Green's function for rf-driven current in a toroidal plasma

On the polarization of shear Alfvén and acoustic continuous spectra in toroidal plasmas

In this work, the FALCON code is adopted for illustrating the features of shear Alfvén and continuous spectra in toroidal fusion plasmas. The FALCON codes employs the local Floquet analysis discussed in [Phys. of Plasmas \textbf{26} (8), 082502 (2019)] for computing global structures of continuous spectra in general toroidal geometry. As particular applications, reference equilibria for the Divertor Tokamak Test and ASDEX Upgrade plasmas are considered. In particular, we illustrate the importance of mode polarization for recognizing the physical relevance of the various branches of the continu…

Investigation of toroidal acceleration and potential acceleration forces in EAST and J-TEXT plasmas

In order to produce intrinsic rotation, bulk plasmas must be collectively accelerated by the net force exerted on them, which results from both driving and damping forces. So, to study the possible mechanisms of intrinsic rotation generation, it is only needed to understand characteristics of driving and damping terms because the toroidal driving and damping forces induce net acceleration which generates intrinsic rotation. Experiments were performed on EAST and J-TEXT for ohmic plasmas with net counter- and co-current toroidal acceleration generated by density ramping up and ramping down. Add…

螺旋波在环形磁约束位形中的传播、等离子体产生及其与低频波的相互作用

Helicon wave propagation, plasma generation and interaction with low-frequency waves in toroidal magnetic configurations

本研究在TORPEX环形装置中首次详细表征了螺旋波，发现主导m=+1模式，振幅随功率线性增加并饱和，且与低频湍流存在非线性耦合。

环形等离子体中漂移阿尔芬波不稳定性激发零频率带状结构时等离子体非均匀性的影响

Effects of plasma nonuniformity on zero frequency zonal structure generation by drift Alfven wave instabilities in toroidal plasmas

本文利用非线性回旋动理学理论推导了ZFZS与DAW相互作用的控制方程和非线性色散关系，研究了等离子体非均匀性对带状结构激发的影响，并指出KBM激发带状流的条件对等离子体参数敏感。

Toroidal modeling of penetration of the resonant magnetic perturbation field

A toroidal, quasi-linear model is proposed to study the penetration dynamics of the resonant magnetic perturbation (RMP) field into the plasma. The model couples the linear, fluid plasma response to a toroidal momentum balance equation, which includes torques induced by both fluid electromagnetic force and by (kinetic) neoclassical toroidal viscous force. The numerical results for a test toroidal equilibrium quantify the effects of various physical parameters on the field penetration and on the plasma rotation braking. The neoclassical toroidal viscous torque plays a dominant role in certain r…

Role of wave-particle resonance in turbulent transport in toroidal plasmas

Wave-particle interaction in toroidal plasmas is an essential transport mechanism in drift wave instability-driven microturbulence. In tokamkas, different wave-particle resonance conditions have been found important for the energy and particle transport of multiple species in various drift wave turbulences. To confirm the transport mechanism for electrons and ions in tokamak drift-wave instabilities, the effect of wave-particle resonance on turbulent transport is studied using global gyrokinetic particle simulations of the plasma core ion temperature gradient (ITG) and collisionless trapped el…

Reconstruction of the magnetic perturbation in a toroidal force-free circular plasma: application to the Reversed Field Pinch

A new method to obtain the radial profile of the magnetic perturbation in a toroidal force-free plasma having circular cross section is developed. The method is quite general and can be applied to any circular low-beta plasma once suitable boundary conditions are imposed. In particular, due to its characteristics, it is appropriate for describing the Reversed Field Pinch (RFP) configuration. The curvilinear metric of the toroidal geometry is described by adopting flux co-ordinates, and the magnetic field is expressed by the contravariant representation with two independent potentials. The meth…

