Electron Cyclotron Absorption Research Articles

Reflection of the Electromagnetic Wave from the Region of Electron Cyclotron Absorption in Thermonuclear Plasma

A new approach to the problem of the passage of the extraordinary wave through the region of the electron–cyclotron resonance in inhomogeneous plasma was considered in the framework of the full set of Maxwell’s equations, taking into account the effects of spatial dispersion and resonance dissipation. For the model one-dimensional geometry, field distributions were calculated in the vicinity of the cyclotron resonance at the second harmonic for the normal incidence of the extraordinary wave and the reflection, transmission, and absorption coefficients were found depending on the parameters of the resonance region. As a result, the fine effect of the reflection of electromagnetic radiation from the cyclotron resonance region in transparent plasma was described and the results were compared with the observations of this effect in the experiments on the microwave heating of the plasma at the L-2M stellarator.

Reflection of the Electromagnetic Wave from the Region of Electron Cyclotron Absorption in Thermonuclear Plasma

A new approach to the problem of the passage of the extraordinary wave through the region of the electron–cyclotron resonance in inhomogeneous plasma was considered in the framework of the full set of Maxwell’s equations, taking into account the effects of spatial dispersion and resonance dissipation. For the model one-dimensional geometry, field distributions were calculated in the vicinity of the cyclotron resonance at the second harmonic for the normal incidence of the extraordinary wave and the reflection, transmission, and absorption coefficients were found depending on the parameters of the resonance region. As a result, the fine effect of the reflection of electromagnetic radiation from the cyclotron resonance region in transparent plasma was described and the results were compared with the observations of this effect in the experiments on the microwave heating of the plasma at the L-2M stellarator.

The Effects of Electron Cyclotron Absorption in Powerful Narrow-Band Sub-THz Oscillators Exploiting Volume and Surface Modes

We present the theory, design, and numerical modeling of novel, pulsed sub-THz oscillators based on cylindrical, 2-D periodic surface lattice (PSL) interaction cavities. Investigation of the electronic efficiency and power dependence on the magnitude of the magnetic guide field and the electron beam current is investigated. While cyclotron absorption effects have been studied in low-order, 1-D backward wave oscillators (BWOs), few studies have considered cyclotron absorption in highly overmoded, 2D-PSL oscillators. Here we investigate certain behavior associated with cyclotron absorption in 2D-PSL devices with over 400 modes. This electron cyclotron absorption is shown to be a universal process, independent of frequency and transverse cavity size. Dispersive behavior shows minimal group velocity at the point of interaction and demonstrates similarities with degenerate band edge (DBE) phenomena. In this work, the fundamental mode selection mechanism relies on the coupling of high-order volume and surface waves. Good agreement between theory and modeling is presented.

Validation of quasi-linear turbulent transport models against plasmas with dominant electron heating for the prediction of ITER PFPO-1 plasmas

Kinetic profile predictions of ITER PFPO-1 plasmas require high accuracy in the central electron temperatures to be applied to the calculation of third harmonic electron cyclotron absorption. Correctly predicting the transition from L-mode to H-mode further requires precise estimates of the ion heat flux in the periphery of the plasma. Recent versions of the quasi-linear transport models TGLF and QuaLiKiz were tested against an extensive set of experimental results from ASDEX Upgrade (AUG) and JET-ILW, where the focus was put on AUG plasmas heated by ECRH. Spectra obtained from TGLF are compared to a set of linear gyrokinetic simulations performed with GKW. Electron and ion temperature profiles obtained with TGLF-SAT1geo show good agreement with the experimental profiles, but there is a slight tendency to underpredict central T e and T i at high ratios T e/T i. QuaLiKiz yields reasonable results for T e and T i profiles in plasmas where the ion temperature gradient mode is dominant, but predicts a significantly too weak transport in the presence of dominant trapped electron modes in conditions of strong central electron heating.

