Parametric Mechanism of Anomalous Microwave Power Absorption in Experiments on Electron Cyclotron Heating in Toroidal Magnetic Traps

The nonlinear stage of the parametric decay instability of an extraordinary wave is analyzed in the presence of a nonmonotonic density profile. The decay excites an electron Bernstein wave, which is localized in the vicinity of a local density maximum, and an ion Bernstein wave, which leaves a nonlinear interaction region and is absorbed by ions in the vicinity of the harmonics of the ion cyclotron frequency. The main mechanism of instability saturation is considered to be a cascade of decays of a primary daughter electron Bernstein wave, which leads to the excitation of localized secondary electron Bernstein waves and ion cyclotron (Bernstein) waves. The localization of electron Bernstein waves causes a significant decrease in the secondary- decay excitation threshold, which is thought to provide saturation of the primary instability at the lowest level. The saturation of the primary parametric decay instability of a pump wave and the anomalous absorption of the pump power are analytically estimated. A numerical simulation is performed using the parameters that are typical of the experiments on the electron cyclotron resonance heating of plasma at the second resonance harmonic in TCV tokamak.     

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 scenario for the saturation of the low-threshold two-plasmon parametric decay instability of an extraordinary wave in the inhomogeneous plasma of magnetic traps

The most probable scenario for the saturation of the low-threshold two-plasmon parametric decay instability of an electron cyclotron extraordinary wave has been analyzed. Within this scenario two upperhybrid plasmons at frequencies close to half the pump wave frequency radially trapped in the vicinity of the local maximum of the plasma density profile are excited due to the excitation of primary instability. The primary instability saturation results from the decays of the daughter upper-hybrid waves into secondary upperhybrid waves that are also radially trapped in the vicinity of the local maximum of the plasma density profile and ion Bernstein waves.     

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.     

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.     

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.     

Generation of cyclotron harmonic waves in the ionosphericmodification experiments

In the present paper, the parametric decay instability of the pump X-mode into electron Bernstein wave (EBW) near second harmonics of electron cyclotron frequency and IBW at different harmonics (ωci; n=2,3,4) is examined. Expressions are derived for homogenous threshold, growth rate and convective threshold for this instability. Applications and relevances of the present investigation to ionospheric modification experiment in the F-layer of the ionosphere as well as during intense electron cyclotron resonance heating in the upcoming MTX tokamak have been given     

Parametric excitation of electrostatic whistler wave and electronBernstein wave by extraordinary EM wave

In the present paper, the parametric decay instability of an extraordinary electromagnetic wave (X-wave) into an electron Bernstein wave (EBW) and an electrostatic whistler wave (W-wave) has been studied. Expressions are derived for homogeneous threshold, growth rate, and convective threshold for this instability. The relevance of the present parametric process has been pointed out to explain the generation of whistler mode radiations in the SL-2 experiment, ionospheric modification experiment, in the polar cusp region of the magnetosphere, as well as during intense electron cyclotron resonance heating in the MTX tokamak     

Threshold of ion cyclotron parametric instability in a multispecies plasma

Experimental and theoretical studies are presented of ion cyclotron parametric instability into two electrostatic ion cyclotron waves in a multispecies plasma. The instability threshold obtained experimentally is in reasonable agreement with that predicted theoretically.     

Nonlinear dynamical modelling of chaotic electrostatic ion cyclotron oscillations by jerk equations

Plasma being a nonlinear and complex system, is capable of sustaining a wide spectrum of waves, oscillations and instabilities. These fluctuations interact nonlinearly amongst themselves and also with particles: electrons/ions and thus lead to nonlinear wave-wave or wave-particle interaction. In the presence of coherent waves the particles are accelerated whereas irregular oscillations can give rise to particle heating which is also called stochastic heating. Particle orbits are known to be randomized by the wave fields such that their motion can also become stochastic. For fusion to be sustained one needs a very high temperature plasma for an extended duration. It quite common to deploy external waves like electron cyclotron waves or ion cyclotron waves for plasma heating and current drive. These external waves also work only in certain regimes. Conventional plasma techniques have been able to answer several of the observations of the above processes related to heating transport etc, but nonlinear dynamics as a tool has helped in comprehending the plasma oscillations better. We have for the first time obtained a Third Order nonlinear ordinary differential equation (TONLODE) also known as jerk equation to describe the electrostatic ion cyclotron plasma oscillations in a magnetic field. The interesting feature of this equation is that it does not require an external forcing term to obtain chaotic behaviour.     

Contribution to the theory of parametric generation of cyclotron radiation

A linear theory of the cyclotron parametric instability in systems which are classical analogues of quantum lasers without inversion is developed. The cyclotron interaction of different types of modulated electron beams with a bichromatic field, produced by waves propagating at an angle with respect to a constant magnetic field, is investigated. It is shown that simultaneous amplification of two parametrically coupled modes with different frequencies and positive energy is possible in this system with modulation of the active and reactive components of the susceptibility of an electronic ensemble. The results obtained are important from the standpoint of the general theory of radiation processes in electron beams and plasma and for the advancement of microwave electronics.     

Doppler-shifted cyclotron absorption of electron Bernstein waves via N( parallel)-upshift in a Tokamak plasma

Extraordinary (X) waves are perpendicularly injected for electron Bernstein (B) wave heating into an Ohmically heated plasma from the inboard side in the WT-3 tokamak. Measurements show that absorption does not take place at the electron cyclotron resonance layer nor the upper hybrid resonance layer, but does happen midway between them. This is consistent with the ray tracing prediction, i.e., the poloidal field and poloidal inhomogeneity of toroidal field lead the B waves to have a large parallel refractive index N( parallel) (>1), and the B waves are damped away via the Doppler-shifted cyclotron resonance.     

