Monte Carlo simulation of lower hybrid current drive in tokamaks

In this paper, we present a method for noninductive current drive studies based on three-dimensional simulation of test particle orbits. A Monte Carlo momentum diffusion operator is developed to model the wave-particle interaction. The scheme can be utilized in studies of current drive efficiency as well as in examining the current density profiles caused by waves with a finite parallel wave number spectrum and a nonuniform power deposition profile in a toroidal configuration space of arbitrary shape. Calculations performed with a uniform power deposition profile of lower hybrid waves for axisymmetric magnetic configurations having different aspect ratios and poloidal cross-section shape confirm the semianalytic estimates for the current drive efficiency based on the solutions of the flux surface averaged Fokker-Planck equation for configurations with circular poloidal cross section. The consequences of the combined effect of radial diffusion, magnetic trapping and radially nonhomogeneous power deposition and background plasma parameter profiles are investigated     

托卡马克等离子体不同运行模式下的电子回旋波电流驱动

在给定等离子体密度分布下，从电子、离子的能量方程出发，根据不同运行模式下等离子体的热传导率不同，分别求出了中心负剪切模式，常规剪切H模式和L模式下的等离子体温度分布，然后通过求解波迹方程与相对论情况下的Fokker-Planck方程，分别计算了这些模式下的电子回旋波电流驱动和波功率沉积.得到在中心负剪切下，驱动电流最大，驱动效率最高，功率沉积和电流分布区间跨度大；在常规剪切H模式下，驱动电流较小，分布区间跨度比较窄，驱动效率相对较低；在常规剪切L模式，驱动电流效率最低，分布区间跨度也非常集中. 关键词： 托卡马克 电子回旋波电流驱动 中心负剪切 常规剪切     

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The synergy current drive by combining electron cyclotron wave (ECW) with lower hybrid wave (LHW) can be used to either increase the noninductive current drive efficiency or shape the plasma current profile. In this paper, the synergy current drive by ECW and LHW is studied with numerical simulation. The nonlinear relationship between the wave powers and the synergy current of ECW and LHW is revealed. When the LHW power is small, the synergy current reduces as the ECW power increases, and the synergy current is even reduced to lower than zero, which is referred as negative synergy in the this context. Research shows that the mechanism of the negative synergy is the peaking effect of LHW power profile and the trapped electrons effect. The present research is helpful for understanding the physics of synergy between electron cyclotron current drive and lower hybrid current drive, it can also instruct the design of experiments.     

托卡马克等离子体不同平衡位形下的电子回旋波电流驱动

在给定的等离子体总电流和中心电流密度条件下,数值求解平衡方程,求出不同拉长比和三角形变因子的托卡马克等离子体温度、密度、磁场分布,然后通过求解波迹方程和Fokker-Planck方程,分别计算这些位形下的电子回旋波波迹和电流驱动.结果表明：电子回旋波X模从顶部发射时,随着拉长比的增大,波迹会向弱场侧偏移.电子回旋波X模从弱场侧发射时,电子回旋波在等离子体中传播沉积的功率份额随着拉长比的增大而增加,驱动电流位置随着三角形变因子的增大向等离子体中心移动.驱动电流位置随环向和极向发射角的减小向中心移动,对应的电流密度峰值也变大.     

Steady-state fully noninductive current driven by electron cyclotron waves in a magnetically confined plasma

A steady-state, fully noninductive plasma current has been sustained for the first time in a tokamak using electron cyclotron current drive only. In this discharge, 123 kA of current have been sustained for the entire gyrotron pulse duration of 2 s. Careful distribution across the plasma minor radius of the power deposited from three 0. 5-MW gyrotrons was essential for reaching steady-state conditions. With central current drive, up to 153 kA of current have been fully replaced transiently for 100 ms. The noninductive scenario is confirmed by the ability to recharge the Ohmic transformer. The dependence of the current drive efficiency on the minor radius is also demonstrated.     

低杂波控制电流分布与改善约束研究

在HT-7超导托卡马克装置上利用低杂波电流驱动有效地控制了等离子体电流分布,并使等离子体约束性能改善。数值模拟与硬X射线测量结果均表明,低杂波的发射功率谱、纵场和等离子体密度对改变等离子体电流分布有明显的影响。在优化低杂波电流驱动实验参数的条件下,等离子体密度、温度分布发生了理想的变化。在电子和离子温度分布上出现了内部输运垒,同时等离子体的能量约束时间和粒子约束时间均有提高。     

On the Choice of Electron Cyclotron Heating Frequency for T-15MD Tokamak

Physics of Atomic Nuclei - Electron cyclotron heating is one of the methods of additional plasma heating and noninductive current drive in the T-15MD tokamak. One to eight gyrotrons with a total...     

