Generation Of Ion Cyclotron Waves Research Articles

Ion-Cyclotron Waves in Elmo Bumpy Torus: Perturbation Analysis of the Effects of Wall Bumpiness

The analysis of ion-cyclotron wave propagation and related plasma heating in the Elmo Bumpy Torus (EBT) magnetic confinement experiment is made difficult by the complex geometry of that device. Characteristic wavelengths are of the order of the device size, and the approximation of geometrical optics, used so successfully in studies of electron-cyclotron heating, is not valid. An analysis of ion-cyclotron wave propagation is presented here which is based on the assumption that EBT may be approximated by a weakly bumpy cylinder. Specifically, a perturbation methodology specially developed to analyze the propagation of waves through media with corrugated boundaries is utilized. It is found that even modest amounts of wall modulation can give rise to striking modifications of the cylindrical eigenmodes. Furthermore, cylindrical eigenmodes may resonate with each other and the wall modulations, giving rise to the occurrence of stopband and passband phenomena and periodic exchanges of energy between propagating modes. The resonant exchange of energy between eigenmodes with sharp axial structure and weak radial structure (readily excited by localized antennae) and eigenmodes with weak axial structure and sharp radial structure (conducive to plasma heating) suggests new ways in which antennae and wall structures may be configured to achieve desirable wave-heating properties.

On the stability of almost perpendicularly propagating ion cyclotron waves

The dispersion relation for the near perpendicular propagation of the electromagnetic ion cyclotron wave, having a wavelength much larger than the ion Larmour radius r L and a frequency ω ≈ Ω + (Ω + is the ion cyclotron frequency), has been derived for a plasma consisting of a hot and a cold ion component. The hot ions and electrons have been described by loss-cone distribution functions; an ordering of the parameters was used to derive the cold ion contributions. Two modes, one with an increasing frequency and another with a constant frequency can propagate in the plasma. The two modes interact resulting in an instability of the former in the wavelength range k ⊥r ⊥ = 0.4−0.6 (for n C / n H = 0) and from k ⊥ r L = 0.5−0.8 (for n C / n H = 1.0) for a propagation angle of 70°. The instability of the mode is found to decrease with increasing cold ion densities and propagation angles.

Wave‐particle interactions near ΩHe+ observed on board GEOS 1 and 2: 2. Generation of ion cyclotron waves and heating of He+ ions

This work is a continuation of paper 1 (Young et al., 1981) and is devoted to the generation process of ion cyclotron waves (ICWs) and the acceleration of He+ ions up to suprathermal energies. Simultaneous measurements are used from the ion composition experiment (0 < E < 16 keV), the energetic particle experiment (24 < E < 3 300 keV), and the ULF wave experiment (0.2–10 Hz) on board the GEOS 1 and GEOS 2 spacecraft. General characteristics of the local time distribution of ICWs will be presented and compared with those of the thermal anisotropy of energetic protons and the He+ abundance. Further calculations of the convective growth rate are conducted by applying two different methods, both of which are based upon the measured proton fluxes. The generation conditions of the ICWs in the presence of He+ ions will be investigated and three possible explanations will be discussed: (1) enhanced convection growth rates, (2) lowering of the threshold for absolute instabilities, and (3) change of the ICWs ray path (laser‐like effect). Finally, it is shown that the flux of suprathermal He+ ions is modulated at the ICW frequency. Owing to nonlinear effects, part of the energy of the energetic protons is transfered via the ICWs to the He+ ions that are essentially accelerated in the direction perpendicular to the static magnetic field. Then in the otherwise collisionless plasma the friction between energetic anisotropic protons and thermal He+ ions is achieved through the ICWs.

