Effect of collisionality on kinetic stability of the resistive wall mode

The impact of collisionless, energy-independent, and energy-dependent collisionality models on the kinetic stability of the resistive wall mode is examined for high pressure plasmas in the National Spherical Torus Experiment. Future devices will have decreased collisionality, which previous stability models predict to be universally destabilizing. In contrast, in kinetic theory reduced ion-ion collisions are shown to lead to a significant stability increase when the plasma rotation frequency is in a stabilizing resonance with the ion precession drift frequency. When the plasma is in a reduced stability state with rotation in between resonances, collisionality will have little effect on stability.     

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.     

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.     

Current-Driven Kink-Like Instability in Collisional Plasmas

The stability of left-hand circularly polarized waves propagating along an external magnetic field with wavelengths much larger than the ion Larmor radius is studied for fully-ionized collisional plasmas carrying a field-aligned current. It is found that, in the presence of electron-ion collisions, this "kink-like" instability has two branches of unstable wavenumbers: a main branch and a resistive branch. The resistive branch owes its existence to electron-ion collisions, but its growth rate is much smaller than that of the main branch, which is typically some fraction of the ion cyclotron frequency. The effect of collisions on the main branch is to reduce its maximum growth rate while extending the range of unstable wavenumbers to larger values. However, these changes are significant only when the electron-ion collision frequency is comparable to the electron cyclotron frequency. The dispersion relation is solved numerically for plasma and magnetic field parameters appropriate to the UCLA arcjet plasma. The results show that, within the framework of an infinite and homogeneous theory, the kink-like instability should occur in this plasma device.     

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.     

平衡电流位形对电阻壁模稳定性影响的数值模拟

数值研究平衡电流位形对电阻壁模式稳定性的影响.研究发现,对于不同的电流位形,当等离子体边缘处安全因子一定时,最不稳定的电阻壁模的环向模数和极向模数相同.在同一壁位置下,非均匀电流位形驱动的电阻壁模的线性增长率比均匀电流位驱动的电阻壁模的线性增长率大.等离子体速度流在不同的初始电流位形下对电阻壁模稳定性的影响不同.由于磁力线在壁上的挤压,经过线性演化后,电阻壁模进入非线性演化并达到饱和状态,非均匀电流位形下的扰动磁能比均匀电流位形下的扰动磁能饱和度低.     

Resonance of static-error-field amplification in tokamak plasmas

With explicit torque expression derived, it is found that the resonance of the static-error-field amplification (i.e., the maximum of the static-error-field-induced torque) in tokamak plasmas lies at the no-wall stability limit, instead of at the resistive wall mode stability limit as given by the existing theories. This brings theoretical predictions into qualitative conformity with experiments.     

温离子对动力迥旋损失锥不稳定性的作用

本文详细研究了温离子对动力论迴旋损失锥(DCLC)不稳定性的作用,并与温离子抑制流体近似下DCLC模的理论进行了比较,发现由于(1)磁漂移共振耗散可以激发负能的DCLC波;(2)另一种新的正能波可以因共振获得能量而增长;因此当流体近似DCLC模被少量温离子所抑制的同时,动力论DCLC模仍然是不稳定的。所以要抑制动力论DCLC不稳定性需要注入更多的温离子,本文给出了定量的结果。 关键词：     

Resonant field amplification near the RWM stability boundary in a tokamak

Evolution of a resistive wall mode (RWM)—a magnetic field perturbation produced by a plasma and partially stabilized by a conducting wall—is considered. It is assumed that there is a small resonant harmonic in the spectrum of the static error field. It is shown that the effect of this harmonic on the dynamics of stable RWMs increases as the plasma approaches the RWM stability boundary. The error field is “amplified” during the transition through this boundary. The smaller the rotation velocity of the perturbation and the longer the time during which the plasma stays near the stability boundary, the stronger this amplification is.     

On the influence of dissipative effects on instabilities of differentially-rotating plasmas

The stability of differentially-rotating cylindrical plasmas in the axial homogeneous magnetic field is studied in the framework of one-fluid dissipative magnetohydrodynamics. The dispersion relation of small-scale axisymmetric perturbations, taking into account the effects of the plasma thermal stratification, its resistivity and its viscosity, is derived. In the limiting cases of negligible resistivity and of negligible viscosity, the criteria of plasma stability are obtained. It is shown that in the case of small viscosity, the azimuthal flow of resistive plasma in the axial magnetic field is unstable due to the buoyancy effect if both the plasma pressure and its entropy either increase or decrease in the radial direction.     

