Ion Sound Waves Research Articles

Ion heating, burnout of the high-frequency field, and ion sound generation under the development of a modulation instability of an intense Langmuir wave in a plasma

The development of one-dimensional parametric instabilities of intense long plasma waves is considered in terms of the so-called hybrid models, with electrons being treated as a fluid and ions being regarded as particles. The analysis is performed for both cases when the average plasma field energy is lower (Zakharov's hybrid model—ZHM) or greater (Silin's hybrid model—SHM) than the plasma thermal energy. The efficiency of energy transfer to ions and to ion perturbations under the development of the instability is considered for various values of electron-to-ion mass ratios. The energy of low-frequency oscillations (ion-sound waves) is found to be much lower than the final ion kinetic energy. We also discuss the influence of the changes in the damping rate of the high-frequency (HF) field on the instability development. The decrease of the absorption of the HF field inhibits the HF field burnout within plasma density cavities and gives rise to the broadening of the HF spectrum. At the same time, the ion velocity distribution tends to the normal distribution in both ZHM and SHM.

LANGMUIR WAVE DECAY IN INHOMOGENEOUS SOLAR WIND PLASMAS: SIMULATION RESULTS

Langmuir turbulence excited by electron flows in solar wind plasmas is studied on the basis of numerical simulations. In particular, nonlinear wave decay processes involving ion-sound (IS) waves are considered in order to understand their dependence on external long-wavelength plasma density fluctuations. In the presence of inhomogeneities, it is shown that the decay processes are localized in space and, due to the differences between the group velocities of Langmuir and IS waves, their duration is limited so that a full nonlinear saturation cannot be achieved. The reflection and the scattering of Langmuir wave packets on the ambient and randomly varying density fluctuations lead to crucial effects impacting the development of the IS wave spectrum. Notably, beatings between forward propagating Langmuir waves and reflected ones result in the parametric generation of waves of noticeable amplitudes and in the amplification of IS waves. These processes, repeated at different space locations, form a series of cascades of wave energy transfer, similar to those studied in the frame of weak turbulence theory. The dynamics of such a cascading mechanism and its influence on the acceleration of the most energetic part of the electron beam are studied. Finally, the role of the decay processes in the shaping of the profiles of the Langmuir wave packets is discussed, and the waveforms calculated are compared with those observed recently on board the spacecraft Solar TErrestrial RElations Observatory and WIND

Global Sound Mode in Plasma with Sloshing Ions

In recent experiments on Gas Dynamic Trap (GDT), as well as in earlier experiments on the GOL-3 device, a new and interesting class of oscillations was observed. Its mode structure and frequency resemble that of a sound wave trapped in the mirror cell as a resonator. Such modes can strongly interact with the bounce motion of ions and thus affect the axial confinement in mirror traps. The modes are probably similar to the global acoustic modes (GAMs) in tokamaks. However, there are significant difficulties in reconciling the existence of such modes with conventional theory of plasma waves. In both GOL-3 and GDT in relevant regimes the electron temperature is far below the theoretical limit for existence (let alone weak Landau damping) of ion-sound waves in homogeneous plasma. We explore different models of inhomogeneous anisotropic non-Maxwellian plasma of a mirror trap in search for possible explanations of the observed phenomena.

Ion sound instability driven by the ion flows

Ion sound instabilities driven by the ion flow in a system of a finite length are considered by analytical and numerical methods. The ion sound waves are modified by the presence of stationary ion flow resulting in negative and positive energy modes. The instability develops due to coupling of negative and positive energy modes mediated by reflections from the boundary. It is shown that the wave dispersion due to deviation from quasineutrality is crucial for the stability. In finite length system, the dispersion is characterized by the length of the system measured in units of the Debye length. The instability is studied analytically and the results are compared with direct, initial value numerical simulations.

