方法求解了相应的微分-积分方程边值问题.数值结果表明,气球模不稳定区随高能粒子压强增大而缩小,充分说明了高能捕获粒子能部分或全部抑制气球模不稳定性.     

Suppression of plasma turbulence during optimized shear configurations in JET

Correlation of density turbulence suppression and reduced plasma transport is observed in the internal transport barrier (ITB) region of JET tokamak discharges with optimized magnetic shear. The suppression occurs in two stages. First, low frequency turbulence and ion transport are reduced across the plasma core by a toroidal velocity shear generated by intense auxiliary heating. Then with the ITB formation, high frequency turbulence and electron transport are reduced locally within the steep pressure gradient region of the ITB.     

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Using the drift kinetic equation the influence of the ballooning component of the perturbed transit ion pressure on the low-frequency Alfvéen waves in a toroidal plasma is considered. It is shown that this contribution to the plasma pressure leads in a relatively cold plasma (plasma edge) to a stabilization of the Alfvéen modes. Taking into account drift effects the modified Alfvéen wave becomes unstable if the temperature gradient is large enough. All the perturbations are strongly localized around the corresponding rational magnetic surface.     

Effect of local toroidal flow on double-tearing modes in cylindrical geometry

The effect of local toroidal flow (LTF) on double-tearing modes (DTMs) is investigated in cylindrical geometry using the reduced magnetohydrodynamics (RMHD) model. The results indicate that the LTF between the two rational surfaces is the dominant suppression effect on DTMs. The suppression effect is enhanced with the flow width increasing, and the DTMs become more stable with the increase of the shear of the LTF between the two rational surfaces. So, in the reversed shear magnetic field configuration, the local flow is driven between the two rational surfaces, which can effectively suppress the development of DTMs and maintain the high-performance state.     

Strong "quantum" chaos in the global ballooning mode spectrum of three-dimensional plasmas

The spectrum of ideal magnetohydrodynamic (MHD) pressure-driven (ballooning) modes in strongly nonaxisymmetric toroidal systems is difficult to analyze numerically owing to the singular nature of ideal MHD caused by lack of an inherent scale length. In this paper, ideal MHD is regularized by using a k-space cutoff, making the ray tracing for the WKB ballooning formalism a chaotic Hamiltonian billiard problem. The minimum width of the toroidal Fourier spectrum needed for resolving toroidally localized ballooning modes with a global eigenvalue code is estimated from the Weyl formula. This phase-space-volume estimation method is applied to two stellarator cases.     

东方超环上低杂波驱动等离子体环向旋转实验研究

旋转和旋转剪切能抑制磁流体不稳定性和增强等离子体约束.低杂波电流驱动作为未来聚变堆上可能的旋转驱动手段,探索低杂波在现有托卡马克装置上驱动等离子体旋转的驱动机制,可以为未来的聚变堆上旋转预测提供重要参考.在东方超环托卡马克装置上,早期发现了2.45 GHz的低杂波能有效驱动等离子体旋转的现象,认为是边界旋转的改变导致芯部旋转的同电流方向的增加造成的.更高频率下4.6 GHz低杂波电流驱动可以更有效地驱动同电流方向的等离子体旋转.本论文分析在欧姆背景等离子体下,不同功率的低杂波对等离子体环向旋转的影响,研究安全因子剖面变化对环向旋转的关系,利用功率调制获得了低杂波驱动旋转实验中的环向动量输运系数变化情况,发现环向动量扩散系数(χφ)、环向动量箍缩系数(Vpinch)的数值大小趋势是从芯部向靠外的区域逐渐变大.这与低杂波驱动环向旋转时,环向旋转速度由靠外的区域向芯部传递的特性吻合.     

The Influence of Stochastic Layers of Magnetic Field Lines on Transport Barrier Formation in a Stellarator System

The results of local measurements of RF discharge plasma parameters in the process of internal transport barriers (ITB) formation in the vicinity of rational magnetic surfaces in the Uragan-3M torsatron are presented. The following phenomena were observed in the process of ITB formation: widening of the radial density distribution, formation of plateaus on radial density and electron temperature distributions, formation of regions with high shear of poloidal plasma rotation velocity and radial electric field in the vicinity of stochastic layers of magnetic field lines, decrease of density fluctuations and their radial correlation length, decorrelation of density fluctuations, and increase of the bootstrap current.After the ITB formation, the transition to the improved plasma confinement regime takes place. The transition moves to the beginning of the discharge with the increase of heating power. The possible mechanism of ITB formation near rational surfaces is discussed.     

