Low-threshold absolute parametric decay instabilities in experiments on electron cyclotron resonance heating in tokamaks

We have analyzed experimental conditions for the excitation of absolute parametric decay instabilities accompanying the electron cyclotron resonance heating (ECRH) of plasma at the second harmonic of resonance in tokamaks. It has been shown that, in the case of a nonmonotonic radial profile of the plasma density, when a heating beam passes near the equatorial plane of a tokamak, the parametric excitation of resonances of ion Bernstein waves accompanied by the generation of the backscattered microwave radiation can occur. The threshold of absolute instability thus developed is determined by the dissipation of an ion Bernstein wave and can be exceeded in current experiments on the ECRH of a plasma in tokamaks.     

On the low-threshold parametric mechanism of the anomalous power absorption in electron cyclotron resonance heating experiments in toroidal devices

The experimental conditions that facilitate the excitation of parametric decay instabilities upon the electron cyclotron resonance heating of a plasma at the second harmonic extraordinary wave in tokamaks and stellarators and, as a result, make anomalous absorption of microwave power possible have been analyzed. It has been shown that, in the case of a nonmonotonic radial profile of the plasma density, when the beam of electron cyclotron waves passes near the equatorial plane of a toroidal device, the parametric excitation of electron Bernstein waves, as well as the generation of ion Bernstein waves propagating from the parametric decay region to the nearest ion cyclotron harmonic, where they efficiently interact with ions, is possible. The proposed theoretical model can explain the anomalous generation of accelerated ions observed upon electron cyclotron heating in small and moderate toroidal facilities.     

On a new mechanism of excitation of the absolute parametric decay instability of an electromagnetic wave in experiments on electron cyclotron resonance heating in toroidal devices

Experimental conditions under which the low-threshold absolute parametric decay instability of an electromagnetic wave with extraordinary polarization at the electron cyclotron resonance heating of a plasma at the second harmonic resonance in toroidal devices are analyzed. A new mechanism is proposed for the localization of a daughter electrostatic wave in the toroidal direction in the region of a high-power pump beam. This mechanism, along with the two-dimensional localization of the daughter wave because of a nonmonotonic radial profile of the plasma density and the poloidal inhomogeneity of the magnetic field, can be responsible for the parametric excitation of a three-dimensional cavity for this wave and, as a result, low-threshold absolute decay instability of the pump wave.     

Saturation of the two-plasmon parametric decay instability in experiments on the electron cyclotron plasma heating due to the extraordinary pump wave depletion

The saturation level of the low-threshold parametric two-plasmon instability of the extraordinary pump wave decay to two upper hybrid plasmons is analyzed under conditions when the only efficient saturation mechanism is the pump depletion. A closed system of differential equations describing both the instability excitation and saturation is derived. The system is solved numerically and an analytic expression is obtained for the anomalous absorption coefficient of the pump wave caused by the development of this instability. The saturation level of the two-plasmon decay instability and the related anomalous absorption efficiency are estimated from data obtained in experiments on the electron cyclotron resonance heating of the plasma by an extraordinary wave in the TEXTOR tokamak.     

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.     

Four-dimensional mapping model for two-frequency electron cyclotron resonance heating

Two-frequency electron cyclotron resonance heating (ECRH) is modelled by a four-dimensional symplectic mapping derived from the nonrelativistic single particle equations of motion. The model includes changes in parallel energy due to the spatially separate resonance zones, not given by previous two-dimensional models. Fixed points are located and their linear stability limits determined. Resonances in action space are calculated along with their widths and used to obtain the adiabatic barrier to heating. Quasilinear diffusion coefficients are derived for the stochastic regime and found to agree well with numerical calculations. The primary diffusion in perpendicular energy can couple to the parallel motion, leading to diffusion in parallel energy. The resulting diffusion coefficient is calculated analytically and compared with numerical results. The much weaker Arnold diffusion along a resonance layer is also treated analytically, yielding diffusion coefficients in reasonable agreement with numerical values.     

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。     

Density profiles in tokamaks from electron cyclotron radiation spectra

Measurement of the line shape of optically thick and optically thin lines in the electron cyclotron radiation spectrum emitted by a tokamak plasma may yield both electron temperature and density profiles. Currently temperature profiles are routinely extracted from optically thick lines. Consequently, this paper is addressed to the density profile problem. Algorithms for extracting density profiles are outlined in the case of uncontrolled reflection and controlled reflection of the cyclotron radiation within the tokamak vacuum chamber.     

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.     

