Geodesic mode spectrum modified by the energetic particles in tokamak plasmas

Effect of a minor concentration of the energetic particles on GAM spectrum in a tokamak is analyzed by drift kinetic theory taking into the account the electron current and diamagnetic drift. A novel method of Jacobi functions is applied to solve the drift kinetic equation for the energetic bounce particles in the limit of high bounce frequency in comparison with the GAM frequency. Using the Q-asymptotic of Jacobi function, it is shown that the energetic minority ions can form the continuum minimum/maximum at the NB or ICR power deposition maximum where the geodesic eigenmode may be excited. In this case, the electron current modeled by shifted Maxwell distribution overcomes the ion Landau damping threshold thus resulting in the GAM instability.     

Splitting Scheme Integration of the Two-and-One-Half-Dimensional Vlasov Equation

A numerical splitting scheme technique is applied to the integration of the Vlasov equation in two-space and three velocity dimensions. Calculations are performed for a cold, stationary ion, mobile electron plasma in the presence of a constant external magnetic field. Results for Landau damping and the two-stream instability are presented in both one and two velocity dimensions. The Landau damping results show a plateau structure in the electron velocity distribution function in both the parallel and perpendicular directions formed as a result of the damping of a high initial electric field propagating at 45° to the parallel velocity axis. The two-stream velocity distribution function shows pitch angle scattering and velocity diffusion for an electron beam initially propagating at 45° to the magnetic field direction through a low-temperature equal density background. The two-stream distribution function evolves to a stable quasi-isotropic plateau structure similar to that found in auroral sounding rocket data.     

Electron current drive by fusion-product-excited lower hybrid drift instability

We present first principles simulations of the direct collisionless coupling of the free energy of fusion-born ions into electron current in a magnetically confined fusion plasma. These simulations demonstrate, for the first time, a key building block of some "alpha channeling" scenarios for tokamak experiments. Spontaneously excited obliquely propagating waves in the lower hybrid frequency range undergo Landau damping on resonant electrons, drawing out an asymmetric tail in the electron parallel velocity distribution, which carries a current.     

Toroidal Effect on Lower Hybrid Current Drive in Tokamak

In the review paper of N. J. Fish, the topics concerning the basic theory of lower hybrid wave heating and current drive are presented. In the consideration of radio-frequency heating and current drive of tokamak plasma near the lower hybrid frequency, the parallel wave length is imposed by the coupling device parallel to the magnetic field and is modified by gradients along the field. The important effects are found on wave penetration and damping when the toroidal aspect ratio is low. It may be possible to change the plasma current via electron Landau damping with a coupler rf power spectrum.     

低混杂波高N‖分量对EAST等离子体电流驱动的影响

EAST等离子体高约束模运行条件下，在等离子体边缘区域观测到明显的等离子体电流带.在EAST托卡马克装置非圆截面平衡位形下，使用射线追踪方法研究低混杂波高平行折射率N_‖分量对电流驱动的影响.结果表明：当-8≤N_‖≤-6时，平行折射率分量能够在小半径（0.7 < r/a < 1）区域驱动kA量级的等离子体电流.对于具有台基区、等离子体边缘温度更高的电子温度剖面，驱动电流的位置r/a>0.9.低混杂波朗道阻尼的理论分析与数值模拟结果一致.另外，高N_‖低混杂波在等离子体边缘的功率沉积和电流驱动与电子温度分布和发射谱分布相关.     

Short-wavelength plasmons in low-dimensional systems

The dispersion of plasma waves in systems of various dimensions is investigated up to the end point of the spectrum. In 2D and 3D systems, the plasmon spectrum still ends (due to Landau damping) within the applicability range of the quasi-classical approximation, i.e., for ?k ? p _F (?k is the plasmon momentum and p _F is the electron Fermi momentum). In 1D systems, the results are qualitatively different, since the Landau damping is concentrated in a region where the quantum effects cannot be ignored. This peculiarity of 1D systems gives rise to undamped branches of acoustic plasmons with a phase velocity lower than the electron Fermi velocity in multicomponent 1D plasmas.     

Ion velocity shear-induced drift wave and momentum transport in non-Maxwellian magnetoplasma flows

We have investigated the diamagnetic flow in a non-uniform partially ionized plasma with non-Maxwellian electron population to explain the dynamics of ion velocity shear-induced low-frequency drift mode and associated instabilities. The dispersion relations are found, and instability threshold conditions are pointed out along with ion-parallel momentum transport due to drift motion with relative phase shift of fluctuating quantities in a non-conservative system. The real frequencies and instability growth rates are studied numerically and illustrated for typical space and laboratory plasmas. This study should be useful in understanding some aspects of low-frequency time-delayed perturbations with sheared flow leading to drift instabilities and cross-field parallel ion momentum transport in nonuniform magnetoplasmas containing a non-Maxwellian electron population.     