Geodesic acoustic mode induced by toroidal rotation in tokamaks

The effect of toroidal rotation on the geodesic acoustic mode (GAM) in a tokamak is studied. It is shown that, in addition to a small frequency upshift of the ordinary GAM, another GAM, with much lower frequency, is induced by the rotation. The new GAM appears as a consequence of the nonuniform plasma density and pressure created by the centrifugal force on the magnetic surfaces. Both GAMs in a rotating plasma are shown to exist both as continuum modes with finite mode numbers m and n at the rational surfaces q=m/n as well as in the form of axisymmetric modes with m=n=0.     

EAST H模等离子体中离子内部输运垒特性 的初步实验研究

为了研究EAST上H模等离子体中离子内部输运垒(ITB)的特性，利用电荷交换复合光谱诊断，分析了离子ITB形成和稳态阶段等离子体离子温度和环向旋转速度的时空演化。结果表明，在离子ITB形成和稳定期间，ITB肩部附近(R=1.928m)的离子温度梯度增加时，ITB区域(R=1.984m)的离子温度梯度会有所降低，反之亦然。考虑到在离子ITB形成前，芯部区域不同半径位置的离子温度梯度同时增加或减小，得到了在R=1.984m处判断离子ITB是否形成的归一化离子温度梯度的阈值。     

Internal kink instability during off-axis electron cyclotron current drive in the DIII-D tokamak

Experimental evidence is reported of an internal kink instability driven by a new mechanism: barely trapped suprathermal electrons produced by off-axis electron cyclotron heating on the DIII-D tokamak. It occurs in plasmas with an evolving safety factor profile q(r) when q(min) approaches 1. This instability is most active when ECCD is applied on the high field side of the flux surface. It has a bursting behavior with poloidal/toroidal mode number = m/n = 1/1. In positive magnetic shear plasmas, this mode becomes the fishbone instability. This observation can be qualitatively explained by the drift reversal of the barely trapped suprathermal electrons.     

Nondiffusive transport in tokamaks: three-dimensional structure of bursts and the role of zonal flows

Large scale transport events are studied in simulations of resistive ballooning turbulence in a tokamak plasma. The spatial structure of the turbulent flux is analyzed, indicating radially elongated structures (streamers) at the low field side which are distorted by magnetic shear at different toroidal positions. The interplay between self-generated zonal flows and transport events is investigated, resulting in significant modifications of the frequency and the amplitude of bursts. The propagation of bursts is studied in the presence of a transport barrier generated by a strong shear flow.     

Discharges in the JET tokamak where the safety factor profile is identified as the critical factor for triggering internal transport barriers

Joint European Torus discharges which demonstrate the critical role the safety factor profile, q, can play in the formation of internal transport barriers (ITB) are examined. In these discharges, the target parameters, including the E x B flows, were kept virtually the same, except for the q profile. In a discharge with a nonmonotonic q, an ITB was triggered whereas a discharge with monotone q made no such transition. Thus, there is strong evidence that the q profile was the critical factor for the triggering of an ITB. Possible interpretations of this finding are discussed.     

环流器等离子体高n气球模的第二稳定区

本文讨论了圆截面高比压等离子体关于高n气球模的稳定性,在高比压情况下,相应的极向磁场对气球模有相当强的驱动作用,从而严重影响了第二稳定区的结构,我们详细计算了不同剪切、不同压强梯度及不同极向场参数对气球模本征函数和本征频率的影响,这些结果比较完善地反映了圆截面环流器中理想磁流体气球模理论所预示的主要结论。 关键词：     

Viscoresistive g-modes and ballooning

The effect of viscosity on resistive g-modes and ballooning is investigated. Simple magnetized plane slab geometry is employed and a gravitational acceleration modulated along magnetic field lines is introduced in order to simulate toroidal curvature. Both g-mode and ballooning-type growth rates are abtained from the same model in the limits of long and short connection length, respectively. Parallel viscosity is involved in stabilizing these modes at sufficiently high values of the density and plasma size. A threshold for instability is found which scales like na². A cutoff also exists when finite perpendicular viscosity is introduced and combined with sufficiently high magnetic shear.     

Energetic-ion excited internal kink modes with weak magnetic shear in q0> 1 tokamak plasmas

The energetic particle driven internal kink mode is investigated in this paper for q0 1 tokamak plasma with weak magnetic shear. With the effect of energetic particles, the m/n = 1/1 internal mode structure in tokamak plasma does not appear as a rigid step-function when safety factor passes through q = 1 rational surface. It is found that even when the rational surface is removed, the mode may be still unstable under the low magnetic shear condition if the energetic particle drive is strong enough; with the low shear region of safety factor profile widening, the mode becomes more unstable with its growth-rate increasing. Furthermore, we find that the existence of the q = 1 rational surface does not have a significant effect on the stability of the plasma if energetic particles are present, which is very different from the scenarios of the ideal-MHD modes.