ELM triggering conditions for the integrated modeling of H-mode plasmas

Recent advances in the integrated modeling of ELMy H-mode plasmas are presented. A new model for the H-mode pedestal and for the triggering of ELMs predicts the height, width, and shape of the H-mode pedestal and the frequency and width of ELMs. The model for the pedestal and ELMs is used in the ASTRA integrated transport code to follow the time evolution of tokamak discharges from L-mode through the transition from L-mode to H-mode, with the formation of the H-mode pedestal, and, subsequently, to the triggering of ELMs. Turbulence driven by the ion temperature gradient mode, resistive ballooning mode, trapped electron mode, and electron temperature gradient mode contributes to the anomalous thermal transport at the plasma edge in this model. Formation of the pedestal and the L-H transition is the direct result of flow shear suppression of anomalous transport. The periodic ELM crashes are triggered by MHD instabilities. Two mechanisms for triggering ELMs are considered: ELMs are triggered by ballooning modes if the pressure gradient exceeds the ballooning threshold or by peeling modes if the edge current density exceeds the peeling mode threshold. The BALOO, DCON, and ELITE ideal MHD stability codes are used to derive a new parametric expression for the peeling-ballooning threshold. The new dependence for the peeling-ballooning threshold is implemented in the ASTRA transport code. Results of integrated modeling of DIII-D like discharges are presented and compared with experimental observations. The results from the ideal MHD stability codes are compared with results from the resistive MHD stability code NIMROD.Presented at the Workshop Electric Fields Structures and Relaxation in Edge Plasmas, Nice, France, October 26–27, 2004.     

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.     

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.     

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.     

Numerical study of physical properties of resistive wall modes in tokamaks

The effect of plasma with toroidal rotation on the resistive wall modes in tokamaks is studied numerically. An eigenvalue method is adopted to calculate the growth rate of the modes for changing plasma resistivity and plasma density distribution, as well as the diffusion time of magnetic field through the resistive wall. It is found that the resistive wall mode can be suppressed by the toroidal rotation of the plasma. Also, the growth rate of the resistive wall mode decreases when the edge plasma density is the same as the core plasma density, but it only changes slightly with the plasma resistivity.     

Experimental and theoretical study of quasicoherent fluctuations in enhanced D(alpha) plasmas in the Alcator C-Mod tokamak

A comparison of experimental measurements and theoretical studies of the quasicoherent (QC) mode, observed at high densities during enhanced D(alpha) (EDA) H mode in the Alcator C-Mod tokamak, are reported. The QC mode is a high frequency ( approximately 100 kHz) nearly sinusoidal fluctuation in density and magnetic field, localized in the steep density gradient ("pedestal") at the plasma edge, with typical wave numbers k(R) approximately 3-6 cm(-1), k(theta) approximately 1.3 cm(-1) (midplane). It is proposed here that the QC mode is a form of resistive ballooning mode known as the resistive X-point mode, in reasonable agreement with predictions by the BOUT (boundary-plasma turbulence) code.     

Proper orthogonal decomposition and galerkin projection for a three-dimensional plasma dynamical system

A general method by which to investigate nonlinear dynamical systems close to a stability threshold is presented. This method combines a proper orthogonal decomposition and a subsequent Galerkin projection. This technique is applied to three-dimensional resistive ballooning plasma fluctuations in a tokamak. The corresponding dynamical system belongs to a large family of convective fluid systems including Rayleigh-Benard convection. A proper orthogonal decomposition of the fluctuating signal obtained by numerical simulation shows that the relevant modes are close to the linear (global) modes. The Galerkin projection provides a low-dimensional system that allows the study of shear flow generation, its subsequent fluctuation reduction, and the evolution to oscillating states.     

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From the point of view of resistive MHD theory, the linear resistive tearing mode model in the low β plasma with macroscopic axial motion of plasma was deduced in a cylindrical geometry. Numerical study shows that the axial velocity of the plasma itself has a stable effect on tearing mode and the axial velocity shear role is not obvious. Analyses indicate that the axial motion reduces the tearing mode growth rate by changing the phase difference between the plasma potential perturbation and magnetic flux perturbation (deviating from π/2), and results in a lower tearing mode frequency.     

等离子体轴向运动对撕裂模不稳定性影响研究

从电阻磁流体模型出发,详细推导了柱形位形下低β等离子体中包括等离子体宏观轴向运动效应的电阻性撕裂模线性不稳定性理论。数值研究发现：等离子体轴向运动速度本身对撕裂模具有明显的稳定作用,而轴向运动速度剪切的作用并不明显。分析表明：轴向运动通过改变扰动势函数和磁通函数之间的相位差(偏离π/2)来降低撕裂模增长率,同时产生一个较低的撕裂模频率。     

离子动力参数区托卡马克电阻性内扭曲模稳定性分析

利用离子动力参数区的内扭曲模色散关系分析了托卡马克等离子体电阻性内扭曲模的频率和增长率随磁剪切量s₀的变化。我们发现:存在一个临界磁剪切量s_0c,只有当s₀>s_0c时,即中心安全因子q₀小于某个临界值q_0c时,电阻性内扭曲模才能被激发。另一方面,随着磁剪切量s₀的加大,增长率增大的趋势比相应的磁流体电阻性内扭曲模快得多,因而与锯齿的快崩裂有内在的联系。所 关键词：     

