Ion-ion Hybrid Resonance Research Articles

Experimental observations of mode-converted ion cyclotron waves in a tokamak plasma by phase contrast imaging.

The process of mode conversion, whereby an externally launched electromagnetic wave converts into a shorter wavelength mode(s) in a thermal plasma near a resonance in the index of refraction, is particularly important in a multi-ion species plasma near the ion cyclotron frequency. Using phase contrast imaging techniques (PCI), mode-converted electromagnetic ion cyclotron waves have been detected for the first time in the Alcator C-Mod tokamak near the H-3He ion-ion hybrid resonance region during high power rf heating experiments. The results agree with theoretical predictions.

Symmetries in dissipation-free linear mode conversion

From properties of wave energy flow conservation and wave energy flow under time reversal, we derive the symmetries in dissipation-free mode conversion in an inhomogeneous plasma. These are applied to high-temperature plasma mode conversions near the ion–ion hybrid and upper hybrid resonances.

The Ion Cyclotron, Lower Hybrid and Alfven Wave Heating Methods

This lecture covers the practical features and experimental results of the three heating methods. The emphasis is on ion cyclotron heating. First, we briefly come back to the main non-collisional heating mechanisms and to the particular features of the quasi linear coefficient in the ion cyclotron range of frequencies (ICRF). The specific case of the ion-ion hybrid resonance is treated, as well as the polarisation issue and minority heating scheme. The various ICRF scenarios are reviewed. The experimental applications of ion cyclotron resonance heating (ICRH) systems are outlined. Then, the lower hybrid and Alfvén wave heating and current drive experimental results are covered more briefly. Where applicable, the prospects for ITER are commented.

The Ion Cyclotron, Lower Hybrid and Alfven Wave Heating Methods

This lecture covers the practical features and experimental results of the three heating methods. The emphasis is on ion cyclotron heating. First, we briefly come back to the main non-collisional heating mechanisms and to the particular features of the quasilinear coefficient in the ion cyclotron range of frequencies (ICRF). The specific case of the ion-ion hybrid resonance is treated, as well as the polarisation issue and minority heating scheme. The various ICRF scenarios are reviewed. The experimental applications of ion cyclotron resonance heating (ICRH) systems are outlined. Then, the lower hybrid and Alfvén wave heating and current drive experimental results are covered more briefly. Where applicable, the prospects for ITER are commented.

Coupled full-wave and ray-tracing numerical treatment of mode conversion in a tokamak plasma

A new approach for the numerical description of tokamak plasma waves in the ion cyclotron range of frequencies is discussed. It implies coupling of the full-wave and ray-tracing codes and is capable of unified treatment of waves of completely different scale and behavior. The method is applied for simulations of the electron heating scenario, based on fast wave (FW)–ion Bernstein wave (IBW) mode conversion near the ion–ion hybrid resonance in Tore Supra [B. Saoutic et al., Phys. Rev. Lett. 76, 1647 (1996)]. The two-dimensional full-wave “ALCYON” code [D. J. Gambier and A. Samain, Nucl. Fus. 25, 283 (1985)] is used to describe the global FW field pattern in the plasma volume. A small-scale-waves filter, introduced into the code, artificially damps the mode-converted power, which is further prescribed to IBW rays. Remnant small-scale fields are extracted from the global pattern to provide information necessary for IBW rays to start. Three-dimensional evolution of IBW rays is simulated by the “RAYS” ray-tracing code [Yu. Petrov, Nucl. Fus. 34, 63 (1994)], being unrestricted by finite mesh size and finite Larmor radius effects.

One-dimensional full wave treatment of mode conversion process at the ion–ion hybrid resonance in a bounded tokamak plasma

A consistent picture of the mode conversion (MC) process at the ion–ion hybrid resonance in a bounded plasma of a tokamak is discussed, which clarifies the role of the global fast wave interference and cavity effects in the determination of the MC efficiency. This picture is supported by simulations with the kinetic code “VICE” [Fraboulet et al., “One-D full-wave description of plasma emission and absorption in the Ion Cyclotron Range of Frequency in tokamaks,” submitted to Phys. Plasmas]. The concept of the “global resonator,” formed by the R=n∥2 boundary cutoffs [Saoutic et al., Phys. Rev. Lett. 76, 1647 (1996)], is justified, as well as the importance of a proper tunneling factor choice ηcr=0.22 [Ram et al., Phys. Plasmas 3, 1976 (1996)]. The MC scheme behavior appears to be very sensitive to the MC layer position relative to the global wave field pattern. Optimal MC regimes are found to be attainable without requirement of a particular parallel wave number choice.

