Ion Hybrid Waves Research Articles

Nonlinear theory of the modulational instability at the ion–ion hybrid frequency and collapse of ion–ion hybrid waves in two-ion plasmas

We study the dynamics of two-dimensional (2D) nonlinear ion–ion hybrid waves propagating perpendicular to an external magnetic field in plasmas with two ion species. We derive nonlinear equations for the envelope of electrostatic potential at the ion–ion hybrid frequency to describe the interaction of ion–ion hybrid waves with low-frequency acoustic-type disturbances. The resulting nonlinear equations also take into account the contribution of the second harmonics of the ion–ion hybrid frequency. A nonlinear dispersion relation is obtained, and, for a number of particular cases, modulational instability growth rates are found. By neglecting the contribution of second harmonics, the phenomenon of the collapse of ion–ion hybrid waves is predicted. It is shown that taking into account the interaction with the second harmonic results in the existence of a stable two-dimensional soliton.

Compressional Alfvén and ion–ion hybrid waves in tokamak plasmas with two ion species

Compressional Alfvén and ion–ion hybrid waves excited by energetic beam ions are studied in plasmas with two ion species. In our experiment, a hydrogen-deuterium (H-D) plasma is used to produce instabilities similar to those likely to be present in the burning deuterium-tritium plasmas of future tokamaks. Modes are suppressed in the deuterium cyclotron frequency range with increasing hydrogen gas puffing. In plasmas with H/D concentrations of 2.57 or higher, short-lived modes with small and predominantly negative toroidal mode numbers are observed at frequencies ω/ωβD0 ≈ 2.25, where ωβD0 = ωβD(R0) is the on-axis deuterium cyclotron frequency. These are the highest mode frequencies yet detected in the ion cyclotron range in a spherical tokamak. Modeling of the transparency regions and plasma resonances using the cold plasma dispersion relation explains the observed features. Mode conversion at ion–ion hybrid resonances and subsequent kinetic damping is believed to be responsible for mode suppression. The high frequency modes are present due to excitation by wave-particle resonances within the transparency region for high hydrogen concentrations. The absence of other wave-particle resonances explains significant features of our experiment. This technique has possible applications in plasma heating, current drive and real-time diagnosis of relative ion concentration in the plasma core.

On the envelope soliton below the H+ gyrofrequency in low auroral region

Two envelope soliton events below the H+ gyrofrequency with localized density depletion were discovered in low auroral region (∼ 1760 km)by Freja satellite. These events were correlated in time with the observations of the ratio of oxygen ion density to hydrogen ion density sharp increase and the electrons energization. These envelope solitons have a characteristic frequency at ∼ 180–190 Hz, which are obviously different from the electron-ion lower hybrid wave frequency and the helium ion gyrofrequency in low auroral plasma, but it is close to the resonancefrequency of hydrogen ion-oxygen ion hybrid wave. A modulational instability model of an ion-ion hybrid wave has been discussed here. It is found that the envelope soliton below the H+ gyrofrequency in low auroral region may be generated by this modulational instability on condition that the local oxygen ion density is larger than the local hydrogen ion density.

A ray-based algorithm for multi-dimensional linear conversion

A numerical algorithm is proposed for connecting the incoming and outgoing wave fields in studies of linear conversion. This is the first such ray-based algorithm for wave conversion in multiple spatial dimensions. It is demonstrated that, aside from the overall phase of the coupling, one can directly evaluate all quantities needed for the connection coefficients from the ray geometry. The ray dynamics is generated using the determinant of the dispersion matrix as the Hamiltonian. Using information available while following an incoming ray, the algorithm automatically detects that the ray has entered a conversion region, evaluates the transmission and conversion coefficients, and launches the transmitted ray. The algorithm does not require any prior knowledge of the geometry of the conversion region. The algorithm is illustrated using a two-dimensional toroidal model with resonant conversion from a magnetosonic to an ion-hybrid wave.

Selective Acceleration in Impulsive Solar Flares

A plasma acceleration mechanism is proposed to explain the dramaticenhancement in the ratio of 3He/4He, (enhancement factor102-103) observed in solar 3He-rich flares. Considering thatcoronal plasma is mainly composed of hydrogen and helium ions, thehydrogen ion-helium ion hybrid waves and quasi-perpendicular waves canbe excited by energetic electron beam during the impulsive solar flares.The frequencies of these waves are close to the 3He+ + iongyrofrequency, but far from the 4He+ + ion gyrofrequency.Most of these waves are selectively absorbed by 3He ions. Thesepreheated 3He ions can be successively stochastic accelerated byAlfvén turbulence, when their velocities are larger than the localAlfvén velocity. It makes the ratio of 3He/4He dramatically enhancedand the acceleration energy spectrum of 3He ions forms a power-lawdistribution during the impulsive solar flares.