Wave‐particle interactions near ΩHe+ observed on GEOS 1 and 2 1. Propagation of ion cyclotron waves in He+‐rich plasma

The GEOS 1 and 2 spacecraft contain a set of particle and wave detectors which allow for a very comprehensive study of wave‐particle interactions occurring within the equatorial region of the magnetosphere. This paper is devoted to interactions involving protons in the energy range 20 keV to 300 keV and ULF waves with frequencies below the proton gyrofrequency. It is shown that most of the ion cyclotron waves (ICW's) detected in this frequency range have spectra whose characteristic frequencies are organized in the vicinity of the He+ gyrofrequency. Simultaneous measurements of the ion composition in the thermal energy range (E ≲110 eV) show these waves to be clearly associated with the abundance of cold He+ as well as the anisotropy of ions above 20 keV. The general characteristics of these helium‐associated ULF events are presented in case studies of four events. The interpretation of this phenomenon is given in the present paper in terms of the propagation of ICW's in a He+‐rich plasma. It is shown that the shape of the cold plasma dispersion curve (for both parallel and non‐parallel propagation) can adequately explain the main characteristics of the observed waves (frequency spectrum, polarization) as well as the differences between observations made onboard GEOS 1 and GEOS 2. The generation conditions of ion cyclotron waves in such a multi‐component plasma, as well as their quasi‐linear effects on both the cold He+ ions and the hot protons, are discussed in a companion paper.

Stimulated Scattering from Ion Cyclotron Wave

A study is made of the stimulated backscattering of electromagnetic ordinary waves from obliquely propagating ion cyclotron waves in a magnetized plasma. It is found that the threshold is considerably lower and the growth rate considerably larger than the corresponding values for backscattering from perpendicularly propagating lower and upper hybrid waves.

440 keV proton precipitation at middle latitudes during the recovery phase of magnetic storms

Quasitrapped ( H min < 100 km) protons with energies E > 440 keV have been detected during magnetic storms by the IK-5 satellite in a narrow zone with a center at L = 3.0−3.2; this zone is well separated from the region of Isotropie fluxes at L > 4. Data for five moderate storms have been analysed in detail. It was found that the quasitrapped proton peaks appear during the recovery phase of magnetic storms and that the scattering of protons toward low mirror points takes place in all local time sectors. The relation between the observed precipitation of the E > 440 keV protons and the intraplasmaspheric precipitation of low-energy protons has been discussed in the light of the theory of generation of ion-cyclotron waves by the ring current and the theory of parasitic interaction of these waves with the radiation belt protons. A series of arguments indicates that the phenomenon under study is connected with the magnetopheric process which generates the SAR arcs.

Current driven ion cyclotron waves in collisional plasma

The stability of obliquely propagating ion cyclotron waves to current flow along the magnetic field lines, in a fully ionised plasma, is examined using fluid equations. It is shown that when a certain threshold current is exceeded, instability results through normally dissipative terms like parallel resistivity, thermal conductivity, etc.

Ion cyclotron waves and fast waves in a toroidal cavity

The propagation of ion cyclotron waves and fast waves in a toroidal cavity with a spatially varying static magnetic field as in a tokamak or stellarator is examined. Using a cold plasma model in a square cross section conducting toroidal cavity and neglecting effects of electron inertia, the wave equation is reduced to an ordinary differential equation which is numerically integrated subject to boundary conditions to find eigenmodes which represent cavity resonances. For the fast wave, only very small perturbations from the corresponding uniform plasma guide problem are found, and it is concluded that effects of toroidicity on the fast wave are not significant. For the ion cyclotron wave it is found that the region of propagation is generally confined to the high magnetic field side of the cyclotron resonance and for low order modes vertically and azimuthally, the region of propagation does not extend to the resonance location. A new type of wave behavior appears due to toroidicity which is similar to the ion cyclotron wave but depends differently on wavelength and may be important for fusion plasma heating because of its possibly greater accessibility. On the basis of the wave profiles, optimum antenna designs will be profoundly affected by toroidicity.