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研究了模与模之间的相互作用对电阻壁模(RWM)稳定性的影响.当存在多个模的相互作用时,最不稳定的(3,1)模的线性增长率有所下降.经过线性演化后,因磁力线在壁上的挤压,电阻壁模进入非线性饱和状态.与单个模的演化相比,多个模存在时,(3,1)模的饱和度会下降,(5,2)模的磁能会有相应的增长,而(2,1)模磁能饱和度变化不大.     

Stability of a self-gravitating homogeneous resistive plasma

In this paper, we analyze the stability of a homogeneous self-gravitating plasma, having a non-zero resistivity. This study provides a generalization of the Jeans paradigm for determining the critical scale above which gravitational collapse is allowed.We start by discussing the stability of an ideal self-gravitating plasma embedded in a constant magnetic field. We outline the existence of an anisotropic feature of the gravitational collapse. In fact, while in the plane orthogonal to the magnetic field the Jeans length is enhanced by the contribution of the magnetic pressure, outside this plane perturbations are governed by the usual Jeans criterion. The anisotropic collapse of a density contrast is sketched in detail, suggesting that the linear evolution provides anisotropic initial conditions for the non-linear stage, where this effect could be strongly enforced.The same problem is then faced in the presence of non-zero resistivity and the conditions for the gravitational collapse are correspondingly extended. The relevant feature emerging in this resistive scenario is the cancelation of the collapse anisotropy in weakly conducting plasmas. In this case, the instability of a self-gravitating resistive plasma is characterized by the standard isotropic Jeans length in any directions. The limit of very small resistivity coefficient is finally addressed, elucidating how reminiscence of the collapse anisotropy can be found in the different values of the perturbation frequency inside and outside the plane orthogonal to the magnetic field.     

剪切磁场位形下电阻壁模不稳定性的数值模拟

数值研究了平衡磁场位形对电阻壁模稳定性的影响。研究发现,磁场剪切对电阻壁模有解稳作用,对于不同的剪切磁场位形,最不稳定的电阻壁模的环向模数和极向模数不同。等离子流对电阻壁模的增长有抑制作用,稳定住电阻壁模的临界流速度随着磁场剪切率的增大而增大。电阻壁模经线性增长后,进入非线性演化阶段,最后达到饱和状态,剪切磁场位形下的扰动磁能比均匀磁场位形下的扰动磁能饱和度高。     

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.     

Sustained stabilization of the resistive-wall mode by plasma rotation in the DIII-D tokamak

Values of the normalized plasma pressure up to twice the free-boundary stability limit predicted by ideal magnetohydrodynamic (MHD) theory have been sustained in the DIII-D tokamak. Long-wavelength modes are stabilized by the resistive wall and rapid plasma toroidal rotation. High rotation speed is maintained by minimization of nonaxisymmetric magnetic fields, overcoming a long-standing impediment [E. J. Strait, Phys. Rev. Lett. 74, 2483 (1995)]]. The ideal-MHD pressure limit calculated with an ideal wall is observed as the operational limit to the normalized plasma pressure.     

Effect of Temperature Anisotropy on Various Modes and Instabilities for a Magnetized Non-relativistic Bi-Maxwellian Plasma

Using kinetic theory for homogeneous collisionless magnetized plasmas, we present an extended review of the plasma waves and instabilities and discuss the anisotropic response of generalized relativistic dielectric tensor and Onsager symmetry properties for arbitrary distribution functions. In general, we observe that for such plasmas only those modes whose magnetic-field perturbations are perpendicular to the ambient magnetic field, i.e., B ₁ $\bot $ B ₀, are effected by the anisotropy. However, in oblique propagation all modes do show such anisotropic effects. Considering the non-relativistic bi-Maxwellian distribution and studying the relevant components of the general dielectric tensor under appropriate conditions, we derive the dispersion relations for various modes and instabilities. We show that only the electromagnetic R- and L- waves, those derived from them (i.e., the whistler mode, pure Alfvén mode, firehose instability, and whistler instability), and the O-mode are affected by thermal anisotropies, since they satisfy the required condition $\mathbf{B}_{1}\bot \mathbf{B}_{0}$ . By contrast, the perpendicularly propagating X-mode and the modes derived from it (the pure transverse X-mode and Bernstein mode) show no such effect. In general, we note that the thermal anisotropy modifies the parallel propagating modes via the parallel acoustic effect, while it modifies the perpendicular propagating modes via the Larmor-radius effect. In oblique propagation for kinetic Alfvén waves, the thermal anisotropy affects the kinetic regime more than it affects the inertial regime. The generalized fast mode exhibits two distinct acoustic effects, one in the direction parallel to the ambient magnetic field and the other in the direction perpendicular to it. In the fast-mode instability, the magneto-sonic wave causes suppression of the firehose instability. We discuss all these propagation characteristics and present graphic illustrations. The threshold conditions for different instabilities are also obtained.     

