Ion-ion Hybrid Resonance Research Articles

Use of the two-ion hybrid as an impurity diagnostic

In a plasma containing more than one ion species, the frequencies of the ion–ion hybrid resonances can be a sensitive measure of the densities of the minor species, but only if the frequency shifts caused by electron motions are small, as experimental observations suggest. By calculating the eigenfrequencies for ion–ion hybrid waves taking into account collisions, Landau damping, electron inertia, electromagnetic effects, and density gradients, it is found that the frequency shifts are not negligible unless k∥ is extremely small. Treatment of the sheath boundary conditions at the ends of a plasma column shows that the effective value of k∥ can indeed be sufficiently small, and that the uncorrected resonance frequency is surprisingly accurate over a wide parameter range. Data from an Ar–Xe discharge demonstrate the usefulness of this technique for measuring impurity concentrations.

Observation of Mode-Converted Ion Bernstein Wave by an HCN Laser Scattering

An HCN laser scattering technique is employed for detecting an electrostatic wave excited by ICRF heating on the JIPP T-IIU tokamak. The frequency spectra and wavenumber of the excited wave were observed during the heating. The measured wave is consistent with the theoretically estimated wave dispersion of the ion Bernstein wave which is mode-converted from the fast wave in the vicinity of the ion-ion hybrid resonance layer. The influence of MHD activity on the mode-converted ion Bernstein wave is examined. When the MUD activity grows and the plasma becomes unstable, the scattered signal from the ion Bernstein wave decreases, being accompanied with large fluctuations.

Mode conversion near ion-ion hybrid and IC harmonic resonances in Tokamaks

The authors propose a model for the investigation of mode conversion near two ion hybrid and cyclotron harmonic resonances in axisymmetric toroidal plasmas. The wave differential equations are derived from Maxwell-Vlasov equations using this model and the assumption of weak dispersion, and are shown to coincide with equations recently obtained in the literature for a slab model including a (B0. Del )B0 term. At the same time the limits of applicability of these equations in a Tokamak are clarified. The wave equation is solved explicitly in two cases of physical interest: near an isolated two-ion hybrid resonance, where the fast wave couples to the cold torsional Alfven wave, leading mainly to electron heating; and near the first harmonic resonance of a single species plasma, where it couples to an ion Bernstein wave. These solutions clarify some aspects of the physics of these resonances, and can be useful for applications in numerical ICR heating codes.

Resonance Surfaces in the Ion Cyclotron Frequency Range in Toroidal Systems

Resonance surfaces are investigated in a toroidal geometry for waves in the ion cyclotron frequency regime. In this geometry stationary waves are described by partial differential equations. Three kinds of resonances appear in this regime of a multicomponent plasma, the fundamental ion cyclotron resonance, the perpendicular ion cyclotron resonance, and Buchsbaum's ion-ion hybrid resonance. In a two-dimensional axially symmetric plasma the last two resonances can be obtained by solving ordinary differential equations. The perpendicular ion cyclotron resonance coincides with a magnetic surface, while the ion-ion hybrid resonance in general makes a small angle of the order of meB/miBP with the magnetic surfaces, except close to the fundamental cyclotron resonances, where the angle becomes large.

Antenna Loading and Electron Heating Experiments of ICRF Wave in TNT-A Tokamak

Antenna loading resistance and electron heating effects of ICRF wave were investigated in TNT-A tokamak. Lodaing resistance increased with the mean plasma density and decreased with the input power. The effect of the distance between the plasma and antenna surface on loading resistance was studied and had good agreements with the calculated results. The increase in the soft Xray emissivity was larger in the presence of ion-ion hybrid and/or ion cyclotron resonance layer in the plasma than that in the absence of them. With the absorbed power up to two times of the ohmic power, the central electron temperature increased by 20%, the soft Xray emissivity increased by 80% and the mean plasma density decreased by 10%, while the total radiation loss increased slightly (by 15%).

Dispersion and resonance-cone near ion-ion hybrid resonance

An experimental and theoretical investigation of the electrostatic wave propagating across the magnetic field at frequencies around the ion-ion hybrid resonance is presented. Firstly, the dispersion relation for the warm electron mode ( omega /k/sub ///<< nu e) is measured in a simple toroidal plasma, which is composed of helium and neon ions, with the ion concentration ratio controlled. The experimental results and the calculations reveal that even a small fraction ( approximately 1%) of the minority concentration leads to an additional cutoff and hybrid resonance near the minority-cyclotron-resonance frequency. Secondly, the ion-ion hybrid resonance cone of the warm electron mode is observed for the first time. The dependence of the resonance cone angle on the frequency and the ion concentration ratio is observed to agree with the theoretical predictions.