Observation of Localized Electron Cyclotron Resonance Heating in a Magnetic Mirror

A right-hand circularly polarized (RHCP) electron cyclotron wave is launched along the axis of a steady-state magnetically confined plasma column. Detailed measurements of the spatial variation of electron temperature, density, plasma potential, and wave amplitude about the resonance zone are presented. In particular, data are presented where the temperature increase due to electron cyclotron resonance heating (ECRH) is strongly localized near the resonance position. A numerical wave heating model has been developed for electrons in a magnetic mirror and is found to be in qualitative agreement with observations.     

捕获电子对低杂波与电子回旋波的协同效应的影响

电子回旋波和低杂波的协同效应可有效地提高两只波的电流驱动效率.本文数值研究了捕获电子效应对电子回旋波和低杂波协同的影响.结果显示,随着捕获角的增大,双波协同驱动电流会减小,且协同因子也会明显减小,即捕获角对两只波协同驱动流的影响要比其对单独驱动电流的影响更加敏感.通过加宽低杂波共振区可减弱电子回旋波电流驱动对捕获角的依赖,同时发现随着电子回旋波功率的增加,捕获角对电子回旋波电流驱动的影响也会变小.     

Design of the Upgraded TJ-II Quasi-optical Transmission Line

TJ-II plasma start-up and heating are made by electron cyclotron resonance waves at the second harmonic of the electron cyclotron frequency. Two quasi-optical transmission lines transmit the microwave power of the gyrotrons to the vacuum vessel. The first line launches the microwave power under fixed injection geometry, i.e. there is no possibility to change the launching angle and the wave polarization. The second line has a moveable mirror installed inside the TJ-II vessel. To get high absorption efficiency and a narrow energy deposition profile the internal mirror focuses the wave beam at plasma center.To get more flexibility in the experiments on heating and current drive the first transmission line needs to be upgraded. The design is presented in this paper. The new launching antenna includes an internal mirror to focus the beam and to change the injection angle. Both launchers are then symmetrical. A polarizer consisting of two corrugated mirrors is used to get any wave polarization. Two mirrors with an array of coupling holes and calorimetric measurements of the energy absorbed in the barrier window allow the estimation of the microwave power launched into the TJ-II.     

On the possibility of harmonic operation of cyclotron waveparametric amplifiers

Cyclotron wave amplifiers at the harmonics of the electron cyclotron frequency are investigated. Since the waves on the beam are electrostatic, harmonics are strongly excited in nonrelativistic beams if they are rotating rather than filamentary. These modes at the harmonics can couple to input Cuccia couplers, and pump fields which drive parametric amplification, in very much the same way as they do on filamentary beams at the cyclotron frequency. Harmonic cyclotron wave amplifiers have the possibility of giving rise to a new class of devices at millimeter wave frequencies     

Stimulated Brillouin scattering in a plasma with ion-acoustic turbulence

A theory of stimulated Brillouin scattering (STBS) in a plasma with ion-acoustic turbulence is developed using concepts of parametric instability under conditions when equations of two-temperature hydrodynamics can be used to describe ion-acoustic perturbations of the electron density. The temporal growth rate of the absolute instability and the spatial gain of the scattered wave are determined. The dependence of the threshold density of the radiation flux on the angle between the scattering wave vector and the direction of anisotropy of the turbulent noise is described. A new effect of STBS forbiddenness caused by anomalous turbulent heating of the ions is predicted for a plasma with a high level of turbulent noise.     

Experimental observation of motion of edge dislocations in Ge/Ge<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Si<Subscript>1–<Emphasis Type="Italic">x</Emphasis></Subscript>/Si(001) (<Emphasis Type="Italic">x</Emphasis> = 0.2–0.6) heterostructures

The rotating magnetohydrodynamic flows of a thin layer of astrophysical and space plasmas with a free surface in a vertical external magnetic field are considered in the shallow water approximation. The presence of a vertical external magnetic field changes significantly the dynamics of wave processes in an astrophysical plasma, in contrast to a neutral fluid and a plasma layer in an external toroidal magnetic field. There are three-wave nonlinear interactions in the case under consideration. Using the asymptotic method of multiscale expansions, we have derived nonlinear equations for the interaction of wave packets: three magneto- Poincare waves, three magnetostrophic waves, two magneto-Poincare and one magnetostrophic waves, and two magnetostrophic and one magneto-Poincare waves. The existence of decay instabilities and parametric amplification is predicted. We show that a magneto-Poincare wave decays into two magneto-Poincare waves, a magnetostrophic wave decays into two magnetostrophic waves, a magneto-Poincare wave decays into one magneto-Poincare and one magnetostrophic waves, and a magnetostrophic wave decays into one magnetostrophic and one magneto-Poincare waves. There are the following parametric amplification mechanisms: the parametric amplification of magneto-Poincare waves, the parametric amplification of magnetostrophic waves, the amplification of a magneto-Poincare wave in the field of a magnetostrophic wave, and the amplification of a magnetostrophic wave in the field of a magneto-Poincare wave. The instability growth rates and parametric amplification factors have been found for the corresponding processes.