Reconstruction of the equilibrium of the plasma in a Tokamak and identification of the current density profile in real time

The reconstruction of the equilibrium of a plasma in a Tokamak is a free boundary problem described by the Grad–Shafranov equation in axisymmetric configuration. The right-hand side of this equation is a nonlinear source, which represents the toroidal component of the plasma current density. This paper deals with the identification of this nonlinearity source from experimental measurements in real time. The proposed method is based on a fixed point algorithm, a finite element resolution, a reduced basis method and a least-square optimization formulation. This is implemented in a software called Equinox with which several numerical experiments are conducted to explore the identification problem. It is shown that the identification of the profile of the averaged current density and of the safety factor as a function of the poloidal flux is very robust.     

Dynamical plasma response during driven magnetic reconnection

Direct measurements of a collisionless current channel during driven magnetic reconnection are obtained for the first time on the Versatile Toroidal Facility. The size of the diffusion region is found to scale with the electron drift orbit width, independent of the ion mass and plasma density. Based on experimental observations, analytic expressions governing the dynamical evolution of the current profile and the formation of the electrostatic potential that develops in response to the externally imposed reconnection drive are established. This time response is closely linked to the presence of ion polarization currents.     

Hall Effects on Magnetic Relaxation

A generalized vorticity is introduced whose self-linkage (the hybrid helicity) and flux are invariants of ideal incompressible magnetohydrodynamics (MHD) when the Hall term is included. A model of magnetofluid relaxation is constructed for Hall magnetohydrodynamics by assuming that the energy seeks the minimum value compatible with constrained values of magnetic helicity, hybrid helicity, axial magnetic flux, and fluid vorticity flux. As a result of the coupling of magnetic field to fluid vorticity in the generalized vorticity, it is found that the relaxed magnetic-field configuration need not be force free. The presence of a nonvanishing fluid vorticity is shown to be necessary for the existence of relaxed magnetic-field configurations that confine a finite plasma pressure. The study has potential relevance to the dynamics and morphology of space and cosmic plasmas, as well as to pressure confinement and current drive in fusion plasmas.     

Laboratory observations of spontaneous magnetic reconnection

Detailed measurements of spontaneous magnetic reconnection are presented. The experimental data, which were obtained in the new closed Versatile Toroidal Facility magnetic configuration, document the profile evolution of the plasma density, magnetic flux function, reconnection rate, and the current density during a spontaneous reconnection event in the presence of a strong guide magnetic field. The reconnection process is at first slow, which allows magnetic stress to build in the system while the current channel becomes increasingly narrow and intense. The onset of a fast reconnection event occurs as the width of the current channel approaches the ion-sound-Larmor radius rho s. During the reconnection event magnetically stored energy is channeled into energetic ion outflows and a rapid increase in the electron temperature.     

Quasisteady high-confinement reversed shear plasma with large bootstrap current fraction under full noninductive current drive condition in JT-60U

A quasisteady reversed shear plasma with a large bootstrap current fraction ( approximately 80%) has been obtained for the first time in the JT-60U tokamak. The shrinkage of reversed shear region was suppressed by the bootstrap current peaked at the internal transport barrier (ITB) layer and the ITBs at a large radius were sustained, which, by combination with an H-mode edge pedestal, resulted in a high confinement or 2.2 times the H-mode scaling for 6 times energy confinement time or 2.7 s. Furthermore, a full noninductive current drive was obtained by the bootstrap current and the beam driven current.     

Study of Conditions for Obtaining Quasi-Stationary Scenarios in T-15 MD Tokamak

The study of conditions for obtaining quasi-stationary scenarios in the T-15MD tokamak is performed. Results of simulation and optimization of T-15MD regimes with a fully noninductive current drive using NBICD systems with the power of 6–8 MW, ECCD system with the power ~8 MW, and RFCD system with power up to 7–8 MW are presented. It is shown that, at the somewhat reduced value as compared to the basic value of the toroidal magnetic field B _t ~ 1.5 T in the T-15MD tokamak, discharges can be produced with a fully noninductive current of about 1 MA, plasma temperature of several keV, plasma density of about (3–7) × 10¹⁹ m^–3, and discharge duration of about 20 s. Such discharges are of interest for further experimental study.     