Anderson-Localized Ballooning Modes in General Toroidal Plasmas

Ballooning instabilities are investigated in three-dimensional magnetic toroidal plasma confinement systems with low global magnetic shear. The lack of any continuous symmetry in the plasma equilibrium can lead to these modes being localized along the field lines by a process similar to Anderson localization. This produces a multibranched local eigenvalue dependence, where each branch corresponds to a different unit cell of the extended covering space in which the eigenfunction peak resides. These phenomena are illustrated numerically for the three-field-period heliac H-1, and contrasted with …

The effect of time-varying flow-shear on the nonlinear stability of the boundary of magnetized toroidal plasmas

We propose a phenomenological yet very general model in a form of generalized complex Ginzburg-Landau equation to understand the dynamics of the quasi-periodic fluid instabilities (called edge-localized modes) in the boundary of toroidal magnetized high-temperature plasmas. The model reproduces key dynamical features of the boundary instabilities observed in the high-confinement state plasmas on the KSTAR tokamak, including quasi-steady states characterized by field-aligned filamentary eigenmodes, transitions between different eigenmodes, and rapid transition to non-modal filamentary structure…

Nonlinear excitation of geodesic acoustic mode by toroidal Alfvén eigenmodes and impact on plasma performance

Spontaneous nonlinear excitation of geodesic acoustic mode (GAM) by toroidal Alfvén eigenmode (TAE) is investigated using nonlinear gyrokinetic theory. It is found that, the nonlinear decay process depends on thermal ion βvalue. Here, βis the plasma thermal to magnetic pressure ratio. In the low-βlimit, TAE decays into a GAM and a lower TAE sideband in the toroidicity induced shear Alfvén wave continuous spectrum gap; while in the high-βlimit, TAE decays into a GAM and a propagating kinetic TAE in the continuum. Both cases are investigated for the spontaneous decay conditions. The nonlinear sa…

Rotation of Tokamak-Plasmas out of Mechanical Equilibria, in Absence of External Torques

Rotation of tokamak-plasmas, not at the mechanical equilibrium, is investigated utilizing a theorem of thermodynamics, established by Prigogine. This theorem, suitably applied to toroidally confined plasmas, suggests that the global barycentric rotations of the plasma, in the toroidal and poloidal directions, are pure reversible processes. In case of negligible viscosity and by supposing the validity of the balance equation for the internal forces, we show that the plasma, even not in the mechanical equilibrium, may freely rotate as a rigid body in the toroidal direction with an angular freque…

随机磁场中等离子体自发环向旋转的动理学模拟

Gyrokinetic simulation of the spontaneous toroidal rotation of plasma in a stochastic magnetic field

本文通过动理学模拟研究了随机磁场中等离子体的自发环向旋转，发现共振磁扰动通过双极径向电场驱动旋转，且碰撞效应在几次离子-离子碰撞时间后将其从回流转变为刚体流动，解释了DIII-D实验观测。

Solution to the Grad-Shafranov Boundary Value Problem for a Thermonuclear Plasma contained in a Toroidal Vase With a Conducting Wall under the Assumption of Constant Sources to the Equilibrium in Flux Space

A method is proposed to solve the Grad-Shafranov partial differential equation for the poloidal flux function associated with the equilibrium of a plasma magnetically confined in an axisymmetric torus under the assumption that the sources to the equilibrium (the gradient of the plasma pressure and the gradient of half the squared toroidal field function in flux space) are constant, and subjected to the condition of constant value of the poloidal flux at the toroidal boundary. The solution to the equation is written as the sum of the particular solution and a combination of N multipole solution…

Diffusive time evolution of the Grad-Shafranov Equation for a Toroidal Plasma

We describe the evolution of a plasma equilibrium having a toroidal topology in the presence of constant electric resistivity. After outlining the main analytical properties of the solution, we illustrate its physical implications by reproducing the essential features of a scenario for the upcoming Italian experiment Divertor Tokamak Test Facility, with a good degree of accuracy. Although we find the resistive diffusion timescale to be of the order of $10^4\,$s, we observe a macroscopic change in the plasma volume on a timescale of $10^2\,$s, comparable to the foreseen duration of the plasma d…

Toroidal equilibria in spherical coordinates

The standard Grad-Shafranov equation for axisymmetric toroidal plasma equilibrium is customary expressed in cylindrical coordinates with toroidal contours, and through which benchmark equilibria are solved. An alternative approach to cast the Grad-Shafranov equation in spherical coordinates is presented. This equation, in spherical coordinates, is examined for toroidal solutions to describe low $β$ Solovev and high $β$ plasma equilibria in terms of elementary functions.

