Electron Cyclotron Frequency Range Research Articles

Electron Cyclotron Heating and Current Drive

Plasma heating and non-inductive current drive by waves in the electron cyclotron range of frequencies are reviewed. Both theoretical aspects concerning wave properties, heating and current drive mechanisms, as well as the major experimental results are summarized.

Quasi-optical description of reflection, focusing and plasma cut-offs of electron cyclotron Gaussian beams

In the analysis of the propagation of electromagnetic waves in the electron cyclotron frequency range, in both isotropic media and magnetoactive plasmas, the role of diffractive effects, which are not accounted for by geometrical optics, may no longer be neglected when highly collimated beams are to be employed. Moreover, when lenses, mirrors, refractive gradients and/or wave cut-offs are placed along the beam trajectory, the very concept of independent optical rays tends to introduce singularities, which do not always correspond to physical features. A quasi-optical approach has previously been shown to present the advantage of allowing a description (at the lowest order of approximation) of the diffractive widening of the beam. The specific aim of this paper is to test, when reflection, refraction or beam focusing indicates the need for particular attention, the solution method employed within such an approach. The results presented here concern the propagation and power deposition profiles, in a number of crucial physical situations, of narrow electron cyclotron beams launched, in Gaussian form, either into isotropic transparent media or through anisotropic toroidal plasmas of fusion interest.

Bursts of electron cyclotron emission during disruptions of high beta discharges in the Tokamak Fusion Test Reactor tokamak

Disruptions are sudden terminations of tokamak plasma discharges. During disruptions at high beta β where β ≡ plasma pressure/magnetic pressure, short (order of μs) and intense bursts of electron cyclotron emission (ECE), an order magnitude above thermal levels, are observed in the second harmonic electron cyclotron frequency range, which corresponds to 100s of GHz in the Tokamak Fusion Test Reactor tokamak. A unique combination of two, fast, 500 kHz, 20-channel grating polychromator instruments, located at different toroidal positions, is used to measure the emission and characterize these bursts. New insights into the three-dimensional dynamics of these disruptions and the accompanying bursts of ECE have been obtained. Bursts of ECE occur at the beginning of the thermal quenches and exhibit strong toroidal asymmetries. Bursts are localized to the vicinity of the ballooning mode, a fast growing (few ms) medium toroidal mode number (n=10–20) precursor, localized toroidally, poloidally, and radially, which triggers the disruptions. Fast-particle losses occur with the explosive growth of the ballooning mode, followed by plasma/wall interaction. Bursts of ECE occur shortly afterwards, within 10s of μs of the fast particle losses. An explanation of the bursting is presented which is consistent both qualitatively and quantitatively, with observations predicting, for example, radiation enhancement factors of ≈10. Bursting can be explained not in terms of enhanced excitation of emission but rather in the reduction of absorption of thermal emission. Bursting is consistent with a modification to the electron distribution function fe due to a rapid energy or particle exchange between hot electrons and cold electrons from the edge, momentarily reducing the velocity gradient of fc in the thermal region. Large edge localized mode events also exhibit bursts of ECE due to a similar sequence of events.

ECRF systems for ITER

ITER, the International Thermonuclear Experimental Reactor, proposes to use electron cyclotron technology on an unprecedented scale. ECRF (electron cyclotron range of frequencies) will be used for start-up, heating, noninductive on-and off-axis current drive, and wall conditioning. Advanced gyrotron sources will be needed in order to fulfill the unique requirements imposed by these applications. Consequently, an international R&D program has been undertaken to develop 170 GHz, CW, 1 MW, /spl sim/50% efficient tubes. The rationale for the R&D program is presented and design issues relating to the efficient generation, transmission, and delivery to the plasma of over 50 MW of ECRF power are discussed.

Wave dispersoin and resonant deposition profiles of electron-cyclotron Gaussian beams in toroidal plasmas

A peculiarity of the quasi-optical propagation of a Gaussian beam of electromagnetic waves is that it requires a treatment taking account, step by step, of all of its rays together. The dispersion relation from which such a ray- tracing may be deduced is in fact characterized not only by the medium where the beam is launched but also by the intrinsic beam structure. The behaviour of three-dimensional Gaussian beams in the electron-cyclotron frequency range is considered, with particular attention paid to their propagation in toroidal plasmas of fusion interest (with ITER-like parameters and various magnetic equilibrium configurations), to the generality of their launching conditions and to their power deposition profiles around resonant layers.

