Low-threshold parametric decay instabilities in the experiments on the electron cyclotron resonance heating in tokamaks and stellarators

The experimental conditions have been analyzed for a significant reduction of the threshold of the reflective parametric decay instabilities under electron cyclotron resonance heating (ECRH) of a plasma in magnetic devices in the absence of the upper hybrid resonance for the pump wave. The role of the nonmonotonic profile of the plasma density near the O point of the magnetic island, which allows for the localization of ion Bernstein waves in the direction of the density gradient and the suppression of convective losses from the decay region has been discussed. It has been shown that the threshold of the instability of the induced backscattering near the local maximum of the density profile is decreased by four orders of magnitude and is easily exceeded in present-day ECRH experiments at a power of several hundred kilowatts.     

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.     

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.     

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.     

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.     

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。     

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.     

Modelling of start-up assist by electron cyclotron waves for large-size tokamaks

Summary This paper presents a model describing the plasma production in a tokamak by means of electron cyclotron microwave power and the initial ohmic current ramp-up. A zero-dimensional code is applied to the case of large-size, high magnetic field tokamaks and, in particular, to the case of the INTOR/NET tokamak. It is shown that the r.f. plasma can be produced and heated to temperatures of a few hundred eV with power densities of the order of 50 kW/m³. Detailed results are given for a case in which 4 MW of electron cyclotron power is used to create a plasma whose steady-state temperature is well above the impurity radiation barriers. For the plasma inductance assumed and a current ramp-up rate of 0.625 MA/s, the ohmic current can be initiated in such a plasma with a total-loop voltageV _L<20 V. The resistive contribution to the loop voltage is of the order of 1 V.

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Riassunto Si descrive un modello di produzione del plasma e dello stadio iniziale di crescita della corrente ohmica in un tokamak, per mezzo di potenza elettromagnetica alla frequenza ciclotronica degli elettroni. Il codice a zero dimensioni che riassume il modello è applicato al caso di tokamak di grandi dimensioni e grandi campi magnetici toroidali ed, in particolare, al caso del tokamak INTOR/NET. Si mostra che il plasma dovuto alle microonde può essere prodotto e portato a temperature elettroniche di qualche centinaio di eV, in questa macchina, con una densità di potenza applicata dell'ordine di 50 kW/m³. Si danno risultati dettagliati, per un caso nel quale una potenza di 4 MW viene applicata per produrre un plasma con temperature di equilibrio molto al di sopra delle barriere di radiazione delle impurezze. Si mostra anche che, per la particolare formula assunta per definire l'induttanza del plasma e per un tasso di salita della corrente ohmica di 0.625 MA/s, la corrente ohmica stessa può salire, in questo tipo di plasma, con una tensione totale di giro inferiore a 20 V. La parte resistiva della tensione di giro si mantiene attorno ad 1 V.

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Резюме В этой статье описывается модель образования плазмы и начальная стадия нарастания омического тока в токамаке с помощью электромагнитной мощности на циклотронной частоте электронов. Код нулевой размерности применяется в случае токамака больших размеров, больших магнитных тороидальных полей, и частности, в случае токамака INTOR/NET. Показывается, что образуется высокочастотная плазма и температура повышается до нескольких сотен эВ при плотности мощности порядка 50 кВТ/м³. Приводятся подробные результаты для случая, когда для образования плазмы исползуется мощность 4 мВт на электронной циклотронной частоте, причем равновесная температура плазмы много выше радиационных барьеров примесей. Показывается, что для принятой индуктивности плазмы и величины наростания омического тока 0.625 MA/c, в плазме этого типа омический ток может быть возбужден при полном напряжении в контуреV _L <20 В. Вклад активного сопротивления в напряжение в контуре составляет порядка 1 В.

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Modeling of electron cyclotron resonance discharges

A simple model to predict the spatially-averaged plasma characteristics of electron cyclotron resonance (ECR) reactors is presented. The model consists of global conservation equations for species concentration, electron density and energy. A gas energy balance is used to predict the neutral temperature self-consistently. The model is demonstrated for an ECR argon discharge. The predicted behavior of the discharge as a function of system variables agrees well with experimental observations     

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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.     

Behaviors of absolute instabilities of electrostatic ion cyclotron waves in an ion beam-plasma system

Experimental results are presented for behaviors of the temporal growth and the threshold beam density of the absolute instability of the electrostatic ion cyclotron waves excited in an ion beam-plasma system, and compared with the linear theory.     

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.     

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.     

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.