非轴对称环形等离子体的电阻性有限压力磁流体动力学平衡的数值解

Numerical solutions of resistive finite-pressure magnetohydrodynamic equilibria for non-axisymmetric toroidal plasmas

开发了一种混合谱/有限元代码，通过结合双曲平行阻尼方程和动态电阻弛豫，无需假设嵌套磁通面即可数值求解非轴对称环形系统中的电阻性有限压力磁流体动力学平衡，并成功应用于stellarator、tokamak和reversed-field pinch等多种系统。

利用正弦扰动构造磁约束等离子体的三维平衡态

A special exact class of three-dimensional equilibria of a magnetized plasma exhibiting closed and nested toroidal magnetic surfaces

通过正弦扰动构建具有压力各向异性和闭合嵌套托卡马克磁面的三维平衡态，揭示磁岛和随机区域的形成及等磁面与准对称性的关系。

Magnetic topology and current channels in plasmas with toroidal current density inversions

The equilibrium magnetic field inside axisymmetric plasmas with inversions on the toroidal current density is studied. Structurally stable non-nested magnetic surfaces are considered. For any inversion in the internal current density the magnetic families define several positive current channels about a central negative one. A general expression relating the positive and negative currents is derived in terms of a topological anisotropy parameter. Next, an analytical local solution for the poloidal magnetic flux is derived and shown compatible with current hollow magnetic pitch measurements sho…

Axisymmetric Plasma Equilibria with Toroidal and Poloidal Velocity Fields: Tokamak Relevant Configurations

We analyze an axisymmetric equilibrium of a plasma endowed with toroidal and poloidal velocity fields, with the aim to characterize the influence of the global motion on the morphology of the magnetic confinement. We construct our configuration assuming that the poloidal velocity field is aligned with the poloidal magnetic field lines and, furthermore, we require that the plasma mass density depend on the magnetic flux function (or equivalently, that the plasma fluid be incompressible). We then derive a sort of Grad-Shafranov equation for such an equilibrium and implement it to tokamak relevan…

无碰撞环向等离子体中微撕裂模的回转动力学色散关系

The gyrokinetic dispersion relation of microtearing modes in collisionless toroidal plasmas

本文通过求解线性化回转动力学方程、准中性条件和安培定律，推导出无碰撞低β环向等离子体中微撕裂模的色散关系，揭示其由电子温度梯度经磁漂移驱动，为聚变装置抑制该不稳定性提供快速评估工具。

环形等离子体中磁力线行为的高效分析

Efficient analysis of magnetic field line behavior in toroidal plasmas

本文提出结合傅里叶变换与高斯窗函数的高效方法，以短积分分析环形等离子体中磁力线转变，用于偏滤器设计与破裂研究，对磁约束聚变至关重要。

新经典托卡马克粘性对存在共振磁扰动时等离子体流动演变的影响

Effects of neoclassical toroidal viscosity on plasma flow evolution in the presence of resonant magnetic perturbation in a tokamak

研究探讨了新经典托卡马克粘性对托卡马克中共振磁扰动下等离子体流动的影响，发现其对核心区域旋转剖面有影响，但对共振表面状态无影响。

A New Paradigm for Turbulent Transport Across a Steep Gradient in Toroidal Plasmas

First principle gyrokinetic simulation of the edge turbulent transport in toroidal plasmas finds a reverse trend in the turbulent transport coefficients under strong gradients. It is found that there exist both linear and nonlinear critical gradients for the nonmonotonicity of transport characteristics. The discontinuity of transport flux slope around the turning gradient shows features of second order phase transition. Under strong gradient the most unstable modes are in non-ground eigenstates with unconventional mode structures, which significantly reduces the effective correlation length an…