Electron cyclotron resonant heating: A simpler method for deriving the linear wave equations in a nonuniform magnetic field

In a recent article Cairns et al. [Phys. Fluids B 3, 2953 (1991)] gave a method for the derivation of full wave equations describing propagation through a cyclotron resonance in an inhomogeneous plasma. The simplicity of this method compares favorably with previous derivations, and the damping resulting from the variation in the magnetic field across a Larmor orbit, described by Lashmore-Davies and Dendy [Phys. Fluids B 1, 1565 (1989)], is included. The effect of the relativistic mass shift on the cyclotron frequency, which plays an important role in the electron cyclotron range of frequencies, was not taken into account, however, and the object of the present work is to remedy this omission. It is shown how equations, valid in the weakly relativistic regime, may be obtained in a rather straightforward way. Results obtained by a number of earlier workers are recovered and can be extended.

A study of a parallel mode launch into a magnetic beach

A parallel mode launch in the electron cyclotron range of frequencies is performed on axis in the east end cell of the Phaedrus-B tandem mirror. Propagation of the energy launched toward a magnetic beach in a radially hollow density profile was studied experimentally. A strong refractive dispersal of the launched energy was observed and shown to be in good agreement with a WKB-type ray tracing model using a cold plasma Appleton-Hartree dispersion relation. Measurements of plasma density and electron temperature indicate that the use of this dispersion relation is well justified. These results are compared with additional ray tracing studies for radially hollow and nonhollow, high (f/sub launch/ f/sub p/) density models. For the experimental conditions examined, a reversal of refractive behavior is shown to exist as the energy propagates from a low density (f/sub launch/>f/sub p/) region to a high density (f/sub launch/ >

Relativistic effects on microwave reflectometry

A simple formula for tracking the cutoffs of waves in the electron cyclotron range of frequencies is presented for plasmas with electron temperatures similar to those of existing large tokamaks (∼10 keV) and conditions of negligible wave absorption.

Influence of fast waves on the collective scattering of microwaves in fusion plasmas

Microwave scattering by the fluctuations of fusion plasmas is one of the most promising α-diagnostic techniques. Previous investigations have concentrated on the fluctuations near the slow wave branch in the lower hybrid range of frequencies. The small signal and the lack of sensitivity to the contribution of α-particles to the total cross-section near the slow branch severely limits the effectiveness of this technique. In this paper, we report results of investigations of scattering by fluctuations in the lower hybrid range of frequencies near the fast branch. Surprisingly, when both fast and slow branches exist, the scattering amplitudes are comparable. More important, the α-contribution is larger for the fast branch and the fast branch has a larger parameter space where it exists. Specifically, the slow branch exists only above the lower hybrid frequency, while the fast branch can exist at all frequencies up to the electron cyclotron range of frequencies. We find numerically that the scattering amplitudes near the fast branch below the lower hybrid frequency are several orders of magnitude larger than those near the slow branch above that frequency where it can exist. This may make microwave scattering by fast waves a more attractive α-diagnostic technique.

A new representation of relativistic wave damping above the electron-cyclotron frequency

The full relativistic dielectric tensor for a Maxwellian plasma in the electron-cyclotron range of frequencies is investigated. A new representation for arbitrary values of the wave frequency and direction of propagation of the anti-Hermitian part is presented that avoids the standard expansions of the Bessel functions. A compact form of the wave damping for ω ≽ 2ωc is obtained that is useful for the investigation of synchrotron radiation in hot plasmas.

Propagation of electron cyclotron waves in a weakly relativistic plasma with steep density and temperature profiles

A detailed analysis is made of the deduction of systems of differential equations describing the propagation of both ordinary and extraordinary waves in the electron cyclotron frequency range in a stratified plasma, perpendicularly to the magnetic field and across the electroncyclotron fundamental resonance layer. The equations are derived under conditions of not too large electron temperature (the so-called weakly relativistic condition) and of very weak nonuniformities of the confining magnetic field. The effects of the nonhomogeneities of the equilibrium plasma density and temperature are carefully examined. It is shown that the propagation equations derived previously in the literature can be extended with only a moderately larger effort in computations to take account also of very strong density and temperature gradients.

Mode-conversion process and overdense-plasma heating in the electron cyclotron range of frequencies.

