Low-threshold Parametric Decay Instability Research Articles

On possibility of anomalous microwave power absorption and gyrotron frequency sub-harmonics emission in X2-mode ECRH experiments at the TCV tokamak

In this paper, we analyze theoretically the low-threshold parametric decay instability (PDI) that can be excited at the tokamak à configuration variable (TCV tokamak, Lausanne, Switzerland) during X2 electron cyclotron resonance heating experiments producing a two-dimensionally localized upper hybrid (UH) wave and a daughter extraordinary wave running from the decay layer outward to the plasma edge. The primary instability is then saturated due to the cascade of secondary decays into two-dimensionally localized UH and ion Bernstein waves. The level of plasma microwave emission in the frequency range substantially below half the pump wave frequency and of anomalous power losses of the pump are predicted.

On the Saturation of the Instability of Induced Ordinary Microwave Scattering in the Edge Transport Barrier of a Tokamak during Electron Cyclotron Resonance Heating of a Plasma

The saturation of the low-threshold parametric decay instability of an ordinary wave during electron cyclotron resonance heating in the edge transport barrier of a tokamak due to the stochastic damping of a daughter two-dimensionally localized oblique Langmuir wave has been considered. It has been found that the saturation of instability in modern devices occurs at a relatively low level and does not affect the energy balance during plasma heating. It has been shown that the efficiency of nonlinear pump under expected conditions of microwave power injection in the International Thermonuclear Experimental Reactor will exceed the maximum efficiency of stochastic damping, which will result in the breaking of amplitude-dependent saturation and can significantly modify the power deposition profile.

Broadening of the power deposition profile in on-axis X2 ECRH experiments in the L-2M stellarator and the low-threshold parametric decay instability of the pump wave

The effect of considerable broadening of the power deposition profile in on-axis X2 electron cyclotron resonance heating experiments observed in the L-2M stellarator is interpreted in the paper as one of the consequences of the low-threshold parametric decay instability of the pump wave, resulting in excitation of ion and electron Bernstein daughter waves. The instability is considered under the specific L-2M experimental conditions and shown to be absolute. The threshold of this instability is exceeded in the experiment. This finally allows explaining, at least qualitatively, the effect of nonlocal microwave power deposition detected in L-2M.

Relativistic analysis of upper hybrid wave propagation and trapping

We investigate the impact of relativistic effects on upper hybrid (UH) waves in plasmas with thermal electrons, particularly focusing on modifications of the conditions under which UH wave trapping and related low-threshold parametric decay instabilities (PDIs) may occur. A moderately relativistic (MR) dispersion relation for UH waves, valid for electron temperatures up to 25 keV and wave frequencies up to twice the electron cyclotron frequency, is obtained from previous results and shown to reduce to the warm non-relativistic result commonly used for PDI studies at low electron temperatures. The conditions under which MR UH waves propagate are then determined and compared with warm and cold plasma theory, showing a general increase in the electron density and background magnetic field strength at which the UH resonance occurs for finite electron temperatures. We next investigate the impact of the MR corrections on the possibility of UH wave trapping for X-mode electron cyclotron resonance heated (ECRH) plasmas at the ASDEX Upgrade tokamak and scaled versions of the ASDEX Upgrade parameters with core electron temperatures resembling those expected in ITER X-mode ECRH plasmas. The MR UH wave trapping conditions are virtually unchanged for ASDEX Upgrade relative to warm theory, due to the low electron temperatures, while potentially important differences between warm and MR theory exist for ITER-like core electron temperatures; cold theory is found to be insufficient in both cases. Finally, the MR dispersion relation is shown to qualitatively reproduce the PDI thresholds from warm theory for previously studied ASDEX Upgrade cases.