等离子体形状对先进托卡马克配置中核心局域环形阿尔法特征模奇偶性的影响

Influence of plasma shaping on the parity of core-localized toroidal Alfvén eigenmode in an advanced tokamak configuration

研究了等离子体形状对先进托卡马克配置中核心局域环形阿尔法特征模奇偶性的影响，发现等离子体形状变化导致模式奇偶性由奇变偶。

Observation of Toroidal Alfven Eigenmodes during Minor Disruptions in Ohmic Plasmas

Toroidal Alfven eigenmodes (TAEs) excited in purely ohmically heated plasmas without any auxiliary heating have been identified for the first time in the SUNIST spherical tokamak. The TAE modes are observed during minor disruptions and have a frequency range of 150-500 kHz. The mode structure analysis indicates the existence of both m/n=-3/-1 and -4/-1 harmonics, propagating in the electron diamagnetic direction in the laboratory frame of reference. These TAEs appear simultaneously with the generation of runaway electrons in the current quench phase, accompanying with the density sweeping duri…

Generalized curvature modified plasma dispersion functions and Dupree renormalization of toroidal ITG

A new generalization of curvature modified plasma dispersion functions is introduced in order to express Dupree renormalized dispersion relations used in quasi-linear theory. For instance the Dupree renormalized dispersion relation for gyrokinetic, toroidal ion temperature gradient driven (ITG) modes, where the Dupree's diffusion coefficient is assumed to be a low order polynomial of the velocity, can be written entirely using generalized curvature modified plasma dispersion functions: Knm's. Using those, Dupree's formulation of renormalized quasi-linear theory is revisited for the toroidal IT…

关于热等离子体非线性效应下环向阿尔芬特征模的非线性饱和

On nonlinear saturation of toroidal Alfvén eigenmode due to thermal plasma nonlinearities

研究热等离子体非线性效应下环向阿尔芬特征模的非线性饱和，通过gyrokinetic粒子-细胞模拟和理论分析，发现热等离子体非线性效应主导饱和水平，且与线性驱动无关，同时发现频率随振幅增加而降低，最终模式与连续谱合并实现饱和。

The plasma boundary in Single Helical Axis RFP plasmas

Single Helical Axis (SHAx) states obtained in high current reversed field pinch (RFP) plasmas display, aside from a dominant mode in the m=1 spectrum, also a dominant m=0 mode, with the same toroidal mode number as the m=1 one. The two modes have a fixed phase relationship. The island chain created by the m=0 mode across the reversal surface gives rise, at shallow reversal of the toroidal field, to an X-point structure which separates the last closed flux surface from the first wall, creating a divertor-like configuration. The plasma-wall interaction is found to be related to the connection le…

Symmetry breaking in MAST plasma turbulence due to toroidal flow shear

The flow shear associated with the differential toroidal rotation of tokamak plasmas breaks an underlying symmetry of the turbulent fluctuations imposed by the up-down symmetry of the magnetic equilibrium. Using experimental Beam-Emission-Spectroscopy (BES) measurements and gyrokinetic simulations, this symmetry breaking in ion-scale turbulence in MAST is shown to manifest itself as a tilt of the spatial correlation function and a finite skew in the distribution of the fluctuating density field. The tilt is a statistical expression of the "shearing" of the turbulent structures by the mean flow…

托卡马克中的环向磁通和分界面效应

The toroidal flux and separatrix effects in tokamaks

本文强调环向磁通在托卡马克中的重要性，通过解析模型展示分界面对平衡的影响，并建议使用环向磁通作为径向坐标以简化参数识别。

Unprecedented confinement time of electron plasmas with a purely toroidal magnetic field in SMARTEX-C