Through a particle-simulation investigation, a new mode-conversion process, through which an incident fast extraordinary mode (fast X mode) is converted into an electron Bernstein mode (B mode) via a (slow extraordinary mode slow X mode), is discovered in plasmas whose maximum density exceeds the cutoff density of the slow X mode. The converted B mode is found to heat the electrons efficiently in an overdense plasma region, when the plasma has the optimum density gradient at the plasma surface.

Absorption of electron cyclotron extraordinary waves in large size, high density plasmas

The absorption of oblique extraordinary waves in the electron cyclotron frequency range is analysed by means of a wave-dynamical scheme in hot high density plasmas. Strong wave damping is found for densities that largely exceed the nominal value of the cold high-density cut-off. The dependence of this phenomenon on the parameters of the plasma is studied and commented upon.

Particle simulation of the OXB mode conversion and overdense plasma heating in the electron cyclotron range of frequencies

Propagation of an electron Bernstein mode (B-mode), converted from an incident ordinary mode (O-mode) via an extraordinary mode (X-mode), is observed in an overdense plasma whose density is higher than the cutoff density of the O-mode. The electron heating due to the B-mode is also observed in its overdense region.

Nonlinear absorption of intense microwave pulses.

Free-electron lasers in the electron cyclotron frequency range have been proposed as an efficient means of heating and driving current in tokamak plasmas. The proposed free-electron laser will have short pulses (\ensuremath{\approxeq}5\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}8}$ sec) with a peak power of (4--8)\ifmmode\times\else\texttimes\fi{}${10}^{9}$ W and electric fields within the plasma in the range ${10}^{5}$--${10}^{6}$ V/cm. At these high intensities nonlinear effects compete with thermal effects in the absorption of microwave power. Analytic and numerical calculations of the nonlinear absorption are presented.

Comparison of theory with electron cyclotron current drive experiments on WT-2

A simple analytical model of the non-Maxwellian electron velocity distribution, whose parameters are constrained by the observed plasma current and soft X-ray emission spectrum, is used in conjunction with a fully three-dimensional ray tracing code to calculate the absorption of radiation in the electron cyclotron range of frequencies by WT-2 discharges. This gives a quantitative, theoretical description of the way in which a drifting population of energetic electrons appears to dominate WT-2 current drive experiments. Calculation of the proportion of source power absorbed by the plasma helps to determine the efficiency factor of the current drive mechanism in this context. The strong dependence of current drive on the extraordinary mode launch direction is given theoretical support.

Modelling of electron-cyclotron plasma formation and preheating in Tokamaks

A zero-dimensional code is described for modelling the plasma formation and preheating in a Tokamak, by means of extraordinary waves in the electron-cyclotron frequency range. Numerical results are presented, which give the increase in time of the electron density and temperature, together with the power balance in the steady-state plasma Extrapolation of these results, shows that the RF plasma in larger size Tokamaks may reach temperatures larger than the impurity radiation barriers.

Short-Wavelength Parametric Absorption at Electron-Cyclotron Harmonics in ELMO Bumpy Torus

A weak-turbulence theory of parametric instabilities in the electron-cyclotron frequency range in ELMO-bumpy-torus plasmas is developed. Parametric turbulence levels of excited modes are evaluated for principal- and second-electron-cyclotron-harmonic-resonance layers. It is shown that short-wavelength parametric turbulence may play a significant role in contemporary experiments of ELMO-bumpy-torus plasmas.

The Generation of Current in Tokamaks by the Absorption of Waves in the Electron Cyclotron Frequency Range

The theory of current generation due to the absorption of high-frequency waves is developed for the case in which the propagation of the waves is described in the geometrical optics approximation. An expression for the current generated is obtained which is similar in fornn to the expression for the rate of energy deposition. This expression is incorporated in a toroidal ray tracing code to study current generation due to the absorption of waves in the electron cyclotron frequency range. The dependence of the current generated on temperature and angle of injection for the joint Naval Research Laboratory-Oak Ridge National Laboratory experiment on ISXB is studied.

Weakly relativistic dielectric tensor and dispersion functions of a Maxwellian plasma

In order to study the absorption and emission properties of a magnetized plasma in the electron cyclotron range of frequencies, the weakly relativistic (Shkarofsky) plasma dispersion functions are simply and exactly expressed in terms of the Z function. This gives a useful working form to the dielectric tensor, for any wave vector and harmonic number, covering also the case of electron Maxwellian distributions drifting along the magnetic field.