Envelope Soliton in Multi-ion Plasma and Ion-Ion Hybrid WaveExcited by Energetic Electron Beam

Another envelope soliton event below the H+ gyrofrequency andlocalized density depletion has been discovered in the low auroral region (~1760 km)by the Freja satellite. This envelope soliton has acharacteristic frequency at ~190 Hz, which is alsoclose to the resonance frequency of hydrogen ion-oxygen ionhybrid wave. This event is correlated in time with the observations ofthe sharp increase of the ratio of oxygen ion density to hydrogen andwith the electronenergization along the magnetic field. A theoretical model on theion-ion hybrid wave excited by an energetic electron beam has also beenpresented. It is found that the ion-ion hybrid wave is mainlyexcited by the Cherenkov instability in the auroral region.

Ion Cyclotron Emission from JET D-T Plasmas

Ion cyclotron emission (ICE) excited by collective instability of fusion $\ensuremath{\alpha}$ particles has been observed during deuterium-tritium experiments with radio-frequency heating and neutral beam injection (NBI) in the Joint European Torus. A model based on classical $\ensuremath{\alpha}$-particle confinement is broadly consistent with this data. ICE spectra from discharges with high-power NBI also show evidence of ion hybrid wave excitation by beam ions, relevant to $\ensuremath{\alpha}$ channeling.

The dissipative Budden problem: Effect of converted-wave damping on primary-wave reflection

The Budden equation represents a double conversion, whereby a primary wave first converts to a localized secondary wave, which then converts to a reflected primary wave. We analyze this process in phase space, to include secondary-wave damping between the two conversions, which reduces the reflection coefficient. The results are then applied to gyroresonant damping of the (secondary) ion-hybrid wave by fusion alpha-particles, suggesting a diagnostic test.

Enhanced coupling of the fast wave to electrons through mode conversion to the ion hybrid wave

An analysis of ion cyclotron resonance heating in a plasma containing two ion species is given. Particular emphasis is placed on the important case of comparable concentrations of the two species. The properties of ion-Bernstein waves in such a plasma are discussed. A summary of the cutoff–resonance (Budden) and cutoff–resonance–cutoff (triplet) configurations is given and an analytic expression obtained for the Budden transmission coefficient (relevant also to the triplet case), which is valid for any concentration ratio of the two-ion species. A formula for the damping coefficient of the ion hybrid wave is obtained and a ray tracing code is used to illustrate the absorption of this mode by electrons close to the two-ion hybrid resonance. The reduced, second-order fast wave equation is solved numerically, illustrating the transition from strong electron heating through mode conversion at the two-ion hybrid resonance to direct electron damping of the fast wave in a high beta plasma.

Instability of the ion hybrid wave in the presence of superthermal alpha-particles

The stability of the ion hybrid wave in a plasma containing two thermal ion species present in comparable proportions and a low density population of superthermal alpha-particles is analyzed. A simple, model distribution function consisting of a ring distribution in the perpendicular velocity and a Maxwellian in the parallel velocity is used for the superthermal alpha-particles. This distribution function is relevant to the core plasma of a tokamak in the immediate post-birth phase before the alpha-particles have had time to relax collisionally and is therefore of interest to the alpha-channelling question. It has also been used to interpret ion cyclotron emission from fusion products in the edge plasma of large tokamaks. An approximate dispersion relation is derived which allows the conditions for instability to be explored and an analytic expression for the growth rate to be obtained. It is found that the ion hybrid wave can be unstable for v⊥0/cA≪1 where v⊥0 is the alpha-particle ring speed and cA is Alfvén speed for a plasma with two ion species. The instability conditions obtained from the analytic approximation are used to guide the solution of the exact dispersion relation. Numerical solutions for the specific cases of deuterium–tritium core and edge plasmas in the Tokamak Fusion Test Reactor (TFTR) [K. M. Young et al., Plasma Phys. Controlled Fusion 26, 11 (1984)] are given.

Alfvén ion–ion hybrid wave heating in the Phaedrus-T tokamak

In the Phaedrus-T tokamak [R. A. Breun et al., Fusion Technol. 19, 1327 (1991)], Alfvén waves are indirectly driven by a fast wave antenna array. Small fractions of minority ions are shown to have a large effect on the Alfvén spectrum, as measured at the edge. An ion–ion hybrid Alfvén mode has been identified by measuring dispersion properties. Landau damping is predicted to be large and spatially localized. These Alfvénic waves are experimentally shown to generate correlated electron heating and changes in density near the core of the tokamak plasma. Fast wave antenna fields can mode convert at a hybrid Alfvén resonance and provide a promising route to spatially localized tokamak heating and current drive, even for low effective ionic charge Zeff≊1.3–2.