Toroidal mode conversion in the ICRF

Mode conversion is studied in the ion cyclotron range of frequencies (ICRF), taking into account the toroidal geometry relevant for tokamaks. The global wavefields obtained using the gyrokinetic toroidal PENN code illustrate how the fast wave propagates to the neighbourhood of the ion-ion hybrid resonance, where it is converted to a slow wave that deposits the wave energy through resonant Landau and cyclotron interactions with the particles. The power deposition profiles obtained are dramatically different from the toroidal resonance absorption, showing that Budden's fluid model is not a good approximation in the torus. Radially and poloidally localized wavefield structures characteristic of slow wave eigenmodes are predicted, which could be used in experiments to form transport barriers and to interact with fast particles.

Mode conversion of fast Alfvén waves at the ion–ion hybrid resonance

Substantial radio-frequency power in the ion-cyclotron range of frequencies can be effectively coupled to a tokamak plasma from poloidal current strap antennas at the plasma edge. If there exists an ion–ion hybrid resonance inside the plasma, then some of the power from the antenna, delivered into the plasma by fast Alfvén waves, can be mode converted to ion-Bernstein waves. In tokamak confinement fields the mode-converted ion-Bernstein waves can damp effectively and locally on electrons [A. K. Ram and A. Bers, Phys. Fluids B 3, 1059 (1991)]. The usual mode-conversion analysis that studies the propagation of fast Alfvén waves in the immediate vicinity of the ion–ion hybrid resonance is extended to include the propagation and reflection of the fast Alfvén waves on the high magnetic-field side of the ion–ion hybrid resonance. It is shown that there exist plasma conditions for which the entire fast Alfvén wave power incident on the ion–ion hybrid resonance can be converted to ion-Bernstein waves. In this extended analysis of the mode conversion process, the fast Alfvén waves can be envisioned as being coupled to an internal plasma resonator. This resonator extends from the low magnetic-field cutoff near the ion–ion hybrid resonance to the high magnetic-field cutoff. The condition for 100% mode conversion corresponds to a critical coupling of the fast Alfvén waves to this internal resonator. As an example, the appropriate plasma conditions for 100% mode conversion are determined for the Tokamak Fusion Test Reactor (TFTR) [R. Majeski et al., Proceedings of the 11th Topical Conference on RF Power in Plasmas, Palm Springs (American Institute of Physics, New York, 1995), Vol. 355, p. 63] experimental parameters.

Mode conversion of fast magnetosonic waves and minority ion heating in a longitudinally inhomogeneous magnetic field

Mode conversion process in ICRF (Ion Cyclotron Range of Frequencies) in a longitudinally inhomogeneous two-ion-species plasma is clarified in the HIEI tandem mirror experiments. Measurements of wave number parallel to the magnetic field reveal that the fast magnetosonic wave of low-field-side incidence converts into the slow ion-cyclotron wave near the ion–ion hybrid resonance. The propagation of the slow wave is detected between the ion–ion hybrid resonance and minority ion cyclotron resonance layers, which shows good agreement with the calculated dispersion relation based on one- and two-dimensional plasma models. Simultaneous minority ion heating is observed, and it is due to the presence of the slow wave that resonates with minority ions at the minority ion cyclotron resonance.