Cyclotron lines in highly magnetized neutron stars

Cyclotron lines, also called cyclotron resonant scattering features are spectral features, generally appearing in absorption, in the X-ray spectra of objects containing highly magnetized neutron stars, allowing the direct measurement of the magnetic field strength in these objects. Cyclotron features are thought to be due to resonant scattering of photons by electrons in the strong magnetic fields. The main content of this contribution focusses on electron cyclotron lines as found in accreting X-ray binary pulsars (XRBP) with magnetic fields on the order of several 1012Gauss. Also, possible proton cyclotron lines from single neutron stars with even stronger magnetic fields are briefly discussed. With regard to electron cyclotron lines, we present an updated list of XRBPs that show evidence of such absorption lines. The first such line was discovered in a 1976 balloon observation of the accreting binary pulsar Hercules X-1, it is considered to be the first direct measurement of the magnetic field of a neutron star. As of today (end 2018), we list 35 XRBPs showing evidence of one ore more electron cyclotron absorption line(s). A few have been measured only once and must be confirmed (several more objects are listed as candidates). In addition to the Tables of objects, we summarize the evidence of variability of the cyclotron line as a function of various parameters (especially pulse phase, luminosity and time), and add a discussion of the different observed phenomena and associated attempts of theoretical modeling. We also discuss our understanding of the underlying physics of accretion onto highly magnetized neutron stars. For proton cyclotron lines, we present tables with seven neutron stars and discuss their nature and the physics in these objects.

Study of transmission line attenuation in broad band millimeter wave frequency range

Broad band millimeter wave transmission lines are used in fusion plasma diagnostics such as electron cyclotron emission (ECE), electron cyclotron absorption, reflectometry and interferometry systems. In particular, the ECE diagnostic for ITER will require efficient transmission over an ultra wide band, 100 to 1000 GHz. A circular corrugated waveguide transmission line is a prospective candidate to transmit such wide band with low attenuation. To evaluate this system, experiments of transmission line attenuation were performed and compared with theoretical loss calculations. A millimeter wave Michelson interferometer and a liquid nitrogen black body source are used to perform all the experiments. Atmospheric water vapor lines and continuum absorption within this band are reported. Ohmic attenuation in corrugated waveguide is very low; however, there is Bragg scattering and higher order mode conversion that can cause significant attenuation in this transmission line. The attenuation due to miter bends, gaps, joints, and curvature are estimated. The measured attenuation of 15 m length with seven miter bends and eighteen joints is 1 dB at low frequency (300 GHz) and 10 dB at high frequency (900 GHz), respectively.

A WHITE DWARF MERGER AS PROGENITOR OF THE ANOMALOUS X-RAY PULSAR 4U 0142+61?

It has been recently proposed that massive fast-rotating highly-magnetized white dwarfs could describe the observational properties of some of Soft Gamma-Ray Repeaters (SGRs) and Anomalous X-Ray Pulsars (AXPs). Moreover, it has also been shown that high-field magnetic (HFMWDs) can be the outcome of white dwarf binary mergers. The products of these mergers consist of a hot central white dwarf surrounded by a rapidly rotating disk. Here we show that the merger of a double degenerate system can explain the characteristics of the peculiar AXP 4U 0142+61. This scenario accounts for the observed infrared excess. We also show that the observed properties of 4U 0142+6 are consistent with an approximately $1.2 M_{\sun}$ white dwarf, remnant of the coalescence of an original system made of two white dwarfs of masses $0.6\, M_{\sun}$ and $1.0\, M_{\sun}$. Finally, we infer a post-merging age $\tau_{\rm WD}\approx 64$ kyr, and a magnetic field $B\approx 2\times 10^8$ G. Evidence for such a magnetic field may come from the possible detection of the electron cyclotron absorption feature observed between the $B$ and $V$ bands at $\approx 10^{15}$ Hz in the spectrum of 4U 0142+61.