Effect of the plasma density profile on ion-cyclotron wave generation

It is shown that the loading of a Stix coil by ion-cyclotron wave production in plasma, which exhibits a second maximum previously reported to be anomalous, can be explained in detail by taking into account the plasma density profile. Data from a number of experiments show that the efficiency for heating the plasma by wave absorption is a monotonically increasing function of density. The reduced heating efficiency observed at the second loading maximum relative to the first can be attributed to damping of the waves responsible for the second maximum in the lower density surface region of the plasma column.

Ion Cyclotron and Fast Hydromagnetic Wave Generation in theSTTokamak

A test coil operating at 25 MHz is used to generate waves in the vicinity of the ion-cyclotron frequency and its harmonics in the $\mathrm{ST}$ tokamak. Coil-loading and magnetic-probe signals show that propagating natural modes are excited efficiently in this plasma torus for both slow (ion cyclotron) and fast hydromagnetic waves. These data permit the formulation of an empirical model for wave propagation in the toroidal plasma.

Ion cyclotron wave generation in a two-ion plasma

Exact calculation of the dispersion relation of a cold plasma shows that the plasma behaviour is different from that predicted by the usual approximate theory which neglects electron inertia in the low-density limit. For example, the limiting value of Ω for optimum coupling is different from 1, where Ω is the wave frequency divided by the ion cyclotron frequency. This fact was ascertained experimentally in the QP-machine.Experimental observations of optimum coupling of the ion cyclotron wave in a two-ion plasma in the QP-machine are presented as functions of the plasma density. The plasma was produced by a PIG discharge with a density from 1010 to 2 × 1012 cm−3. The wave was generated by a Stix-type coil (coil wavelength 50 cm), which was fed by a 4.4-MHz, 20-kW oscillator. Experimental data lay within the band of H+ concentration between 10–90% of the dispersion relation of a homogeneous cold plasma column with a sharp boundary. However, the dependence of optimum loading on the diameter of the plasma column disagrees with the theoretical prediction.

Ion Cyclotron Wave Generation in the Model C Stellarator

To permit quantitative comparisons between experiment and theory, ion cyclotron wave generation by the Stix coil system of the Model C stellarator is analyzed using a coil-plasma model which closely approximates the physical system: filamentary currents at the coil loop positions induce plasma waves which propagate along the “cold” plasma column which is coaxial with a cylindrical waveguide. Most important in the analysis is the inclusion of finite electron inertia effects which cause the natural modes of the system to be characterized by two radial wavenumbers in place of one and which can seriously modify the properties of the ion cyclotron waves. Coil loading predictions are in good absolute agreement with experimental observations for wide ranges of plasma density and magnetic field, thus demonstrating the relevance of the cold theory to the laboratory plasma. However, magnetic field predictions are larger than the fields measured far from the Stix coil, suggesting wave attenuation by processes not contained in the theory.

Dominant Influence of Electron Inertia on Ion Cyclotron-Wave Generation in Plasma

Electron inertia is predicted to have a dominant influence on ion cyclotron-wave propagation as the wave frequency approaches the ion cyclotron frequency. This influence should effect a reduction in the Stix coil coupling to a plasma column as the plasma density is lowered. Experimental coupling measurements, taken over an appropriate range of plasma density (2\ifmmode\times\else\texttimes\fi{}${10}^{10}$ to 2.8\ifmmode\times\else\texttimes\fi{}${10}^{12}$ ${\mathrm{cm}}^{\ensuremath{-}3}$) on the Model-C stellarator, demonstrate the validity of the theoretical conclusion.

Experimental Investigation of Harmonic Ion Cyclotron Wave Propagation and Attenuation

A new wave phenomenon was observed in the course of an experimental investigation of ion cyclotron resonance heating of hydrogen and deuterium plasmas in strong magnetic fields. It was found that the waves can propagate for frequencies larger than the ion cyclotron frequency fc, and attenuate at harmonics of fc with resulting increase in the transverse temperature-density product nβT⊥. The harmonic number at which the waves attenuate increases with increasing gas pressure. Attenuation at harmonics up to the 8th was observed. The plasma density is typically 6 × 1017 m−3, the transverse plasma temperature (Te⊥ + Ti⊥) ⪕ 50-eV equivalent, and the magnetic field 1–9 kG. A magnetic beach geometry is employed and the waves are excited by a Faraday shielded Stix coil from a 30 kW, 5.8 MHz driver. Harmonic cyclotron heating is related to large transverse wave numbers which are shown to exist in the experiment.