Discrete spectrum of Alfvén ion–ion hybrid waves

In the Phaedrus-T tokamak [R. Majeski et al., Phys Fluids B 5, 2506 (1993)], Alfvén waves are indirectly driven by a fast wave antenna array. Small fractions of minority ions can couple Alfvén and ion–ion hybrid waves and have a large effect on the wave numbers accessible for a given launched frequency. A discrete spectrum and toroidal damping for these modes has been identified by measuring dispersion properties at the edge. Landau damping is predicted to be large and spatially localized and to be responsible for the experimentally observed electron heating (T. Intrator et al., ‘‘Alfvén ion–ion hybrid wave heating in the Phaedrus-T tokamak,’’ to appear in Phys. Plasmas) and current drive near the core of the tokamak plasmas.

A simulation study of multiple ion wave generation downstream of lOW Mach number quasiperpendicular shocks

The behavior of minor ions just downstream of a low Mach number quasiperpendicular shock is investigated both theoretically and by computer simulations. Because all ions see the same cross shock electric field their deceleration depends on their charge to mass ratio, yielding different downstream velocities. It is shown that these differences in velocity can lead to coherent wave structures in the downstream region of quasiperpendicular shocks with a narrow transition layer. These waves are shown to be multi ion hybrid waves in contrast to mirror waves and ion cyclotron waves. Under favorable conditions these waves should be observable both at interplanetary shocks and at planetary bowshocks.

Subcritical multiple‐ion shocks

Low Mach number collisionless shocks in a multiple‐ion plasma are investigated theoretically using multiple‐ion Rankine‐Hugoniot relations (MIRHR) and hybrid simulations. The derived MIRHR permit tractable solutions for perpendicular shocks. It is found that starting from a synchronous flow of a mixture of different ion species, light ions and heavy ions jump to different downstream velocities. Although the resulting differential velocities between the species are unstable, they produce coherent gyration of the ion species around each other. This gyration excites standing ion hybrid waves in the downstream region. Both of these effects (the jump of different ion species to different downstream velocities and the excitation of the ion hybrid waves) are confirmed by hybrid simulations.

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.

Instability of ion–ion hybrid waves in current-carrying collisional plasmas with two ion species

The stability of electrostatic waves propagating at large angles with respect to the background magnetic field is studied in collisional, fully ionized plasmas with two types of ion species and carrying a field-aligned current. By considering plasmas with ma/mb ≪ Nb/Na ≪ mb/ma where m and N denote mass and density respectively and subscripts a and b refer to the two ion species, a complicated dispersion relation is reduced to two simple equations for the determination of the real and imaginary parts of the frequency. It is found that, under appropriate conditions, an instability occurs at frequencies slightly above but very close to the ion–ion hybrid frequency. The growth rate scales directly as the electron–ion collisional frequency.

Stimulated backscattering of electromagnetic waves from ion–ion hybrid waves in a magnetized plasma

In a high-density magnetized plasma composed of two ion species of different charge-to-mass ratios, electrostatic waves propagating across the magnetic field exhibit a resonance at the Buchsbaum or ion-ion hybrid frequency, in addition to the resonances at the upper and lower hybrid frequencies. In this paper, the possibility of stimulated scattering of electromagnetic waves incident normal to the magnetic field from electrostatic waves at the ion-ion hybrid frequency is investigated. Based on the cold-plasma equations, it is found that such a process is theoretically possible. Formulas for the threshold power and growth rate are obtained, which show that the threshold power is much greater, and the growth rate much less, than those of stimulated scattering from upper and lower hybrid waves.

Propagation and absorption of ion hybrid waves in a weakly inhomogeneous plasma layer. II

Propagation and absorption of ion hybrid waves in a weakly inhomogeneous plasma layer. II

Propagation and absorption of ion hybrid waves in a weakly inhomogeneous plasma layer—I

Propagation and absorption of ion hybrid waves in a weakly inhomogeneous plasma layer—I

Propagation and absorption of ion hybrid waves in a weakly inhomogeneous plasma laser. I

The problem of electromagnetic wave propagation and absorption in weakly inhomogeneous plasma layer (in the geometrical optics approximation) is solved. The plasma density increases in the direction perpendicular to the magnetic field. The excitation of the waves occurs in the low density region. It is shown that deceleration of the wave along the magnetic field is necessary for its propagation into the plasma layer. As the wave penetrates the plasma layer its phase velocity reduces and at a certain plasma density the electromagnetic wave transforms into a plasma wave. The conditions for such a transformation of electromagnetic wave into plasma wave have been calculated in the hydrodynamic approximation.