Observation of Mode-Converted Ion Bernstein Waves in the Microtor Tokamak

Mode-conversion processes play an important role in the radio-frequency heating of tokamak plasmas. This paper reports the first direct observation of externally driven ion Bernstein waves in a tokamak plasma. The waves are only observed in mixed-species plasmas near the ion-ion hybrid resonance layer and are interpreted as being the result of linear mode conversion of the fast magnetosonic wave.

The plasma dispersion relation near the two–ion hybrid resonance

The dispersion relation of a deuterium –hydrogen plasma is investigated near the ion cyclotron frequency of hydrogen at varying hydrogen temperatures. It is found that at low hydrogen-to-deuterium temperature ratios, only the fast mode and the ion Bernstein mode are coupled around the hybrid layer. Above a certain critical temperature ratio Th&lt; Thc, these two modes become coupled also to a third mode. Around and above Thc, the wave equation is of sixth order rather than of the fourth order previously discussed.

The influence of oxygen impurities on ion cyclotron and ion hybrid resonances in deuterium-hydrogen-plasmas

The properties of plane electromagnetic waves propagating in a temperature plasma at about the ion cyclotron frequencies are discussed. The plasma consists of deuterium in a high relative concentration, and hydrogen and oxygen in minority concentrations between 1 and 10%. The left hand polarized wave exhibits high damping at the cyclotron frequencies of the ions. Small amounts of oxygen impurity destroy the hydrogen ion cyclotron resonance completely. At low ion temperatures the separate ion cyclotron resonances combine to form new resonances weighted according to mass and concentration. At right angles to the magnetic field lines the extraordinary wave exhibits the ion hybrid resonances with strong damping. The resonances lie close to the cyclotron frequencies of the minority ion species. At low ion temperatures even small oxygen admixtures destroy the hybrid resonance between the hydrogen and the bulk of the plasma. At higher temperatures the hybrid resonances between the several ionization states of oxygen and the bulk of the plasma are pronounced; their absorption maxima lie close to the cyclotron frequency of the deuterium ions.

Wave propagation in a temperate multi-species plasma around the ion cyclotron frequency range

Plane wave propagation in temperate plasmas consisting of n ion species is calculated analytically for collisionless plasmas of arbitrary composition. Numerical results are given for the complex refractive index of plasmas including collisions between particles of any kind and at arbitrary angles of propagation. There are two waves propagating at all angles other than 90°, one wave showing resonances at each of the n cyclotron frequencies of the ions involved. High ion-ion collision frequencies combine the motions of the ions to give new mass and composition weighted hybrid ion cyclotron resonances. At right angles to the external magnetic field one wave will propagate in the ion cyclotron range showing n – 1 ion-ion hybrid resonances and n – 1 hybrid cut-offs. The ion-ion hybrid resonances can be traced down to propagation at angles smaller than 90°, disappearing for parallel propagation. The hybrid resonance frequencies are close to the cyclotron frequencies of the ions with small relative concentrations. Damping of the waves in the neighbourhood of the ion-ion hybrid resonances is strongly affected by ion-ion collisions.

The approximation of confluence by resonance in inhomogeneous plasmas

The degree to which a Budden-type equation describes the behaviour of the long wavelength branches of the modes of a higher order differential equation such as governs confluence in a plasma at ion-ion and upper hybrid resonance frequencies and at cyclotron harmonics is examined.

Fast-slow mode conversion near the ion-ion hybrid resonance

Fast-slow mode conversion in deuterium plasma with a small amount of hydrogen impurity, for frequencies close to the two-ion hybrid frequency, is investigated. It is shown that while electron thermal effects tend to inhibit the wave conversion process, ion thermal effects tend to restore the cold plasma properties, favouring, therefore, the energy exchange between the two modes. The aforementioned effects are competitive for zeta 0e=c/n/sub /// nu e>or approximately=1. For zeta 0e<1, electron thermal effects, particularly Landau damping, dominate over ion Larmor radius effects, drastically diminishing the wave conversion efficiency. For zeta 0e<<1, the coupling between the modes disappears altogether. Furthermore, by studying the coupled equations describing the system, a coupling parameter is defined and shown to be the same in a plane slab geometry and cylindrical geometry.

Magnetoacoustic Oscillations of a Plasma Containing Two Species of Ions

Numerical calculations of linear magnetoacoustic resonant phenomena in a plasma containing two species of ions have been made for a cylindrical plasma with a model which includes the effects of collisional damping and radial non-uniformities in temperature and number density. At sufficiently high temperatures two frequencies are predicted at which magnetoacoustic resonances for the first radial mode will occur. These are expected from considerations of the effects of the ion-ion hybrid resonance.

