Fokker-planck study of tokamak electron cyclotron resonance heating

A Fokker－Planck study is carried out for tokamak electron cyclotron resonance heating by writing the quasi-linear diffusion operator into a form adaptive to the collision operator and considering the wave absorption characteristics of both the O-mode and the X-mode in different magnetic surfaces. Though the Fokker－Planck code is non-relativistic in nature, however, if the relativistic resonance condition for the nearly perpendicularly propagating waves is treated suitably, we can obtain correct results. The energy loss mechanism through anomalous transport is also modelled using a suitable loss term. In the heating phase, the electron distribution deviates from the Maxwellian distribution substantially, which leads to non-linear absorption characteristics. The wave damping rate is non-linear and changes with time. The electron pressure is usually anisotropic under different conditions: p_{e⊥}/p_{e‖}>2 for different D_0 and τ_e.     

Stochastic heating of plasma at electron cyclotron resonance

It is shown theoretically and experimentally that stochastic heating of plasma electrons is highly efficient. Calculations have shown that over the course of 100 periods of an external microwave field the kinetic energy of the particles reaches values of around 1.0 MeV and the average energy reaches values of the order of 0.3 MeV in the field of two oppositely propagating characteristic (eigen) waves of a cylindrical waveguide, with amplitudes 24 kV/cm in a 1 kG stationary magnetic field. Stochastic instability develops as a result of overlapping of non-linear cyclotron resonances. The experimental results agree with the theory: When these waves are excited by a 0.9 MW external source, above a threshold of 0.45 MW one obtains x rays with a photon energy corresponding to a maximum electron energy of the order of 1 MeV over about 800 periods of the external microwave field. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 11, 806–811 (10 June 1999)     

Complex ray tracing study of electron cyclotron resonance heating

In the up-to-date ray tracing study of electron cyclotron resonance heating (ECRH) of fusion plasmas, energy absorption effect has never been considered into the wave trajectory computation. Thus all the work has been done in real space so far. In this paper we consider coupling of energy absorption to wave trajectory for the first time, and numerically solve the formal complex Hamilton equations in complex space, then take the real-space-projected wave trajectories and group velocities to be the corresponding concrete ones. It is shown that both ordinary wave and extraordinary wave injected from the inner side of the tokamak plasmas approach the electron cyclotron resonance surface step by step and their group velocities become exceedingly small as they move toward this surface. Those clearly show that the resonance between the electron cyclotron waves and the fusion plasmas takes place in the electron cyclotron resonance region, which is just the case the ECRH experimental results and the plasma kinetic theory of waves demonstrate.     

Determination of the electron temperature of a degenerate semiconductor in quantizing fields under heating by an electric field

Investigations of the Shubnikov-de Haas oscillation of the transverse magnetoresistance due to the magnitude of the electric field in n-type InSb with 5 · 10¹⁵, 3 · 10¹⁶ cm^–3 concentrations at a 4.2 °K temperature are carried out herein. A method is proposed to determine the electron temperature T_e; dependences of T_e on the electric and magnetic fields in the sample are obtained for a transversely oriented magnetic field. The relaxation time of the electron energy is estimated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 96–100, February, 1972.     

Calculation of parameters of krypton plasma excited by electron beam with additional heating by high-frequency electric field

The electron energy-distribution functions, the rates of plasmochemical reactions, and the densities of various plasma components have been calculated for a microwave discharge (f = 1000 MHz, P = 100–700 mW) in krypton plasma (p = 0.5 atm) excited by an electron beam with an energy of 12 keV. It has been found that the heating by a microwave field shifts the peak of the electron energy-distribution function (EEDF) from 0.5 to 2 eV, which leads to higher rates of reactions with excitation thresholds lying near the EEDF peak. As a result, the population of excited levels increases by two to three times.     

Study of runaway electron behaviour during electron cyclotron resonance heating in the HL-2A Tokamak

During the current flat-top phase of electron cyclotron resonance heating discharges in the HL-2A Tokamak, the behaviour of runaway electrons has been studied by means of hard x-ray detectors and neutron diagnostics. During electron cyclotron resonance heating, it can be found that both hard x-ray radiation intensity and neutron emission flux fall rapidly to a very low level, which suggests that runaway electrons have been suppressed by electron cyclotron resonance heating. From the set of discharges studied in the present experiments, it has also been observed that the efficiency of runaway suppression by electron cyclotron resonance heating was apparently affected by two factors: electron cyclotron resonance heating power and duration. These results have been analysed by using a test particle model. The decrease of the toroidal electric field due to electron cyclotron resonance heating results in a rapid fall in the runaway electron energy that may lead to a suppression of runaway electrons. During electron cyclotron resonance heating with different powers and durations, the runaway electrons will experience different slowing down processes. These different decay processes are the major cause for influencing the efficiency of runaway suppression. This result is related to the safe operation of the Tokamak and may bring an effective control of runaway electrons.     