Confinement time of electron plasmas trapped using a purely toroidal magnetic field has been extended to $\sim 100$ s in a small aspect ratio ($R_{o}/{a} \sim {1.59}$, $R_o$ and $a$ are device major and minor radius, respectively), partial torus. It surpasses the previous record by nearly two orders of magnitude. Lifetime is estimated from the frequency scaling of the linear diocotron mode launched from sections of the wall, that are also used for mode diagnostics. Confinement improves enormously with reduction in neutral pressure in the presence of a steady state magnetic field. In addition, …

Studies of DC biasing of internal ring on plasma rotation and transport in a toroidal geometry

We report results from experiments performed to study how a DC bias with respect to the plasma potential is affecting the plasma states in the toroidal geometry of the Blaamann device in Tromso. In the experiments discussed here, a ring with smaller diameter than the limiter was centered inside the bulk of the plasma and its bias varied with respect to the plasma potential. In the electron saturation current regime of the ring, a significant reduction of the fluctuation levels was observed, and a shear in the poloidal velocity occurred at the low-field side of the ring. This shear was position…

On scattering and damping of Toroidal Alfven eigenmode by drift wave turbulence

We demonstrate analytically that, in toroidal plasmas, scattering by drift wave turbulence could lead to appreciable damping of toroidal Alfven eigenmodes via generation of short-wavelength electron Landau damped kinetic Alfven waves. A corresponding analytic expression of the damping rate is derived, and found to be, typically, comparable to the linear drive by energetic particles. The implications of this novel mechanism on the transport and heating processes in burning plasmas are also discussed.

环向旋转等离子体中湍流与新经典钨输运的自洽回旋动理学建模

Self-consistent gyrokinetic modelling of turbulent and neoclassical tungsten transport in toroidally rotating plasmas

本文利用全局非线性回旋动理学代码GYSELA模拟环向旋转下钨的湍流与新经典输运，揭示离心力导致的极向不对称、向内聚集及旋转扩散引发的向外湍流通量。

An Overview of Plasma Confinement in Toroidal Systems

This overview presents a tutorial introduction to the theory of magnetic plasma confinement in toroidal confinement systems with particular emphasis on axisymmetric equilibrium geometries, and tokamaks. The discussion covers three important aspects of plasma physics: Equilibrium, Stability, and Transport. The section on equilibrium will go through an introduction to ideal magnetohydrodynamics, curvilinear system of coordinates, flux coordinates, extensions to axisymmetric equilibrium, Grad-Shafranov Equation (GSE), Green's function formalism, as well as analytical and numerical solutions to GS…

Interplay of transitions between oscillations with emergence of fireballs and quantification of phase coherence, scaling index in a magnetized glow discharge plasma of toroidal assembly

Interplay of transition of floating potential fluctuations in a glow discharge plasma in the toroidal vacuum vessel of SINP tokamak has been observed. With variation in the strength of the vertical and toroidal magnetic fields, regular and inverted relaxation oscillations as well as sinusoidal oscillations are observed with the slow and fast time scale of the relaxation oscillations reversing their nature at a high value of vertical magnetic field strength. However for small value of toroidal magnetic field the transitions follow relaxation $\rightarrow$ chaotic oscillations with the chaotic n…

Nonlinear Saturation of Kinetic Ballooning Modes by Zonal fields in Toroidal Plasmas

Kinetic ballooning modes (KBM) are widely believed to play a critical role in disruptive dynamics as well as turbulent transport in tokamaks. While the nonlinear evolution of ballooning modes has been proposed as a mechanism for detonation in tokamak plasmas, the role of kinetic effects in such nonlinear dynamics remains largely unexplored. In this work global gyrokinetic simulation results of KBM nonlinear behavior are presented. Instead of the finite-time singularity predicted by ideal MHD theory, the kinetic instability is shown to develop into an intermediate nonlinear regime of exponentia…

Zero-Turbulence Manifold in a Toroidal Plasma

Sheared toroidal flows can cause bifurcations to zero-turbulent-transport states in tokamak plasmas. The maximum temperature gradients that can be reached are limited by subcritical turbulence driven by the parallel velocity gradient. Here it is shown that q/ε(magnetic field pitch/inverse aspect ratio) is a critical control parameter for sheared tokamak turbulence. By reducing q/ε, far higher temperature gradients can be achieved without triggering turbulence, in some instances comparable to those found experimentally in transport barriers. The zero-turbulence manifold is mapped out, in the ze…