Heating tokamaks via the ion-cyclotron and ion-ion hybrid resonances

The ion-ion hybrid resonance can occur at high plasma densities in tokamaks and thereby absorb energy from the fast magnetosonic mode which would otherwise propagate freely. Ion-cyclotron resonance regions, although they occur in the low-density peripheral plasma, can nonetheless cause sufficient absorption to compete with fundamental cyclotron resonance damping by ions. For the ion-ion hybrid resonance it is shown that: (1) the energy absorption occurs via a sequence of mode conversions. (2) A poloidal field component normal to the ion-ion hybrid mode conversion surface strongly influences the mode conversion process, so that roughly equal electron and ion heating occurs in the present proton-deuterium experiments, while solely electron heating is predicted to prevail in deuterium-tritium reactors. (3) The ion-ion hybrid resonance suppresses toroidal eigenmodes. (4) Wave absorption in minority fundamental ion-cyclotron heating experiments will be dominated by ion-ion hybrid mode conversion absorption for minority concentrations exceeding roughly 1%.

Decay instability at the ion-ion hybrid resonance

The parametric decay of a large amplitude AC field oscillating near the ion-ion hybrid frequency is studied in a homogeneous two ion-species plasma. Two different decay modes are considered: (i) a low frequency ion acoustic wave propagating parallel to the ambient magnetic field and (ii) a 'cold' ion-Bernstein mode propagating almost perpendicular to the magnetic field. A third possibility (of decay into two ion-ion hybrid modes) is also investigated and estimates of threshold powers and growth rates are discussed in each instance.

RF plasma heating in the Uragan stellarator. I. Wave launching and plasma heating

Experiments are described in which the launching of r.f. waves in the Uragan stellarator has been studied, in the ion cyclotron and the ion-ion hybrid resonance regions. A wave launching structure was used which produced a non axially symmetric (m=1) r.f. field in the plasma. The excited waves propagated along the stellarator and were damped, without a special magnetic beach, causing an ion heating which was uniform along the length of the stellarator. By this method a plasma was obtained having a pressure which approached the limiting value for stellarator equilibrium: beta =8 pi nT/H02 approximately=10-3.

High-frequency heating of plasma with two ion species

The authors consider the penetration of electromagnetic waves with a frequency of the order of the ion cyclotron frequencies and with a fixed longitudinal wave number k‖, so that N‖ = k‖cω ≫ 1 deep into an inhomogeneous plasma with two ion species. The propagation of two kinds of waves (fast and slow) with widely differing polarization and transverse refraction index is possible. For both types of waves there is an evanesence region at the plasma periphery.The evanescence region is narrow for slow waves and the y easily penetrate the plasma. In a dense plasma they become electrostatic and can reach the ion-ion hybrid resonance region. However, the damping of these waves due to Cherenkov interaction with electrons in a high-temperature plasma is strong and therefore they are not suitable for heating plasma of large dimensions, as they are absorbed at the plasma periphery.The fast waves have a wider evanescence region and can be excited effectively only if N2 is not too high. These waves can be completely absorbed in the plasma (due to Cherenkov interaction with electrons) if where a is the plasma radius and . Fast waves can also reach the region where they are transformed into slow waves. In this region their damping increases considerably. It is shown that the transformation region in an inhomo-geneous plasma with two ion species in a non-uniform magnetic field may be at the centre of the plasma. Fast waves can be used effectively for heating plasma of large dimensions.

Messung und Analyse der Ionen-Ionen-Hybridresonanzen bei Plasmen endlicher Länge

The ion-ion hybrid resonances are investigated in hot cathode hydrogen and deuterium discharges. There are no observations suggesting an effective angle of propagationΦ<90°. The effect of finite components of the propagation vector in the direction of the magnetic field are discussed. Relations are given allowing determination of the ion concentrations from the positions of the ion-ion hybrid resonances.

Ion-ion hybrid resonances of H 2- and D 2-discharges

Ion-ion hybrid resonances are observed at a positive column. Violations of theoretical predictions previously reported by Buchsbaum are not observed. The effects of finite components of the propagation constant in the magnetic field direction are considered.

Accessibility of Ion-Ion Hybrid Resonance

The dispersion relation for the ion-ion hybrid resonance has been investigated in the density region of 106 cm-3 to 1017 cm-3 with the parallel wave number as the parameter, and the accessibility condition is presented.