Quasi-optical simulation of the electron cyclotron plasma heating in a mirror magnetic trap

The resonance microwave plasma heating in a large-scale open magnetic trap is simulated taking into account all the basic wave effects during the propagation of short-wavelength wave beams (diffraction, dispersion, and aberration) within the framework of the consistent quasi-optical approximation of Maxwell’s equations. The quasi-optical method is generalized to the case of inhomogeneous media with absorption dispersion, a new form of the quasi-optical equation is obtained, the efficient method for numerical integration is found, and simulation results are verified on the GDT facility (Novosibirsk).     

Generation and amplification of electromagnetic waves by an annular electron beam in a radial electric field in free space

Mechanisms for the generation and amplification of electromagnetic waves by a thin-walled annular beam of electrons rotating in a radial electric field in free space are studied theoretically. It is shown that electromagnetic waves can be generated and amplified under the Cherenkov resonance conditions. The frequencies and growth rates of the generated waves are determined, and the propagation characteristics and amplification coefficients of the amplified waves are found.     

Long-pulse improved central electron confinement in the TCV tokamak with electron cyclotron heating and current drive

Current profile tailoring by electron cyclotron heating (ECH) and current drive (ECCD) is used to improve central electron energy confinement in the TCV tokamak. Counter-ECCD on axis alone achieves this goal in a transient manner only. A stable scenario is obtained by a two-step sequence of off-axis ECH, which stabilizes magnetohydrodynamics modes, and on-axis counter-ECCD, which generates a flat or inverted current profile. This high-confinement regime, with central temperatures up to 9 keV (at a normalized beta(N) approximately 0.6), has been sustained for the entire duration of the heating pulse, or over 200 electron energy confinement times and 5 current redistribution times.     

Behaviour of the peripheral electron temperature at the H-mode transition induced by the peripheral electron cyclotron heating of a tokamak plasma

The behaviour of the peripheral electron temperature at the H-mode transition induced by the peripheral electron cyclotron heating shows that the H-mode transition is triggered at the crash phase of the sawteeth and the concept of the “threshold temperature” well describes the condition for the H-mode transition. The particle confinement seems to be improved during the H-mode, which is deduced from a simple model.     

Beam damage by the induced electric field in transmission electron microscopy

Electric fields can be induced by electron irradiation of insulating thin film materials. In this work, the electric fields under a broad beam illumination in transmission electron microscopy (TEM) are analyzed for insulating samples. Some damage phenomena observed can be interpreted by the mechanism of damage by the induced electric field (DIEF). For broad-beam illumination in an ultra-thin specimen, the electric field near the center of the illumination may not be strong, but at the periphery of the illumination the electric field can be significant. Therefore, damage may be easily observed in these regions rather than at the center of the illumination. For a beam which is broad compared to the specimen thickness, e.g. 100 ∼ 1000 nm, a strong electric field pointing inward into the specimen near the surface region may result in cation diffusion into the specimen and/or anion diffusion out to the surface region. Meanwhile, a strong electric field perpendicular to the beam direction near the edge of the illumination may attract anions into the illuminated region, but eject cations to the periphery. For a wedge-shaped specimen, the electric field points inward into thicker region, driving cations toward the thicker region, while attracting anions to the edge region. On the sharp edge, a strong electric field pointing outward may be responsible for the edge-smoothing effect observed in insulating materials.     

Investigation of the effect of electron cyclotron heating on runaway generation in the KSTAR tokamak

Wave enhanced runaway generation is expected to play an important role in the conversion of plasma current into runaway current during major disruptions. The fast electrons created by electron cyclotron heating (ECH) were used to study this issue in KSTAR. It is found that the fast electrons driven by ECH can enhance runaway production in the flat top phase with high loop voltage. The runaway current in disruptions was not enhanced by the ECH produced fast electron population due to the strong magnetic fluctuations which inhibited the generation of runaway electrons. It is found that a complete loss of existing REs during thermal quench has occurred in KSTAR limiter configuration discharges.     

HF heating of a plasma column at frequencies below the electron cyclotron frequency

Dispersion of waves, excited by the helical structure in a plasma column and the heating of a tail of the electron distribution function is studied at frequencies below the electron plasma and the electron cyclotron frequency.We wish to thank Dr. R.Klíma for valuable discussions and Dr. J.Lacina and Mrs. P.Jaroová for the computational work. We also thank Dr. L.Bárdo, Dr. L.Kryka and Dr. G. L.Khorosanov from Sukhumi Institute, USSR, for their help during different stages of the experiment. We are indebted to Mr. J.Dvoák, Mr. F.Jiránek and Mr. B.usta for their expert technical assistance.     

EAST 电子回旋共振加热效果的数值模拟和分析

为了给EAST 电子回旋共振加热物理实验提供理论依据和模拟预测,从电子热输运方程出发,运用 CRONOS 输运程序对不同等离子体和波参数下,电子回旋加热效果进行了数值模拟计算。给出不同电子回旋波功率、入射角、电子密度和纵场等参数对电子回旋加热效果的影响,预测在不同参数下,电子温度、等离子体总内能和能量约束时间的变化,分析了其原因,并与实验结果进行了初步的比较。