Inductance of rf-wave-heated plasmas

The inductance of rf-wave-heated plasmas is derived. This inductance represents the inductance of fast electrons located in a plateau during their acceleration due to electric field or deceleration due to collisions and electric field. This inductance has been calculated for small electric fields from the two-dimensional Fokker-Planck equation as the flux crossing the surface of critical energy mv(2)(ph)/2 in the velocity space. The new expression may be important for radio-frequency current drive ramp-up, current drive efficiency, current profile control, and so on in tokamaks. This inductance may be incorporated into transport codes that study plasma heating by rf waves.     

Novel Applications of Millimeter and Submillimeter Wave Gyro-Devices

The possible applications of high-power millimeter (mm) and submillimeter waves from gyro-devices span a wide range of technologies. The plasma physics community has already taken advantage of recent advances in applying high-power micro- and mm-waves generated by gyrotron oscillators in the areas of RF-plasma production, heating, noninductive current drive, plasma stabilization and active plasma diagnostics for magnetic confinement thermonuclear fusion research, such as lower hybrid current drive (8 GHz), electron cyclotron resonance heating (ECRH) (28–170 GHz), electron cyclotron current drive (ECCD), collective Thomson scattering and heat-wave propagation experiments. Other important applications of gyrotrons are electron cyclotron resonance (ECR) discharges for generation of multi-charged ions and soft X-rays, as well as industrial materials processing and plasma chemistry. Submillimeter wave gyrotrons are employed in high-frequency broadband electron paramagnetic resonance (EPR) spectroscopy. Future applications which await the development of novel high-power gyro-amplifiers include high resolution radar ranging and imaging in atmospheric and planetary science as well as deep-space and specialized satellite communications and RF drivers for next-generation high-gradient linear accelerators (supercolliders). The present paper reviews the state-of-the-art and future prospects of these recent applications of gyro-devices.     

Validation of neoclassical bootstrap current models in the edge of an H-mode plasma

Analysis of the parallel electric field E(parallel) evolution following an L-H transition in the DIII-D tokamak indicates the generation of a large negative pulse near the edge which propagates inward, indicative of the generation of a noninductive edge current. Modeling indicates that the observed E(parallel) evolution is consistent with a narrow current density peak generated in the plasma edge. Very good quantitative agreement is found between the measured E(parallel) evolution and that expected from neoclassical theory predictions of the bootstrap current.     

磁场中电弧等离子体柱的螺旋不稳定性

讨论了具有抛物互形电流分布的电弧等离子体柱在磁场中的不稳定性问题，从磁流体力学方程组出发，推导出电弧柱扰动满足的方程与边界条件，求得了这些方程的解析解，进而导出了在趋中心电流分布情形下电弧运动所满足的微分方程，由此给出了稳定性判据。将所得结果与均匀电流分布情形做了比较，稳定区域增宽，与实验结果相符。     

Steady state self-focusing, self-modulation of laser beam in an inhomogeneous plasma

Laboratory as well as PIC simulation experiments reveal strong flow of energetic electrons co-moving with laser beam in laser plasma interaction. Equation governing the evolution of complex envelope in slowly varying envelope approximation is nonlinear parabolic equation. Variational approach is used to solve this problem and a Lagrangian for the problem is set up. Assuming a trial Gaussian profile, authors solve the reduced Lagrangian problem for beam width and curvature. Two scale lengths for inhomogenity along the direction of propagation, one for nonlinearity and other for diffraction management are introduced. Self-focusing, self-modulation as well as self-trapping of the laser-electron-beam plasma system is studied under variety of parameters.     

Stabilization of tearing mode by current drive

The major disruption limits the operation of present tokamaks. Experimental evidences point out that the growth of tearing modes or the magnetic islands is primarily responsible for the occurrence. Taking the non-inductive current drive effects into account, a set of 3D nonlinear equation is derived. It is shown from simulation that the growth of the magnetic island is suppressed effectively by RF current drive. It is consistent with recent experiments on the HL-1 tokamak in which the plasma is stabilized by an RF current drive.     

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将等离子体作为磁流体,考虑其流体属性和电磁属性,介绍了利用FLUENT软件包并将其进行二次开发,解算电磁场方程、质量连续性方程、动量守恒方程、以及能量守恒方程的数值模拟方法,得到了以磁矢势为表达形式的电磁场分布、温度分布和速度分布.数值模拟了粉末球化所用的感应耦合等离子体炬电磁场分布、温度分布、速度分布.分析了温度分布、速度分布产生的物理原因,为感应耦合等离子体炬球化粉末颗粒提供理论性指导.