A comparison of weak-turbulence and particle-in-cell simulations of weak electron-beam plasma interaction

Quasilinear theory has long been used to treat the problem of a weak electron beam interacting with plasma and generating Langmuir waves. Its extension to weak-turbulence theory treats resonant interactions of these Langmuir waves with other plasma wave modes, in particular, ion-sound waves. These are strongly damped in plasma of equal ion and electron temperatures, as sometimes seen in, for example, the solar corona and wind. Weak turbulence theory is derived in the weak damping limit, with a term describing ion-sound wave damping then added. In this paper, we use the EPOCH particle-in-cell code to numerically test weak turbulence theory for a range of electron-ion temperature ratios. We find that in the cold ion limit, the results agree well, but for increasing ion temperature the three-wave resonance becomes broadened in proportion to the ion-sound wave damping rate. Additionally, we establish lower limits on the number of simulation particles needed to accurately reproduce the electron and wave distributions in their saturated states and to reproduce their intermediate states and time evolution. These results should be taken into consideration in, for example, simulations of plasma wave generation in the solar corona of Type III solar radio bursts from the corona to the solar wind and in weak turbulence investigations of ion-acoustic lines in the ionosphere.

On the interaction between the ion cyclotron resonance heating and scrape-off layer turbulence via coherent waves

It was reported on the ASDEX-Upgrade tokamak and recently confirmed on the Tore Supra tokamak (Antar 2010 et al Phys. Rev. Lett. 105 165001, Antar 2012 Nucl. Fusion 52 103005) that ion cyclotron resonance heating (ICRH) reduces turbulence in the scrape-off layer (SOL) by strongly affecting the large intermittent structures. In this paper, and for the first time, we show that ICRH, with a frequency at 57 MHz, excites waves at frequencies about 1.7 MHz as a consequence of parametric decay instability. This is reflected in the power spectra of the ion saturation signals, measured by fixed Langmuir probes acquired at 200 MHz, as well as in the cross-correlation between two toroidally distanced probes and in the bicoherence spectra. The velocity and the wavenumber of this perturbation is determined indicating that they may be ion sound waves. Furthermore, it is shown that they are nonlinearly coupled to the turbulent fluctuations leading to the strong modification of the power spectrum and could provide explanations about the decrease in the level of turbulence in the SOL during ICRH. This aspect is reflected in the enhanced three-wave coupling between these waves and turbulence studied by applying the bispectral analysis. Turbulence appears thus to be affected when ICRH is applied by the intermediate of ion sound waves.

Ponderomotive transport of a variable-charge granule in a dusty plasma in the field of an intense ion-sound wave

The ponderomotive force acting on a variable-charge granule in a dusty plasma from an intense ion-sound wave is considered. Allowance for oscillations of the granule charge in the field of an ion-sound wave makes it possible to reveal new components of this force that are proportional to the wave vector of the field and the cube of its amplitude. These components do not vanish in the case of a uniform field and also lead to a directed transport of the dust plasma fraction.

Negative ion sound solitary waves revisited

AbstractSome years ago, a group including the present author and Padma Shukla showed that a suitable non-thermal electron distribution allows the formation of ion sound solitary waves with either positive or negative density perturbations, whereas with Maxwellian electrons only a positive density perturbation is possible. The present paper discusses the qualitative features of this distribution allowing the negative waves and shared with suitable two-temperature distributions.