Interferometery measurement of line average electron density in alvand IIC Tokamak

ALVAND IIC is a small research Tokamak with a minor radius of 12.6 cm, and a major radius of 45.5 cm. The research program has been directed toward the generation of a low beta plasma for developing diagnostic systems and studying the effects of some operating parameters, e.g., filling pressure, gas purity, final equilibrium and plasma conditions. In addition, it is planned to study the application of radio frequency heating at two - ion hybrid and lower hybrid resonances - for controlling the profile of plasma current. The recent developed tool was a microwave interferometer system which serve for plasma density diagnostic. As density is one of the crucial parameters for fusion experiments this instrument is considered as the basic monitor for the average electron density in the plasma. For this reason a very flexible electronic device has been developed, the output of which can be used simultaneously for visual digital display, for analog representation on an oscilloscope and for 8 bit digital output for computer usage. 5 refs., 2 figs.

Observation of ion-cyclotron heating due to mode conversion of fast waves in a simple mirror

In this paper the observation of mode conversion of the m=−1 (right-rotating propagation) fast magnetosonic wave into the slow ion-cyclotron wave via the ion–ion hybrid resonance in a mirror magnetic field is presented. The left-circularly polarized component of the wave magnetic field strongly depends on the minority ion concentration in a helium–hydrogen plasma. The associated ion heating up to 250% of the initial value is in correlation with the enhancement of the left-circularly polarized component of the wave field, showing evidence of ion cyclotron heating due to the mode conversion. The two-dimensional calculation of the wave propagation and mode conversion is performed and compared with the experiment.

A parameter study of mode conversion at ion-ion hybrid resonances for ICRF-heating

By solving the wave equation for the radial electric field with constant poloidal electric field around the resonance layer of the fast Alfvén wave, various complex characteristics of mode conversion physics can be elucidated and analyzed for ion cyclotron heating of tokamaks. The validity of the Budden and tunnelling model [Ngan, Y. C. and Swanson, D. G., Phys. Fluids 20, 1920 (1977)] for the conversion studies is explored, and the conversion coefficient for the ion-ion hybrid resonance in the presence of cyclotron damping is found in closed form. The analytical results are compared with the numerical solution of the full wave equations expanded to second order in ion Larmor radius. It is found that the standard tunnelling solutions can be erroneous, not only in the case of strong damping, but also when the linearization of the plasma parameters around the resonance, peculiar to the tunnelling model, becomes inaccurate. The effects of the damping and cavity resonances on the conversion are separated in the derived analytical estimates, and the limits of the local theory of conversion are determined.

Absorption at the ion–ion hybrid resonance in the presence of incoherent density fluctuations

A numerical study is made of the effects caused by incoherent fluctuations in the minority density concentration on the absorption of fast Alfven waves at the ion–ion hybrid resonance. This work extends to the incoherent regime of a previous study by Romero and Morales [Phys. Fluids B 2, 2007 (1990)], which surveyed in detail the effects of single‐mode (coherent) fluctuations. The system is represented by a Budden equation that properly describes the resonance and cutoff structure arising from spatial variations of the equilibrium magnetic field. For wave incidence such that the cutoff is encountered before the resonance layer, the absorption coefficient increases monotonically as the fluctuation amplitude is increased. A specific case is presented in which the absorption changes from ∼0% to ∼70% for minority density fluctuations δn/n0∼60% that correspond to electron density variations of less than 5%. For wave incidence such that the resonance is encountered before the cutoff, the reflection coefficient ...

Effects of coherent density fluctuations on the ion–ion hybrid resonance

An analytic and numerical study is made of the effects caused by coherent density fluctuations, localized near the ion–ion hybrid resonance, on the propagation and absorption of fast Alfven waves. The system is represented by a Budden equation that incorporates static fluctuations in the ion density profiles. The unperturbed system contains a resonance at x=0 and a cutoff at x=d; the Alfven wave number at resonance is kA. Two cases are considered: fluctuations in the ion concentration ratio η and bulk density fluctuations. When the incident wave directly approaches the resonance, the fluctuation in the concentration ratio δη/η0 is less than 20%, and kAd 1, and concentration fluctuations 2%<δη/η0<5%, enhanced reflection leads to decreased absorption. ...

The dispersion relation for D(3He) ion-cyclotron resonance heating

The fourth-order dispersion relation for D(3He) obtained from a straightforward small k⊥ρD expansion does not properly reproduce the exact kinetic dispersion relation near ion–ion hybrid resonance. It is shown that, in general, whenever the majority is not resonant the expanded dispersion relation may break down. A method to obtain a correct approximate fourth-order dispersion relation has been developed.