On the feasibility of electron cyclotron heating of overcritical plasma in a magnetic mirror trap

The feasibility of matching electromagnetic radiation in the electron cyclotron frequency range to a dense plasma in an open magnetic trap by producing an inverted (with a minimum on the axis) plasma density profile is discussed. The use of such a profile shows promise for the implementation of efficient cyclotron heating at plasma densities above the critical density, at which the Langmuir frequency is equal to the heating radiation frequency. Examples of the magnetic field and plasma density distributions in a mirror trap are presented for which analysis of the beam trajectories shows the feasibility of efficient electron cyclotron absorption of microwave beams in overcritical plasma.

Study of energy transfer by electron cyclotron resonance in tokamak plasma

A theoretical study of energy transfer by electron cyclotron resonance to tokamak plasma is presented. Then the predictions of linear theory including relativistic effects on the wave absorption are examined. Electron-cyclotron (EC) absorption in tokamak plasma is based on interaction between wave and electron cyclotron movement when the electron passes through a layer of resonance at a fixed frequency which depends on the magnetic field. This technique is the principle of additional heating (ECRH) and the generation of non-inductive current drive (ECCD) in modern fusion devices. The power absorbed depends on the optical depth which in turn depends on coefficient of absorption and the order of the excited harmonic for O-mode or X-mode

Diagnostic techniques for measuring suprathermal electron dynamics in plasmas (invited)

Plasmas, both in the laboratory and in space, are often not in thermodynamic equilibrium, and the plasma electron distribution function is accordingly non-Maxwellian. Suprathermal electron tails can be generated by external drives, such as rf waves and electric fields, or internal ones, such as instabilities and magnetic reconnection. The variety and importance of the phenomena in which suprathermal electrons play a significant role explains an enduring interest in diagnostic techniques to investigate their properties and dynamics. X-ray bremsstrahlung emission has been studied in hot magnetized plasmas for well over two decades, flanked progressively by electron-cyclotron emission in geometries favoring the high-energy end of the distribution function (high-field-side, vertical, oblique emission), by electron-cyclotron absorption, by spectroscopic techniques, and at lower temperatures, by Langmuir probes and electrostatic analyzers. Continuous progress in detector technology and in measurement and analysis techniques, increasingly sophisticated layouts (multichannel and tomographic systems, imaging geometries), and highly controlled suprathermal generation methods (e.g., perturbative rf modulation) have all been brought to bear in recent years on an increasingly detailed, although far from complete, understanding of suprathermal electron dynamics.

Chapter 3: Microwave Diagnostics

Microwave-based diagnostics have found broad application in magnetic fusion plasma diagnostics and are expected to be widely employed in future burning plasma experiments (BPXs). Most of these techniques are based directly on the dispersive properties of the plasma medium that, as shown in the body of the paper, results in the microwave/millimeter wave portion of the electromagnetic spectrum being particularly well suited for a variety of measurements of both magnetic fusion plasma equilibrium parameters and their fluctuations. Electron cyclotron emission provides a measurement of electron temperature and its fluctuations while electron cyclotron absorption potentially can provide a measurement of electron pressure (the product of electron density and temperature) as well as information on the suprathermal electron distribution. Electron Bernstein wave emission is also employed for electron temperature radiometric measurements in devices including reversed field pinches, spherical tori, and higher-aspect-ratio tokamaks and stellarators that operate at high β. The radar-based microwave reflectometry technique measures the electron density profile and its fluctuations by means of the reflection of electromagnetic waves at the plasma cutoff layer. Coherent Thomson scattering in the microwave region yields information on the fast ion population. Wave number resolved microwave collective scattering is also widely employed for measuring nonthermal (turbulent) density fluctuations or coherent electrostatic waves. The approach taken in this review is to address each technique separately beginning with the physical principles followed by representative implementations on magnetic fusion devices. In each case, the applicability to future BPXs is discussed. It is impossible in a short review to capture fully the numerous significant accomplishments of the many clever scientists and engineers who have advanced microwave plasma diagnostics technology over many decades. Therefore, in this paper, we can reveal only the basic principles together with some of the most exciting highlights while outlining the major trends, and we hope it will serve as an exciting introduction to this rich field of plasma diagnostics.