Influence of edge plasma turbulence on the low-threshold parametric decay instability at ECRH

The saturation level of the two Upper-Hybrid-plasmon low-threshold parametric decay instability (PDI) depends on the pump wave beam width. The edge plasma turbulence may lead to drastic distortion of the pump beam, thus generating PDI characteristic changes. Numerical evaluations of the PDI process are provided in this work for different turbulence scenarios. The average PDI characteristics are evaluated and compared to the simulation results for the pump beam unperturbed by the edge plasma turbulence. It is shown that up to the intermediate turbulence level, the PDI characteristics are only gently modified. But at high edge turbulence level, which can happen in tokamaks, the threshold increases and the growth rate reduces. It is important to note that the anomalous absorption keeps a little reduction value, whatever the edge turbulence regimes.

Impact of trapped waves radiation losses on the saturation of low threshold two-UH-plasmon parametric decay instability

The dispersion equation for metastable states in a finite tower of eigenmodes of trapped upper hybrid (UH) waves arising from a non-monotonic density profile is derived and then solved both analytically and numerically. The influence of the UH eigenmode damping due to the radiation losses on the saturation level of the two-UH-plasmon low-threshold parametric decay instability is analyzed. Transitions from the odd-step number secondary decay saturation cascade to the even one and vice versa at the radiation loss variation are investigated and shown to initiate a substantial change of the anomalous absorption.

On a Strong Effect of Nonresonant Three-Wave Interactions on the Saturation of Low-Threshold Parametric Decay Instability

On a Strong Effect of Nonresonant Three-Wave Interactions on the Saturation of Low-Threshold Parametric Decay Instability

Methods for Reducing Anomalous Losses in ECRH Experiments at Second Resonance Harmonic

An approach is analyzed that makes it possible to reduce anomalous absorption in experiments on electron cyclotron resonance heating (ECRH) at the second harmonic of the electron cyclotron resonance. The anomalous absorption is associated with excitation of the low-threshold parametric decay instability of the extraordinary pump wave at the local maximum of the nonmonotonic density profile. The general case is considered, which corresponds to nonlinear excitation of only one localized daughter upper-hybrid wave occurring as a result of the primary decay process. It is shown that, due to rather low instability threshold, it could hardly be completely suppressed in ECRH experiments using megawatt microwave beams. However, an increase in the radius of the pump wave cross section can considerably reduce the corresponding anomalous absorption.

Density Region of Low-Threshold Parametric Decay Instabilities in Electron Cyclotron Resonance Heating Experiments in Tokamak

The density conditions under which low-threshold parametric decay instabilities occur are analyzed by a physical model. Calculations show that low-threshold parametric decay instabilities occur in the density region. Magnetic field effects on the density region are analyzed. The maximum width of the density region is found. The plasma temperature has little effect on the density region. In order to avoid the low-threshold parametric decay instabilities, the daughter wave’s frequency must be far from the UH frequency inside magnetic island. It’s the key to control the magnetic field inside the magnetic island.

On the Issue of Possibility of Low-Threshold Nonlinear Excitation of Oblique Langmuir Waves in Plasma Filament Using Ordinary Polarized Microwaves

The results are presented from the theoretical analysis of the low-threshold parametric decay instability of the pumping microwave beam with the ordinary polarization and the frequency in the electron cyclotron resonance frequency range. This instability develops in the cylindrical plasma filament, which results in the excitation of two oblique Langmuir waves.

Nonlinear excitation of electron plasma waves trapped in a blob in the O1-mode ECRH experiments

We analyze a scenario of low-threshold parametric decay instability of the pump ordinary wave associated with excitation in a plasma blob of two trapped electron plasma waves at frequencies smaller than the local Langmuir frequency.

Influence of the pump depletion on the anomalous absorption of the extraordinary wave in the second harmonic ECRH experiments

The saturation analysis for the two-upper-hybrid-plasmon low-threshold parametric decay instability of the extraordinary wave is carried out for the conditions of the second harmonic ECRH experiments with due account of the daughter wave secondary decay and of the pump depletion. The anomalous absorption rate in the range of 10% is demonstrated for the parameters of the TEXTOR tokamak second harmonic X-mode ECRH experiment at a single-mode primary decay.