Alfvén surface waves in a two-ion-species cylindrical plasma with finite edge density

Dispersion relations are obtained for Alfvén surface waves in a two-ion-species cylindrical plasma with finite edge density. A simple step density profile is used. The results are compared with those obtained in a plasma surrounded by a vacuum layer. For modes with positive poloidal mode number m the finite-density edge region introduces an ion-cyclotron resonance and a waveguide cutoff in the surface-wave dispersion relation at the cyclotron frequency of each ion species. For negative-m modes a new dispersion-relation branch is introduced at frequencies just below the ion-cyclotron frequency of each species. The origin of these effects is analysed in terms of the wave types that can propagate in the regions of constant density, and their interaction with the Alfvén and ion-ion hybrid resonances in these regions. This interaction is shown to be determined by the polarization of the wave fields. The relevance of the results to the Alfvén-wave and ion-cyclotron-resonance heating schemes is discussed. The possibility that the excitation of high-m surface waves contributes to the anomalously large fraction of power that is found to be deposited in the plasma edge during ion-cyclotron-resonance heating is considered.

Comments on ICRH current drive in JET

To study current drive via the mode-converted slow wave during ICRH the authors assess for which plasma compositions and wave numbers mode conversion from the magnetosonic wave to the slow wave can dominate. They have used a simple slab model to investigate the competition between mode conversion and minority cyclotron absorption for a deuterium plasma with H+ and 3He2+ minority species in JET. A 3He2+ minority should be more appropriate for mode conversion current drive than H+ because the 3He2+ concentration can be chosen near its optimum for the 'Budden absorption' without bringing the ion hybrid resonance and the cyclotron resonance so close that the minority absorption dominates. 3He2+ minority also allows operation at toroidal numbers which are characteristic of present JET antennae.

Wave propagation across ion cyclotron resonance harmonic layers

Wave propagation across ion cyclotron resonance layers is investigated by use of a boundary layer analysis for a perpendicularly stratified, weakly inhomogeneous plasma. Corresponding to the situation in many plasmas of interest, it is assumed that the wave frequency is much less than the ion plasma frequency, but that the ratio of ion plasma frequency to wave frequency times the ratio of ion thermal speed to the speed of light is small. Nontrivial effects of the cyclotron resonance appear in the boundary layer and modify the current density from the cold plasma limit. These corrections suggest the breakdown of the geometrical optics limit. Wave equations for the field valid within an arbitrary harmonic resonance layer are derived, as well as for the two ion hybrid resonance case. Analytical proofs of reciprocity relations are given for the general wave propagation problems.

Numerical modelling of the cold ion-ion hybrid resonance

A new way is discussed to handle numerically the ion-ion hybrid resonance appearing in the cold plasma model for plasma heating in the ion-cyclotron range of frequency (ICRF). It is shown that this singularity can be correctly treated without introducing artificial and unphysical damping outside the resonance domain. This feature is particularly important for computations in two dimensions. This note supplements and corrects a recently published conference contribution [Comput. Phys. Commun. 43 (1986) 125].

Surface waves in a two-ion-species magnetized plasma

The spectrum of waves in a two-ion-species plasma at frequencies up to the ion-ion hybrid resonance frequency is investigated. A cylindrical plasma column of uniform density and magnetic field, and surrounded by a vacuum, is firstly analysed, and the results are checked when plasma and magnetic field nonuniformities are allowed for. A new m=-1 mode is found to exist at frequencies just above the ion-ion hybrid resonance frequency. This mode has much in common with a previously reported m=-1 mode above the Alfven resonance frequency in that it can have surface wave properties and its dispersion curve merges into the ion-ion hybrid resonance at a critical value of the axial wavenumber. The mode survives as an ion-ion resonance damped wave in a nonuniform density plasma or magnitude field. The m=+1 wave dispersion relation is found to pass through the ion-ion hybrid resonance via a mode crossing, with connection to a hybrid global eigenmode below the hybrid resonance, and connection to a surface wave above the hybrid resonance.