Electron cyclotron wave power loss in fusion plasmas: a model comparison**This article is dedicated to the memory of Ignazio Fidone.

For the modelling of hot reactor-grade plasmas a way to compute local electron cyclotron wave losses efficiently and with good accuracy is required. Thereby the approach to calculating the electron cyclotron absorption coefficient is an essential element. A comparison of three available analytical forms (a ‘quasi-exact’ one and the asymptotic forms due to Trubnikov and to Robinson) shows that, overall, the use of Robinson's formula is the most suitable choice.

On estimating the role of diffraction in electron cyclotron absorption at the periphery of the plasma column

The propagation and absorption of microwave radiation at the periphery of a tokamak plasma under ECR conditions are considered. For microwaves propagating in a quasi-transverse direction, the range of plasma parameters is determined in which the effective plasma permittivity can be approximated by a piecewise linear function. With this approximation, it is possible to obtain analytic solutions to the wave equation and to use them to estimate the width of the power deposition region for different modes of microwave launching. A detailed analysis is given of tangential launching—the propagation of microwaves along a tangent to the resonance magnetic surface at which they begin to be absorbed under ECR conditions. Using the ITER tokamak as an example, it is shown that this launching method is most efficient in providing the narrowest power deposition profile at the plasma periphery. The results obtained are of interest for the problems of suppressing tearing-mode instabilities by localized ECR heating.

Recent Developments in Electron Cyclotron Emission Research on Magnetically Confined Plasmas

Electron cyclotron emission (ECE) has been an important diagnostic for measuring the temporal evolution of the electron temperature profile in magnetically confined plasma devices for more than 25 years. Recent advances in ECE measurements, such as two-dimensional ECE imaging and ECE intensity correlation techniques, have provided detailed information on sawtooth reconnection, neoclassical tearing mode behavior, electron heat transport, fast electron dynamics, and fast particle-driven Alfvén eigenmodes. ECE spectral analysis is benefiting from improved ECE modeling and significant increases in computational power that allow fast, real-time, temperature measurements. Mode-converted electron Bernstein wave emission (EBE) diagnostics are being developed to study overdense (ɷpe ≫ ɷce) plasmas, a regime where conventional ECE diagnostics cannot be applied and one commonly encountered in high-β devices, such as the spherical torus and reversed-field pinch. While ECE diagnostic techniques are now well established on many existing magnetically confined plasmas, significant challenges lie ahead for applying ECE techniques to reactor-grade plasmas such as ITER, where Te(0) is expected to reach 20 to 40 keV. This paper reviews the recent advances in ECE, electron cyclotron absorption, and EBE diagnostics and discusses the challenges for ECE measurements on ITER.

A Quasi-Optical Beam-Tracing Code for Electron Cyclotron Absorption and Current Drive: GRAY

The theoretical framework of quasi-optical propagation power absorption and driven current of a Gaussian beam of electron cyclotron (EC) waves in a general tokamak equilibrium implemented in the code GRAY is presented. Within the framework of the complex eikonal approach, the propagation of a general astigmatic Gaussian beam is described in terms of a set of coupled rays, allowing for diffraction effects. The computation of the EC wave absorption and current drive is performed for each ray of the beam, by means of a relativistic dispersion relation for EC waves and of a neoclassical response function for the current. The code has been designed and tested for calculations of propagation, power absorption, and current drive of realistic EC beams in ITER.