Optimum Generation of Ion-Cyclotron Waves in a Cylindrical Two-Ion Plasma

Ion-cyclotron waves have been generated in a hydrogen-deuterium plasma (previously formed by Ohmic heating) contained in the Model C stellarator, using an induction coil of finite wavelength. The conditions for optimum generation of waves, found experimentally, were in good agreement with theoretical predictions.

Ion-cyclotron resonance in a moving plasma

Observations were made of the generation and absorption of ion cyclotron waves in a moving plasmoid. Absorption of the high-frequency power took place at two frequencies shifted by the Doppler effect to both sides of a mean frequency. It appeared that magnetic beaches play an essential part in the damping of ion-cyclotron waves; thus, in the absence of one beach the second absorption peak was not observed. The results of measuring the Doppler shift and resonance frequencies make it possible to determine the mean velocity of the plasmoid and the plasma density (6.7 × 106 cm/sec and 7 × 1012 cm-3).

Propagation of ion-cyclotron plasma waves in a weak inhomogeneous field

Propagation of ion-cyclotron waves along a plasma cylinder in a longitudinal magnetic field that slowly changes along the cylinder axis is discussed. An integro-differential equation has been obtained for the electric-wave field, and the solution has been found for this equation in a geometrical-optics approximation.

Experiments on Ion Cyclotron Waves

Experiments have been performed on the generation of ion cyclotron waves and their propagation into a magnetic beach. The experiments were carried out on the B-66 machine, which is currently a magnetic mirror device. Studies of the production of neutrons have provided evidence for the absorption of the energy of these waves via ion cyclotron damping. Microwave phase-shift measurements have now been made, and the addition of electron density completes the list of parameters required for direct comparison of experimental and theoretical dispersion relations. The experimental data yield a smooth monotonic relation between density and frequency which is qualitatively similar to that predicted by theory. There are, however, unexplained quantitative differences. Wave propagation into the magnetic beach region was observed with a single turn rf magnetic probe. The variation of the amplitude of these waves in the magnetic beach is in qualitative agreement with the theory of ion cyclotron wave propagation and cyclotron damping.

Experiments on Ion Cyclotron Resonance

Theoretical calculations have indicated that an attractive possibility for heating the ions of a plasma directly, swiftly, and efficiently is to feed energy into ion cyclotron waves and cause this wave energy to thermalize. Experiments at the milliwatt power level verify the existence of a resonance in a helium plasma at the cyclotron frequency of the doubly charged helium ion. The variation of the plasma loading with magnetic field strength is markedly asymmetrical, in agreement with the theory of ion cyclotron wave generation. The observed plasma loading indicates an efficiency of power transfer between the induction coil and the plasma greater than 60%.

Generation and Thermalization of Plasma Waves

Generation of hydromagnetic and ion cyclotron waves by an induction coil is considered for a cylindrical plasma in a uniform confining magnetic field. Resonance widths are calculated and power absorption is calculated and compared to ohmic losses in the induction coil. Rapid thermalization of transverse plasma waves occurs when appreciable numbers of ions stream through the periodic perturbation with velocities such that, in their own rest frames, these ions ``feel'' the perturbation at their own cyclotron frequency. This effect, termed cyclotron damping, makes possible an efficient plasma heating scheme for thermonuclear reactors. Radio-frequency power can be transferred from an induction coil into ion cyclotron waves with an efficiency typically greater than 65%. The wave energy can be quickly transformed into energy of effectively random transverse ion motion by causing the ion cyclotron wave to travel along a magnetic field which decreases slowly with distance.