托卡马克中快波电流驱动下全波方程的数值求解

用全波方法研究环形对称托卡马克等离子体中离子回旋频率范围内(ICRF)的快波电流驱动(FWCD)问题,考虑有限拉莫尔半径(FLR)效应和平行色散,建立全波计算的物理模型—全波方程,通过对全波方程的数值求解得到快波在等离子体中激发的电场强度分布.结果表明:快波可以传播到高温高密度等离子体的中心;快波在磁轴附近发生了模式转换;快波可以驱动中心的等离子体电流以改善等离子体的平衡位型;平行电场比垂直电场小三个数量级,通过垂直方向的回旋共振和平行方向的穿越期磁泵效应达到驱动电流的目的.     

Gradient Driven Azimuthal Ion Acoustic Waves

An instability of a magnetized plasma column in the frequency range has been identified as an ion acoustic one. The waves are azimuthally driven by the electron diamagnetic velocity due to the radial gradient of a fast electron tail. The strongest peaks in the frequency spectrum correspond to m = 6 or 8 wave lengths on one turn. This selection can be explained as an optimum value between increasing growth rate and the resonance disturbing phase mismatch at higher mode numbers.     

Change of zonal flow spectra in the JIPP T-IIU tokamak plasmas

When Ohmically heated low-density plasmas are additionally heated by higher-harmonics ion-cyclotron-range-of frequency heating, heated by neutral beam injection, or strongly gas puffed, the intensity of zonal flows in the geodesic acoustic mode frequency range in the tokamak core plasma decreases sharply and that of low-frequency zonal flow grows drastically. This is accompanied by a damping of the drift wave propagating in the electron diamagnetic drift direction, turbulence by trapped electron mode (TEM), and the increase of the mode propagating to ion diamagnetic drift direction (ITG). In the half-radius region, TEM and high-frequency zonal flows remain intense in both OH and heated phases. ITG and low-frequency zonal flows grow in heated plasmas, suggesting a strong coupling between ITG and low-frequency zonal flow.     

Stability of ion acoustic turbulent states

Several proposed renormalized theories for strong ion acoustic turbulence are compared to the direct interaction approximation. These are applied to the calculation of the stability of ion acoustic turbulent states to the excitation of Langmuir waves. A kinetic instability proposed by Tsytovich, Stenflo, and Wilhelmsson is shown to be stabilized by resonant and nonresonant decay processes. The global kinetic stability of the Langmuir spectrum is enhanced through the coupling of opposite phase velocity Langmuir waves by the decay processes and by nonresonant scattering to regions of strong Landau damping.     

Experimental verification of the shear-modified ion-acoustic instability

The predicted shear-induced shift of the wave phase velocity, the essence of the shear-modified ion-acoustic (SMIA) instability mechanism that reduces ion Landau damping for otherwise damped ion-acoustic waves [V. Gavrishchaka et al., 80, 728 (1998)], is verified with direct measurements in a strongly magnetized laboratory plasma. The SMIA growth rate is shown to increase with increasing shear, as predicted. SMIA wave propagation is shown to be possible at both small and large angles to the magnetic field, consistent with space observations of ion-acoustic-like waves.     

Instability of Bose-Einstein condensates moving in optical lattices

We investigate the Landau damping of Bogoliubov excitations in a dilute Bose gas moving in an optical lattice at a finite temperature. Using a 1D tight-binding model, we explicitly obtain the Landau damping rate, the sign of which determines the stability of the condensate. We find that the sign changes at a certain velocity, which is exactly the same as the critical velocity determined by the Landau criterion of superfluidity. This coincidence reveals the microscopic mechanism of the Landau instability.     

Magnetic domains in non-ferromagnetic metals: The non-linear de Haas-van Alphen effect

This review is devoted to an exposition of the principles of the physics of magnetic domains in non-ferromagnetic metals and diamagnetic phase transitions, which lead to the formation of the so-called Condon domains during magnetic oscillations in a three-dimensional electron gas. One of the goals of the review is to provide a deeper insight into the nature of this instability of the electron gas in normal metals and improve the understanding of this type of non-spin magnetism. We discuss theoretical aspects of the physics underlying magnetic ordering of conduction electrons in bulk metals and in thin films, and describe the behaviour of the susceptibility, thermal expansion, specific heat, compressibility, sound velocity, magnetic induction bifurcation, the order parameter, domain formation, wetting of domain walls, nucleation and kinetics of diamagnetic phase transitions. In the vicinity of diamagnetic phase transitions the results obtained coincide with those following from the Landau theory of phase transitions. The existence of the critical sample size for the diamagnetic phase transition in thin films is considered. We place special emphasis on the problem of the order of diamagnetic phase transitions. The survey is partly motivated as complementary to the recent review by G. Solt and V. Egorov describing the experimental situation in the field. Contents PAGE 1. Introduction 386 2. Diamagnetic phase transitions and Condon domains 390 2.1. Shoenberg's and Condon's consideration of the phenomena 390 2.2. Phase diagrams for one de Haas-van Alphen cycle 395 3. Critical phenomena at second-order diamagnetic phase transitions in three-dimensional metals 397 3.1. Introduction 397 3.2. Order parameter and susceptibility 397 3.3. Specific heat jump 403 3.4. Phase diagrams 407 3.5. Finite-size effects 410 3.6. Compressibility, thermal expansion and sound velocity 414 4. Condon domains and resonance methods of their investigation 417 4.1. Introduction 417 4.2. Nuclear magnetic resonance and Condon domains 418 4.3. Muon spin resonance spectroscopy and Condon domains 420 4.4. Critical exponents at diamagnetic phase transitions in silver and beryllium 426 4.5. Helicon resonance and Condon domains 428 4.6. Critical dynamics of the diamagnetic phase transition in aluminium 430 5. First-order diamagnetic phase transitions 431 5.1. Introduction 431 5.2. Domain formation 433 5.3. Kinetics 436 5.4. Wetting 441 5.5. Nucleation 442 5.6. Order of diamagnetic phase transitions 444 5.7. Hysteresis and Condon domains 445 6. Summary 446 7. Some open issues 448 Acknowledgements 450 References 451     