Ray trajectories and electron cyclotron absorption in an axisymmetric magnetic confinement system

The propagation and cyclotron absorption of electromagnetic waves lauched into an axisymmetric magnetic confinement system in a quasi-longitudinal direction is studied in the geometrical-optics approximation. Cyclotron absorption in a dense plasma is described by solving an approximate dispersion relation that is valid for small angles between the magnetic field B and the wave vector k. This approach makes it possible to avoid the difficulty associated with a transition from large propagation angles to the case of strictly longitudinal propagation. It is shown that electron cyclotron absorption can be efficient only when the plasma density is below the critical density. The numerical results obtained for the device for producing multicharged ions in experiments at the Institute of Applied Physics of the Russian Academy of Sciences agree qualitatively with the experimental data.

Measurement of Single Pass Electron Cyclotron (EC) Absorption Using Transmitted Waves in Heliotron J

Single pass absorption of second-harmonic EC waves propagating obliquely to the magnetic field has been studied in Heliotron J. Two orthogonal signals of transmitted high power EC waves are measured to estimate the single pass absorption rate. The experimental results agree well with ray tracing calculation results based on a linear absorption theory under the condition that the refraction effect is not strong, ne/nc < 0.3 (nc is a cut-off density of second-harmonic X-mode), that is, the waves reach the diagnostic port.

Electron-cyclotron absorption in high-temperature plasmas: quasi-exact analytical evaluation and comparative numerical analysis**Presented in part at the 14th Joint Workshop on Electron Cyclotron Emission and Electron Cyclotron Resonance Heating, Santorini, Greece, 9–12 May 2006.

On the basis of the electromagnetic energy balance equation, a quasi-exact analytical evaluation of the electron-cyclotron (EC) absorption coefficient is performed for arbitrary propagation (with respect to the magnetic field) in a (Maxwellian) magneto-plasma for the temperature range of interest for fusion reactors (in which EC radiation losses tend to be important in the plasma power balance). The calculation makes use of Bateman’s expansion for the product of two Bessel functions, retaining the lowest-order contribution. The integration over electron momentum can then be carried out analytically, fully accounting for finite Larmor radius effects in this approximation. On the basis of the analytical expressions for the EC absorption coefficients of both the extraordinary and ordinary modes thus obtained, (i) for the case of perpendicular propagation simple formulae are derived for both modes and (ii) a numerical analysis of the angular distribution of EC absorption is carried out. An assessment of the accuracy of asymptotic expressions that have been given earlier is also performed, showing that these approximations can be usefully applied for calculating EC power losses from reactor-grade plasmas.

Effect of nonlinear wave–particle interaction on electron-cyclotron absorption

We perform a self-consistent analysis of the nonlinear interaction of magnetized plasmas with electron-cyclotron (EC) waves. A closed set of equations is derived, which consists of the relativistic equations of motion under the wave field and the wave equation for the vector potential. The plasma is described in terms of ensembles of electrons which collectively determine the evolution of the wave amplitude and frequency through the current response. This description allows for effects of the electron motions on the efficiency of the wave absorption, for example, the asynchrony between the wave phase and the gyroperiod. As an application, we study the absorption of an EC wave beam in a simplified tokamak geometry, for plasma parameters relevant to current and future fusion experiments. We conclude that, within the limits of our model, there are cases where the linear theory for the absorption of EC waves, used widely in the current literature, may overestimate the energy deposition. In such cases, nonlinear effects are essential for the accurate estimation of the plasma-wave coupling and their inclusion should be considered, especially when the wave power is dramatically increased as in the case of ITER.

A theoretical analysis of the X-ray cyclotron absorption lines of the isolated neutron star 1E1207.4-5209

As revealed by recent observations, in the X-ray continuum of the radio quiet isolated neutron star 1E1207.4-5209 there exist several equidistant absorption lines, and their energies are, respectively, 0.7, 1.4 and 2.1 keV. According to the theory of quantum cyclotron radiation under the quadrupolar approximation developed in recent years, we have clarified some existing doubts and affirmed that these lines are electron cyclotron absorption lines instead of proton cyclotron lines. Besides, the spatial orientation of the spin axis of this neutron star has been theoretically determined.