Low-threshold parametric decay of the ordinary wave in ECRH experiments at toroidal devices

In this paper we analyse low-threshold parametric decay instability (PDI) of the ordinary wave in first harmonic O-mode ECRH experiments at toroidal devices. The corresponding expressions for the PDI power threshold and its growth rate are derived analytically and evaluated numerically for the conditions of the ECRH experiments on the W7-A stellarator. The possibility of low-threshold parametric decay of the pump ordinary wave on the FTU tokamak is also considered.

Theory of anomalous backscattering in second harmonic X-mode ECRH experiments

A quantitative model explaining generation of the anomalous backscattering signal in the second harmonic X-mode electron cyclotron resonance heating (ECRH) experiments at TEXTOR tokamak as a secondary nonlinear process which accompanies a primary low-threshold parametric decay instability (PDI) leading to excitation of two—upper hybrid (UH)—plasmons trapped in plasma is developed. The primary absolute PDI enhancing the UH wave fluctuations from the thermal noise level is supposed to be saturated due to a cascade of secondary low-threshold decays of the daughter UH wave leading to excitation of the secondary UH waves down-shifted in frequency and the ion Bernstein wave. A set of equations describing the cascade is derived and solved numerically. The results of numerical modelling are shown to be in agreement with the analytical estimations of the growth rate of the initial and secondary parametric decays and the saturation level. The generation of backscattering signal is explained by coupling of the daughter UH waves. The fine details of the frequency spectrum of the anomalously reflected extraordinary wave and the absolute value of the observed backscattering signal in the second harmonic X-mode ECRH experiments at TEXTOR are reproduced.

Saturation of low-threshold two-plasmon parametric instability of an extraordinary wave in an inhomogeneous plasma

Saturation of low-threshold parametric decay instability of an electron cyclotron wave of extraordinary polarization is analyzed; the development of this instability near a local maximum of the plasma density profile gives rise to two upper hybrid (UH) plasmons at frequencies close to the half of the pump wave frequency. As a saturation mechanism of this instability, a cascade decay of daughter UH waves is used, which leads to the excitation of secondary UH and lower hybrid (LH) waves that are also radially localized in the vicinity of a local maximum and minimum of the plasma density profile, respectively.

Trapping of electron Bernstein waves in drift-wave eddies and parametric decay instability at second harmonic ECRH in toroidal devices

The possibility of 3D electron Bernstein wave trapping in intensive magnetic field aligned density fluctuation or blobs in toroidal plasma is demonstrated. A semi-analytic approach for the description of associated plasma cavity is developed. A mechanism of low-threshold parametric decay instability driven by extraordinary pump microwave and leading to the excitation of localized second harmonic electron Bernstein waves and low-frequency heavily damped oscillations is proposed and analysed.

Anomalous phenomena in ECRH experiments at toroidal devices and low-threshold parametric decay instabilities

In the paper the possibility of total 3D trapping of electron Bernstein ( EB) waves in the tokamak equatorial plane in the vicinity of the local density maximum produced by electron pump -out-effect is demonstrated. Thresholds and growth rates of the associated absolute (temporally growing) parametric decay instability (PDI) leading to anomalous absorption ispredicted in the range of less than 10 0 kW.Itspossible role inexplanation of ion acceleratio n observed inECRH experiments as well as in redistribution of the deposited power is discussed .

Low threshold parametric decay instabilities in ECRH experiments at toroidal devices

Experimental conditions leading to a substantial reduction in the backscattering decay instability threshold in electron cyclotron resonance heating (ECRH) experiments in toroidal devices are analysed. It is shown that the drastic decrease in threshold due to suppression of convective losses is provided by the nonmonotonic behaviour of plasma density, which is often observed due to the so-called density-pump-out effect or the presence of magnetic islands, and by poloidal magnetic field inhomogeneity making localization of ion Bernstein decay waves possible. The corresponding ion Bernstein wave gain and the convective parametric decay instability pump power threshold are calculated. The possible experimental consequences of easy backscattering decay instability excitation are discussed.

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.