离子驱动的环形电子等离子体失稳——一项3D3V PIC模拟

Ion-driven destabilization of a toroidal electron plasma -- A 3D3VPIC Simulation

本文利用高保真3D3V PIC模拟研究紧长宽比环形电子等离子体中Ar+离子引发的共振失稳，揭示了模耦合、电流增长、离子加热及温度标度规律。

托卡马克等离子体中环向阿尔芬本征模对漂移波的非线性散射

On Nonlinear Scattering of Drift Wave by Toroidal Alfven Eigenmode in Tokamak Plasmas

本文以电子漂移波为范例，解析研究了托卡马克等离子体中其与环向阿尔芬本征模的直接波-波相互作用，发现TAE非线性散射对eDW稳定性的净效应可忽略，与反向过程存在显著差异。

Statistical description of turbulent transport for flux driven toroidal plasmas

A novel methodology to analyze non-Gaussian probability distribution functions (PDFs) of intermittent turbulent transport in global full-f gyrokinetic simulations is presented. In this work, the Auto-Regressive Integrated Moving Average (ARIMA) model is applied to time series data of intermittent turbulent heat transport to separate noise and oscillatory trends, allowing for the extraction of non-Gaussian features of the PDFs. It was shown that non-Gaussian tails of the PDFs from first principles based gyrokinetic simulations agree with an analytical estimation based on a two fluid model.

碰撞离子轨道损失对L模等离子体托卡马克径向电场和环向旋转的影响

Effects of collisional ion orbit loss on tokamak radial electric field and toroidal rotation in an L-mode plasma

本文利用XGC模拟研究DIII-D L模等离子体中碰撞离子轨道损失，发现其使边缘径向电场向负方向移动，并驱动共电流方向的边缘环向旋转。

Efficient magnetic fields for supporting toroidal plasmas

The magnetic field that supports tokamak and stellarator plasmas must be produced by coils well separated from the plasma. However the larger the separation, the more difficult it is to produce a given magnetic field in the plasma region, so plasma configurations should be chosen that can be supported as efficiently as possible by distant coils. The efficiency of an externally-generated magnetic field is a measure of the field's shaping component magnitude at the plasma compared to the magnitude near the coils; the efficiency of a plasma equilibrium can be measured using the efficiency of the …

环形等离子体约束装置中电阻壁模的扩展变分方法

An Extended Variational Method for the Resistive Wall Mode in Toroidal Plasma Confinement Devices

该研究扩展了环形等离子体电阻壁模的经典变分分析，推导了厚壁条件下电阻壁模的广义增长率公式与旋转稳定公式，揭示了厚壁效应对模式增长/衰减特性及旋转稳定的影响规律。

磁约束等离子体中的磁力线混沌、康托集与转子

Magnetic Field Line Chaos, Cantori, and Turnstiles in Toroidal Plasmas

本文综述了磁约束等离子体中混沌、康托集和转子数学概念的物理意义及其在磁重联、非共振分流器和失控电子等关键问题中的应用。

On resistive magnetohydrodynamic equilibria of an axisymmetric toroidal plasma with flow

It is shown that the magnetohydrodynamic equilibrium states of an axisymmetric toroidal plasma with finite resistivity and flows parallel to the magnetic field are governed by a second-order partial differential equation for the poloidal magnetic flux function $ψ$ coupled with a Bernoulli type equation for the plasma density (which are identical in form to the corresponding ideal MHD equilibrium equations) along with the relation $Δ^\star ψ=V_c σ$. (Here, $Δ^\star$ is the Grad-Schlüter-Shafranov operator, $σ$ is the conductivity and $V_c$ is the constant toroidal-loop voltage divided by $2 π$)…

反磁剪切对托卡马克中电阻壁模等离子体旋转稳定的影响

Effects of reversed magnetic shear on the plasma rotation stabilization of resistive wall modes in tokamaks