Evidence for four- and three-wave interactions in solar type III radio emissions

Abstract. The high time resolution observations obtained by the STEREO/WAVES experiment show that in the source regions of solar type III radio bursts, Langmuir waves often occur as intense localized wave packets with short durations of only few ms. One of these wave packets shows that it is a three-dimensional field structure with WLneTe ~ 10−3, where WL is the peak energy density, and ne and Te are the electron density and temperature, respectively. For this wave packet, the conditions of the oscillating two-stream instability (OTSI) and supersonic collapse are satisfied within the error range of determination of main parameters. The density cavity, observed during this wave packet indicates that its depth, width and temporal coincidence are consistent with those of a caviton, generated by the ponderomotive force of the collapsing wave packet. The spectrum of each of the parallel and perpendicular components of the wave packet contains a primary peak at fpe, two secondary peaks at fpe ± fS and a low-frequency enhancement below fS, which, as indicated by the frequency and wave number resonance conditions, and the fast Fourier transform (FFT)-based tricoherence spectral peak at (fpe, fpe, fpe + fS, fpe − fS), are coupled to each other by the OTSI type of four-wave interaction (fpe is the local electron plasma frequency and fS is the frequency of ion sound waves). In addition to the primary peak at fpe, each of these spectra also contains a peak at 2fpe, which as indicated by the frequency and wave number resonance conditions, and the wavelet-based bicoherence spectral peak at (fpe, fpe), appears to correspond to the second harmonic electromagnetic waves generated as a result of coalescence of oppositely propagating sidebands excited by the OTSI. Thus, these observations for the first time provide combined evidence that (1) the OTSI and related strong turbulence processes play a significant role in the stabilization of the electron beam, (2) the coalescence of the oppositely propagating up- and down-shifted daughter Langmuir waves excited by the OTSI probably is the emission mechanism of the second harmonic radiation, and (3) the Langmuir collapse follows the route of OTSI in some of the type III radio bursts.

Exact evaluation of the rates of electrostatic decay and scattering off thermal ions for an unmagnetized Maxwellian plasma

Electrostatic decay of Langmuir waves into Langmuir and ion sound waves (L→L′+S) and scattering of Langmuir waves off thermal ions (L+i→L′+i′, also called “nonlinear Landau damping”) are important nonlinear weak-turbulence processes. The rates for these processes depend on the quadratic longitudinal response function α(2) (or, equivalently, the quadratic longitudinal susceptibility χ(2)), which describes the second-order response of a plasma to electrostatic wave fields. Previous calculations of these rates for an unmagnetized Maxwellian plasma have relied upon an approximate form for α(2) that is valid where two of the wave fields are fast (i.e., vϕ=ω/k≫Ve where ω is the angular frequency, k is the wavenumber, and Ve is the electron thermal speed) and one is slow (vϕ≪Ve). Recently, an exact expression was derived for α(2) that is valid for any phase speeds of the three waves in an unmagnetized Maxwellian plasma. Here, this exact α(2) is applied to the calculation of the three-dimensional rates for electrostatic decay and scattering off thermal ions, and the resulting exact rates are compared with the approximate rates. The calculations are performed using previously derived three-dimensional rates for electrostatic decay given in terms of a general α(2), and newly derived three-dimensional rates for scattering off thermal ions; the scattering rate is derived assuming a Maxwellian ion distribution, and both rates are derived assuming arc distributions for the wave spectra. For most space plasma conditions, the approximate rate is found to be accurate to better than 20%; however, for sufficiently low Langmuir phase speeds (vϕ/Ve≈3) appropriate to some spatial domains of the foreshock regions of planetary bow shocks and type II solar radio bursts, the use of the exact rate may be necessary for accurate calculations. The relative rates of electrostatic decay and scattering off thermal ions are calculated for a range of parameters using the exact expressions for the rates; electrostatic decay is found to have the larger growth rate over the whole range of parameters, consistent with previous approximate calculations.

Compressive and Rarefactive Solitons for Fast and Slow Ion Acoustic Waves in Multi-Ion Plasmas

The Kadomtsev–Petviashvili (KP) equation is derived for an electrostatic wave in unmagnetized multi-ion plasmas using the reductive perturbation method. It is found that two ion sound waves with fast and slow speeds can propagate in such a multi-ion plasma provided both ions are considered to be inertial and one of the ion component in two ion species plasma is taken to be warm as well. The potential hump (compressive) and dip (rarefactive) structures of the slow and fast ion acoustic waves are obtained for different combinations of multi-ion plasmas i.e., H+(warm)–O+(cold)–e, H+(warm)–H+(cold)–e, O+(cold)–H-(warm)–e, and H+(cold)–H-(warm)–e. It is found that, in the case of multi-ion H+(warm)–O+(cold)–e and H+(warm)–H+(cold)–e plasmas, the slow ion acoustic wave solitons form both potential hump (compressive) and dip (rarefactive) profiles depending on the temperature and concentration of the warm ion species, while the fast ion acoustic wave solitons only form the potential hump structures. However, in ...