Super-thermal particles in hot plasmas—Kinetic models,numerical solution strategies,and comparison to tokamak experiments

The excitation of collective instabilities by super-thermal particles in hot plasmas and the related transport processes attract increasing interest due to their fundamental challenges for theoretical models and their practical importance for burning fusion plasmas. In fact, the physics of a self-heated thermonuclear plasma due to fusion-born 3.5 MeV α$\alpha$-particles is one of the most important outstanding fundamental research topics on the way to a fusion power plant with magnetic confinement. Within the last 10 years significant advances on both the theoretical and the experimental sides have been made leading to a more detailed and quantitative understanding of fast-particle-driven instabilities. On the theoretical side, the crucial step was to move from fluid models for the plasma background with a hybrid kinetic expression for the energetic particles to a fully kinetic model for all the plasma species, i.e. background ions, background electrons, and fast ions. This improvement allows one to describe consistently the resonant interaction between global plasma waves such as shear Alfvén and Alfvén–acoustic waves, and the particles via Landau damping, i.e. the dynamics parallel to the magnetic background field. Also, mode conversion mechanisms require the inclusion of background ion scales in a kinetic, non-perturbative way. This accurate treatment of the plasma background leads not only to changes in the linear mode properties such as frequency, growth/damping rate, and mode structure but also influences the non-linear dynamics. Due to major advances, innovations and installation of diagnostics in present day experiments, this comparison can be carried out in a more detailed and comprehensive way than a few years ago. For example, the measurement of damping rates via active external antennas, the imaging of 2D mode structures via electron–cyclotron-emission spectroscopy, and the direct detection of escaping fast ions allow to diagnose various kinetic features of the plasma modes that are responsible for the transport of energetic particles. Furthermore, the fast particle distribution function itself can also be measured with much greater confidence. Therefore, the new physics accessible due to a more comprehensive model and numerical implementation can be directly verified and validated with experimental data.     

First observation of edge localized modes mitigation with resonant and nonresonant magnetic perturbations in ASDEX Upgrade

First experiments with nonaxisymmetric magnetic perturbations, toroidal mode number n=2, produced by newly installed in-vessel saddle coils in the ASDEX Upgrade tokamak show significant reduction of plasma energy loss and peak divertor power load associated with type-I edge localized modes (ELMs) in high-confinement mode plasmas. ELM mitigation is observed above an edge density threshold and is obtained both with magnetic perturbations that are resonant and not resonant with the edge safety factor profile. Compared with unperturbed type-I ELMy reference plasmas, plasmas with mitigated ELMs show similar confinement, similar plasma density, and lower tungsten impurity concentration.     

Antenna coupling study for ICWC plasma characterization in TEXTOR

Ion cyclotron wall conditioning (ICWC) discharges, in pulsed-mode operation, were carried out in the limiter tokamak TEXTOR to explore safe operational regimes for the experimental parameters for possible ICWC-discharge cleaning in International Thermonuclear Experimental Reactor (ITER) at half field. Antenna coupling properties obtained during the ion cyclotron range of frequencies (ICRF) wall conditioning experiments performed in helium–hydrogen mixture in TEXTOR were analysed in relation to the obtained ICWC-plasma characterization results. Satisfactory antenna coupling in the mode conversion scenario along with reproducible generation of ICRF plasmas for wall conditioning, were achieved by coupling radio frequency (RF) power from one or two ICRF antennas. The plasma breakdown results obtained in the TEXTOR tokamak have been compared with the predictions of a zero-dimensional RF plasma production model. The present study of ICWC emphasizes the beneficial effect of application of an additional (along with toroidal magnetic field) stationary vertical (B _V???B _T) or oscillating poloidal magnetic field (B _P???B _T) on antenna coupling and relevant plasma parameters.