Splitting of the cyclotron resonance in two-dimensional electron systems

A large splitting of the cyclotron resonance line, observed in two different two-dimensional electron systems, remains unexplained. The splitting resembles an anti-level crossing with an unidentified mode of the semiconductor system. Here, we review our data on this splitting, and highlight some results of recent experiments.     

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The hardware design of solid-state anode high-voltage power supply in electron cyclotron resonance heating system (ECRH) is presented. The anode power supply uses the method that combined high-frequency pulse width modulation (PWM) and phase shift modulation (PSM) control technology. The former in the supply uses the SG3525 to control the IGBT to complete the high frequency invert. The latter is made up of a total of 59 modules connected in series. The output voltage of each module is basically stabilized by feedback of the first stage module output voltage. DSP controls the number of PSM module on and off and the 59th module BUCK circuit duty cycle to achieve the output voltage of the superimposed output, and the output voltage can be adjusted within the full range of 35kV with accuracy less than 0.1kV, the output current up to 200mA, modulation frequency more than 1kHz. The anode power supply has three operating modes, and the rising edge time of the waveform can be adjusted within 3ms. The results tested from dummy load and ECRH experimental platform show that its performance is stable, and the hardware design method is feasible.     

Electron-phonon interaction and cyclotron resonance in two-dimensional electron gas

Results for the influence of electron-phonon interaction on the cyclotron effective mass and the resonance linewidth in a two-dimensional electron gas are presented. The temperature and magnetic field dependence is studied and the existence of quantum oscillations is demonstrated. It is shown that the relevant phonon frequency in typical MOS inversion layers is very small so that magneto-transport properties are temperature dependent even at a few degrees Kelvin. Results are consistent with the observed temperature, magnetic field and frequency dependence in Si(100) inversion layers.     

Electron cyclotron resonance heating in a short cylindrical plasma system

Electron cyclotron resonance (ECR) plasma is produced and studied in a small cylindrical system. Microwave power is delivered by a CW magnetron at 2.45 GHz in TE¹⁰ mode and launched radially to have extraordinary (X) wave in plasma. The axial magnetic field required for ECR in the system is such that the first two ECR surfaces (B = 875.0 G andB = 437.5 G) reside in the system. ECR plasma is produced with hydrogen with typical plasma density n^e as 3.2 × 10¹⁰ cm^-3 and plasma temperature T^e between 9 and 15 eV. Various cut-off and resonance positions are identified in the plasma system. ECR heating (ECRH) of the plasma is observed experimentally. This heating is because of the mode conversion of X-wave to electron Bernstein wave (EBW) at the upper hybrid resonance (UHR) layer. The power mode conversion efficiency is estimated to be 0.85 for this system. The experimental results are presented in this paper.     

On the cyclotron resonance at skipping orbits in electron liquid

The possibility of the surface cyclotron waves propagation in metals with noncylindrical Fermi surface, placed in a weak magnetic field, is shown in the degenerate electron liquid theory case. Connected with the Fermi liquid constantA the contribution of such waves in the surface impedance of metals is calculated.     

Temperature dependence of the cyclotron resonance in electron inversion layers on Si

A study has been made of the adsorption of sulphur on the (110) face of molybdenum using LEED and AES combined with a radioactive tracer technique employing ³⁵S. The content of the surface unit mesh can thus be determined precisely. By applying the 2D space groups, information can be obtained concerning the distribution of the adsorbed atoms. The hypothesis of a high symmetry has been assumed. In this case the observed patterns correspond to structures made of adjacent rows of occupied sites separated by one row of vacancies.     

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.     

Submillimetric cyclotron resonance linewidths and electron relaxation time in copper

For the first time submillimetric microwaves (λ<1 mm) are used to observe Azbel' Kaner cyclotron resonance in metals. The very high frequency used (typicallyF≅400 GHz) gives a large value ofωτ (typically 500) and therefore very sharp peaks. The fundamental resonance fieldH _c=m ^* cω/e is rather high (typically 200 KG), so subharmonicsH _c/n can be observed at many values ofH in the field region 0–27 KG. If relatively few electrons participate in the resonance and ifω _cτ≧50 (ω _c=eH/m ^* c,τ relaxation time) thenChambers has shown that the line shapes are independent of relaxation time while the fractional linewidthΔH/H varies as l/ωτ. For the belly orbit in pure copper the conditions of Chambers' theory are satisfied forH≧20 KG parallel to [111] axis.m ^* is a minimum andτ=1.8×10⁻¹⁰ s.