Irregular modulation of non-linear Alfvén/Beltrami wave coupled with an ion-sound wave

A singularity of a system of differential equations may produce “intrinsic” solutions that are independent of initial or boundary conditions—such solutions represent “irregular behavior” uncontrolled by external conditions. In the recently formulated non-linear model of Alfvén/Beltrami waves [Commum Nonlinear Sci Numer Simulat 17 (2012) 2223], we find a singularity occurring at the resonance of the Alfvén velocity and sound velocity, from which pulses bifurcate irregularly. By assuming a stationary waveform, we obtain a sufficient number of constants of motion to reduce the system of coupled ordinary differential equations (ODEs) into a single separable ODE that is readily integrated. However, there is a singularity in the separable equation that breaks the Lipschitz continuity, allowing irregular solutions to bifurcate. Apart from the singularity, we obtain solitary wave solutions and oscillatory solutions depending on control parameters (constants of motion).

Electrostatic Decay in a Weakly Magnetized Plasma

The kinematics of the electrostatic (ES) decay of a Langmuir wave into a Langmuir wave and an ion sound wave are generalized to a weakly magnetized plasma. Unlike the unmagnetized case, ES decay in a magnetized plasma is always kinematically permitted and can produce daughter Langmuir waves with very small wave numbers, which we demonstrate by quasilinear simulations. The simulations further show that ES decay in magnetized plasmas is consistent with STEREO spacecraft observations of transversely polarized Langmuir waves in the solar wind.

A second-order semi-implicit [formula omitted] method for hybrid simulation

A second-order accurate semi-implicit Lorentz force ions, fluid electrons δf hybrid model has been developed using a “current closure” scheme. The model assumes quasi-neutrality and is fully electromagnetic. The implicit field solver improves numerical accuracy by separating the equilibrium terms in the presence of small perturbations. The equilibrium part of the generalized Ohm’s law is solved by direct matrix inversion along the direction of gradients for every Fourier mode in the other two directions, while the nonlinear part is solved iteratively. The simulation has been benchmarked on Alfvén waves, ion sound waves and whistler waves against analytical dispersion relation in a slab. In particular, the first-order and second-order schemes are compared by studying the numerical damping of whistler waves. The full evolution of the resistive tearing mode using the Harris sheet equilibrium is also investigated. The linear growth rate and mode structure are compared with the resistive MHD theory. Important tearing mode nonlinear phenomena such as the Rutherford regime and saturation are demonstrated. We also presented systematic study of Rutherford growth rates and saturation island width, which is consistent with previous MHD studies.

高压下LaBr3电子结构与光学性质的第一性原理

In some events, weak fast solar bursts (near the level of the quiet Sun) were observed in the background of numerous spikes in emission and absorption. In such a case, the background contains the noise signals of the receiver. In events on 2005 September 16 and 2002 April 14, the solar origin of fast bursts was confirmed by simultaneous recording of the bursts at several remote observatories. The noisy background pixels in emission and absorption can be excluded by subtracting a higher level of continuum when constructing the spectra. The wavelet spectrum, noisy profiles in different polarization channels and a spectrum with continuum level greater than zero demonstrates the noisy character of pixels with the lowest levels of emission and absorption. Thus, in each case, in order to judge the solar origin of all spikes, it is necessary to determine the level of continuum against the background of which the solar bursts are observed. Several models of microwave spikes are discussed. The electron cyclotron maser emission mechanism runs into serious problems with the interpretation of microwave millisecond spikes: the main obstacles are too high values of the magnetic field strength in the source (omega_(Pe) ≤ omega_(Be)). The probable mechanism is the interaction of plasma Langmuir waves with ion-sound waves (l + s t) in a source related to shock fronts in the reconnection region.