ITER装置中等离子体旋转和反馈控制对电阻壁模影响的数值研究

在托卡马克等离子体中,电阻壁模是非常重要的磁流体不稳定性,特征时间在毫秒量级.对长时间稳态运行下的先进托卡马克,电阻壁模限制着聚变装置的运行参数空间(放电时间和比压),影响经济效益,所以研究电阻壁模稳定性至关重要.本文使用MARS程序,针对ITER装置上9 MA先进运行平衡位形,研究了等离子体旋转和反馈控制对电阻壁模的影响.结果表明,在没有反馈控制时,当比压参数Cβ取0.7,等离子体环向旋转频率达到1.1%的阿尔芬频率时,可以完全稳定电阻壁模;在等离子体环向旋转和反馈控制共同作用时,比压参数Cβ取0.7,反馈增益|G|取0.6时,稳定电阻壁模所需要的等离子体旋转频率为0.2%的阿尔芬频率.可见,单独靠等离子体环向旋转稳定电阻壁模所需的旋转频率较大;而等离子体环向旋转和反馈控制共同作用可以降低稳定电阻壁模的旋转频率临界值,符合先进托卡马克的运行.本文的研究结果对中国聚变工程试验堆CFETR的工程设计和运行具有一定指导意义.     

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.     

Resistive wall mode in collisionless quasistationary plasmas

The stability analysis of the n=1 resistive wall mode is carried out for a simplified model of collisionless tokamak plasma. It is found that the trapped particle compressibility and the resonance between the mode and the precession drift frequency lead to a significant improvement of the beta stability limits. It is shown that, within the frame of the simplified model, the resistive wall mode can be fully suppressed and the plasma can be stable up to the wall beta limits for a slow plasma rotation.     

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：     

Effect of shear equilibrium flow in Tokamak plasma on resistive wall modes

A code named LARWM with non-ideal magnetohydrodynamic equations in cylindrical model is used to describe the instability in Tokamak plasma surrounded by a conducting wall with finite resistivity. We mainly take three factors related to the shear equilibrium plasma flow into consideration to study the stabilizing effect of the shear flow on the resistive wall modes (RWMs). The three factors are the velocity amplitude of flow, the shear rate of flow on plasma surface, and the inertial energy of equilibrium plasma flow. In addition, a local shear plasma flow is also calculated by the LARWM code. Consequently, it is found that the inertial energy of the shear equilibrium plasma flow has an important role in the stabilization of the RWMs.     

CRITICAL MAGNETIC SHEAR FOR THE TOKAMAK IDEAL INTERNAL KINK MODE IN THE ION KINETIC REGIME

It is shown that for the ideal internal kink mode of tokamak plasma, there exists a critical magnetic shear s_0c for its excitation when the finite ion Larmor radius effect is considered in the mode singular layer. This can be related to the sudden onset of the sawtooth and also to the stabilization of the sawtooth by the trapped hot ions observed experimentally. The alpha particle effect on this mode is revisited and some new results are reported.     

Parameter estimation in a tokamak transport model and applicationto L- and H-mode simulations

A systematic parameter estimation method has been established and applied to estimating a priori uncertain multipliers of flux formulas in a gyro-Bohm tokamak transport model. Results from simulating two tokamak discharge profiles with the model calibrated here are shown. The method used here can deal with limited and relatively uncertain experimental data by using estimates of prior knowledge concerning the accuracy of the data. Confidence regions are given to assess the accuracy of estimators. The estimated multipliers are much larger than in a similar study using a nongyro-Bohm transport model suggesting that mechanisms, in addition to early estimates of E×B driven fluxes from resistive ballooning and quasi-linear drift/η_i turbulence, are needed for a complete theoretical model of flux surface-averaged transport in tokamaks     

Evidence for the importance of trapped particle resonances for resistive wall mode stability in high beta tokamak plasmas

Active measurements of the plasma stability in tokamak plasmas reveal the importance of kinetic resonances for resistive wall mode stability. The rotation dependence of the magnetic plasma response to externally applied quasistatic n=1 magnetic fields clearly shows the signatures of an interaction between the resistive wall mode and the precession and bounce motions of trapped thermal ions, as predicted by a perturbative model of plasma stability including kinetic effects. The identification of the stabilization mechanism is an essential step towards quantitative predictions for the prospects of "passive" resistive wall mode stabilization, i.e., without the use of an "active" feedback system, in fusion-alpha heated plasmas.     

Measurement and analyses of the mean effective ion charge in the centre of tokamak discharges

There are two different definitions for specifying the mean effective ion charge Z_eff in plasmas: a) from the Spizer electrical resistivity of the plasma and b) from bremsstrahlung radiation losses of the plasma. In this paper Z_eff in the centre of tokamak ohmic discharges has been determined from information on sawtooth-relaxations of the steady state plasma, based on the analysis for the power balance of the plasma electrons in the plasma centre during the period of recovery after the sawtooth crashes. This method is found to supply reliable results for tokamak parameters. While its application requires some efforts in data analysis, it can provide a reliable determination of Z_eff, independent of the information from bremsstrahlung radiation losses of the plasma.     

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基于磁流体理论利用CIP方法数值对电阻磁流体中的磁岛演化动力学行为进行了长时间模拟。研究发现,磁岛饱和后流体演化并未结束,磁场重联将导致流体的宏观剪切流动。这一物理图象可用于解释托卡马克等离子体L-H模转换过程中观察到的磁流体行为。