EAST装置上W波段多道极向相关反射仪的研制

在EAST装置上安装了X模极化W波段多道相关反射仪,用于测量等离子体芯部密度涨落。该诊断利用低损耗(<3dB)多工器将4个不同频率(79.2GHz,85.2GHz,91.8GHz和96GHz)的微波耦合在一起,通过同一个天线发射。反射波由两个极向分离(~5cm)的天线接收,通过下变频技术实现外差测量。通过对两个极向天线接收的信号进行相关分析,获得芯部湍流垂直速度。对2018年低约束模式(L模)放电进行分析发现,在电子回旋共振加热(ECRH)等离子体中,芯部湍流垂直速度在电子逆磁漂移方向。而在注入同向中性束(co-NBI)后,芯部湍流垂直速度变为离子逆磁漂移方向。     

Study of dust ion-acoustic wave propagation in the Lorentzian magnetized dusty plasma

Dust ion-acoustic waves propagation in the magnetized dusty plasma including ions, electrons and dust particulates are studied by using kinetic equation. For unbounded and collisionless plasma and in the presence of uniform external magnetic field B₀, electrons and ions with Lorentzian distribution function and dust particles with Maxwellian one are considered. Calculating dielectric tensor through the Vlasov equation solution, in the parallel propagation, dispersion relation is derived and suprathermal particle effects on the Landau damping is studied. It is shown that the Landau damping effect vanishes for parallel propagation.     

Wave Trajectories and Damping of Lower Hybrid Wave in Tokamak Plasmas

Incident lower hybrid waves (LHW) propagate toward the center of the plasma in a spiral form in the poloidal and the toroidal sections, and finally are absorbed by the ion Landau damping (ILD) and/or the electron Landau damping (ELD) in accordance with the refractive index parallel to the magnetic field N?, which is varied considerably along the trajectory because of the toroidicity and the rotational transform. We propose the scaling law of the wave trajectories on plasma parameters, which shows that the control of N? or the applied frequency is necessary during the lower hybrid heating (LHH).     

Nonlinear dispersion relation of geodesic acoustic modes

The energy input and frequency shift of geodesic acoustic modes (GAMs) due to turbulence in tokamak edge plasmas are investigated in numerical two-fluid turbulence studies. Surprisingly, the turbulent GAM dispersion relation is qualitatively equivalent to the linear GAM dispersion but can have drastically enhanced group velocities. In up-down asymmetric geometry the energy input due to turbulent transport may favor the excitation of GAMs with one particular sign of the radial phase velocity relative to the magnetic drifts and may lead to pulsed GAM activity.     

Aspects of Nonlinear Heating by Lower Hybrid Waves

Nonlinear instabilities driven by waves with frequencies comparable to the lower hybrid frequency are examined both analtyically and numerically using particle simulation techniques. Both the oscillating two-stream and ion-cyclotron instabilities are discussed. It is found that ion-cyclotron damping can be a more effective mechanism for driving instabilities in a hot tokamak plasma than electron Landau damping. Despite the one-dimensional nature of the simulation, the simulation results are useful for the interpretation of data obtained in recent lower hybrid heating experiments.     

Conditions for the Stable Acceleration of Ion Rings by Collapsed Liners

The conditions of suppressing the collective slowing-down of an ionic beam on electrons, which is caused by the excitation of electron plasma oscillations (beam instability) by ions, are found. In contrast to available explicit and implicit indications, a large spread of the energies only in an ionic beam is insufficient for this suppression. The acceleration of ions is shown to become stable when a sufficiently large spread of the electron velocities is simultaneously present. The beam instability of ions is suppressed by the Landau damping of the ion-excited plasma waves at electrons. The results obtained are used to analyze the possibility of ion acceleration by collapsed cylindrical plasma liners.