Concerning spikes in emission and absorption in the microwave range

In some events, weak fast solar bursts (near the level of the quiet Sun) were observed in the background of numerous spikes in emission and absorption. In such a case, the background contains the noise signals of the receiver. In events on 2005 September 16 and 2002 April 14, the solar origin of fast bursts was confirmed by simultaneous recording of the bursts at several remote observatories. The noisy background pixels in emission and absorption can be excluded by subtracting a higher level of continuum when constructing the spectra. The wavelet spectrum, noisy profiles in different polarization channels and a spectrum with continuum level greater than zero demonstrates the noisy character of pixels with the lowest levels of emission and absorption. Thus, in each case, in order to judge the solar origin of all spikes, it is necessary to determine the level of continuum against the background of which the solar bursts are observed. Several models of microwave spikes are discussed. The electron cyclotron maser emission mechanism runs into serious problems with the interpretation of microwave millisecond spikes: the main obstacles are too high values of the magnetic field strength in the source (ωPe ≤ ωBe). The probable mechanism is the interaction of plasma Langmuir waves with ion-sound waves (l + s → t) in a source related to shock fronts in the reconnection region.

On the destruction of ion-sound waves in plasma with strong space-time dispersion

On the destruction of ion-sound waves in plasma with strong space-time dispersion

ASYMMETRIC SOLAR WIND ELECTRON DISTRIBUTIONS

The present paper provides a possible explanation for the solar wind electron velocity distribution functions possessing asymmetric energetic tails. By numerically solving the electrostatic weak turbulence equations that involve nonlinear interactions among electrons, Langmuir waves, and ion-sound waves, it is shown that different ratios of ion-to-electron temperatures lead to the generation of varying degrees of asymmetric tails. The present finding may be applicable to observations in the solar wind near 1 AU and in other regions of the heliosphere and interplanetary space.

In situ detection of strong Langmuir turbulence processes in solar type III radio bursts

The high time resolution observations obtained by the WAVES experiment of the STEREO spacecraft in solar type III radio bursts show that Langmuir waves often occur as intense localized wave packets. These wave packets are characterized by short durations of only a few ms and peak intensities, which well exceed the supersonic modulational instability (MI) thresholds. These timescales and peak intensities satisfy the criterion of the solitons collapsed to spatial scales of a few hundred Debye lengths. The spectra of these wave packets consist of primary spectral peaks corresponding to beam‐resonant Langmuir waves, two or more sidebands corresponding to down‐shifted and up‐shifted daughter Langmuir waves, and low frequency enhancements below a few hundred Hz corresponding to daughter ion sound waves. The frequencies and wave numbers of these spectral components satisfy the resonance conditions of the modulational instability (MI). Moreover, the tricoherences, computed using trispectral analysis techniques show that these spectral components are coupled to each other with a high degree of coherency as expected of the MI type of four wave interactions. The high intensities, short scale lengths, sideband spectral structures and low frequency spectral enhancements and, high levels of tricoherences amongst the spectral components of these wave packets provide unambiguous evidence for the supersonic MI and related strong turbulence processes in type III radio bursts. The implication of these observations include: (1) the MI and related strong turbulence processes often occur in type III source regions, (2) the strong turbulence processes probably play very important roles in beam stabilization as well as conversion of Langmuir waves into escaping radiation at the fundamental and second harmonic of the electron plasma frequency,fpe, and (3) the Langmuir collapse probably follows the route of MI in type III radio bursts.

Exact evaluation of the quadratic longitudinal response function for an unmagnetized Maxwellian plasma

The quadratic longitudinal response function describes the second-order nonlinear response of a plasma to electrostatic wave fields. An explicit expression for this function in the weak-turbulence regime requires the evaluation of velocity-space integrals involving the velocity distribution function and various resonant denominators. Previous calculations of the quadratic longitudinal response function were performed by approximating the resonant denominators to facilitate the integration. Here, we evaluate these integrals exactly for a non-relativistic collisionless unmagnetized isotropic Maxwellian plasma in terms of generalized plasma dispersion functions, and correct certain aspects of expressions previously derived for these functions. We show that in the appropriate limits the exact expression reduces to the approximate form used for interactions between two fast waves and one slow wave, such as the electrostatic decay of Langmuir waves into Langmuir waves and ion sound waves, and the scattering of Langmuir waves off thermal ions.