本研究利用AEGIS代码探究反磁剪切对托卡马克电阻壁模旋转稳定的影响，发现反磁剪切会拓宽不稳定窗口、降低旋转稳定效果，提高完全抑制所需的旋转频率阈值，对先进托卡马克的旋转稳定提出更严苛要求。

Simultaneous feedback control of toroidal magnetic field and plasma current on MST using advanced programmable power supplies

Programmable control of the inductive electric field enables advanced operations of reversed-field pinch (RFP) plasmas in the Madison Symmetric Torus (MST) device and further develops the technical basis for ohmically heated fusion RFP plasmas. MST's poloidal and toroidal magnetic fields ($B_\text{p}$ and $B_\text{t}$) can be sourced by programmable power supplies (PPSs) based on integrated-gate bipolar transistors (IGBT). In order to provide real-time simultaneous control of both $B_\text{p}$ and $B_\text{t}$ circuits, a time-independent integrated model is developed. The actuators considered…

Neoclassical toroidal viscosity torque in tokamak edge pedestal induced by external resonant magnetic perturbation

The characteristic profile and magnitude are predicted in theory for the neoclassical toroidal viscosity (NTV) torque induced by plasma response to the resonant magnetic perturbation (RMP) in a tokamak with an edge pedestal. For a low-$β$ equilibrium, the NTV torque is dominated by the toroidal component with the same dominant toroidal mode number of RMP. The NTV torque profile is found to be localized, whose peak location is determined by profiles of both the equilibrium temperature (pressure) and the plasma response. In general, the peak of NTV torque profile is found to track the pedestal p…

Production of overdense plasmas by launching 2,45 GHz electron cyclotron waves in a helical device

For production of low temperature plasmas with low collisionality, 2.45GHz microwave power up to 20kW is injected perpendicularly to the toroidal field at very low toroidal field Bt

Islands and current singularities in quasisymmetric toroidal plasmas

The presence of current singularities in a quasisymmetric magnetic field is explored. Quasisymmetry is shown effective in isolating Pfirsch-Schlüter singularities, to leading order, to a single magnetic surface resonant with the helicity of the symmetry. The effects of pressure driven currents are analysed, indicating that exclusion of this surface from the plasma volume reduces the potential opening of islands, but does not generally eliminate them completely due to higher order asymmetric geometric effects. These three-dimensional effects are contained in quasisymmetry and indicate the compl…

Reevaluation of the Braginskii viscous force for toroidal plasma

The model by Braginskii for the viscous stress tensor is used to determine the shear and gyroviscous forces acting within a toroidally confined plasma. Comparison is made to a previous evaluation which contains an inconsistent treatment of the radial derivative and neglects the effect of the pitch angle. Parallel viscosity contributes a radial shear viscous force which may develop for sufficient vertical asymmetry to the ion velocity profile. An evaluation is performed of this radial viscous force for a tokamak near equilibrium which indicates qualitative agreement between theory and measureme…

Kinetic theory of geodesic acoustic modes in toroidal plasmas: a brief review

Geodesic acoustic modes (GAM) are oscillating zonal structures unique to toroidal plasmas, and have been extensively studied in the past decades due to their potential capabilities of regulating microscopic turbulences and associated anomalous transport. This article reviews linear and nonlinear theories of GAM; with emphases on kinetic treatment, system nonuniformity and realistic magnetic geometry, in order to reflect the realistic experimental conditions. Specifically, in the linear physics, the resonant wave-particle interactions are discussed, with the application to resonant excitation b…

Aspect ratio scaling of the Single Helical states in the Reversed Field Pinch plasmas

In this paper a new idea is presented which is able to predict the scaling law with the aspect ratio for the toroidal mode number of the so called Single Helicity states in Reversed Field Pinch plasmas. The model starts considering the pure electromagnetic interaction of an helical current with a conductive toroidal shell. The stability properties of the plasma become then essential in determining the emergence of the observed dominant mode.