Nonlinear frequency shift and self-modulation of the quasi- monochromatic whistlers in the inhomogeneous plasma (magnetosphere)

The nonlinear frequency shift arising from the interaction of the quasimono- chromatic whistler-mode wave with resonant particles in an inhomogeneous plasma is derived. The modulational instability caused by this shift is investigated. The results are applied to the propagation of long-duration VLF whistler-mode signals along the magnetic field in the magnetosphere. It is shown that the modulational instability of these waves in the equatorial region leads to pulsations very similar to those observed experimentally     

Low-frequency electric field fluctuations excited by ring current protons

Energetic protons haying ring type distributions are shown to generate low-frequency electrostatic waves, propagating nearly transverse to the geomagnetic field lines, in the ring current region by exciting Mode 1 arid Mode 2 nonresonant instabilities and a resonant instability. Mode 1 nonresonant instability has frequencies around ~4 Hz with transverse wavelengths of ~(8–80) km, and it is likely to occur in the region L = (7–8). Mode 2 nonresonant instability can generate frequencies ~(850–1450) Hz with transverse wavelengths ~(2–20) km. The typical frequencies and transverse wavelengths associated with the resonant instability are (950–1250) Hz and (30–65) km. Both the Mode 2 nonresonant instability and the resonant instability can occur in the ring current region with L = (4–6). The low-frequency modes driven by energetic protons could attain maximum saturation electric field amplitude varying from 0.8 mV/m to 70 mV/m. It is suggested that the turbulence produced by the low-frequency modes may cause pitch angle scattering of ring current protons in the region outside the plasmapause resulting in the ring current decay.     

Alfvén turbulence in collisionless plasmas

The evolution of Alfvén turbulence due to three-wave interactions is discussed using kinetic theory for a collisionless, thermal plasma. In particular, we consider decay of Alfvén waves through three-wave coupling with an ion sound mode in the random-phase approximation. Two decay processes are of particular interest: an Alfvén wave decays into a backward propagating Alfvén wave and a forward propagating ion sound wave, and an Alfvén wave decays into a backward propagating fast magnetoacoustic wave and a forward ion sound wave. The former was widely discussed in the literature, particularly under the coherent wave assumption. The latter was not well explored and is discussed here.     

The sideband instability of electrostatic waves in an inhomogeneous medium

The work deals with the resonant particle excitation of two electrostatic waves with closely spaced wave numbers, when there is an inhomogeneity present in the form of a spatially dependent wave number. Resonant particle behaviour in such a field is investigated and the resonant particle current is computed for a variety of cases. If the inhomogeneity is such that resonant particles see the wave numbers of the waves increasing, then it turns out that the wave of greatest wave number is preferentially amplified. If the gradient is reversed it is the opposite wave which grows. Thus when a narrow band electrostatic wave is subject to beam excitation, only one of the sideband waves is unstable.The theory is applied to the closely analogous problem of sideband formation in the case of triggering of VLF emissions by magnetospheric whistler pulses, and seems to account for much of the observed behaviour.     

Nonlinear Interaction of 3D Kinetic Alfvén Waves and Ion Acoustic Waves in Solar Wind Plasmas

We have investigated the nonlinear interaction between a 3D kinetic Alfvén wave (KAW) and an ion acoustic wave (IAW) in solar wind plasmas. A set of dimensionless equations was developed that describes the pump KAW perturbed by a low-frequency ion acoustic wave. The dependence of the growth rate of the modulational instability on the perturbation wave number was studied. We simulated numerically the dynamical equation of KAW with a pseudo-spectral method, taking ponderomotive nonlinearity into account. The 3D KAW itself propagates in the form of a vortex beam in a magnetised plasma, which manifests the presence of orbital angular momentum of the wave eigenmodes. We discuss the evolution of these vortex structures. Our results reveal that the Kolmogorov scaling is followed by a steeper scaling of power spectra, which is consistent with the solar wind observations by the Cluster spacecraft. We discuss the relevance of our investigation for solar wind plasmas.     

Nonlinear stability of an infinite cylinder in the presence of a uniform axial magnetic field

The effect of a uniform axial magenetic field on the nonlinear instability of a self-gravitating infinite cylinder is examined. Using the method of multiple scales, it is found that while the nonlinear (modulational) instability cannot be completely suppressed, the presence of a magnetic field does increase the range of stable wave numbers. The evolution of the amplitude is governed by a non-linear Schrödinger equation which gives the criterion for modulational instability.Department of Chemical Engineering and Technology.Department of Mathematics.     

Modulational instability of fast magnetosonic waves in a solar plasma

Transverse amplitude modulations of fast magnetosonic waves propagating perpendicular to the background magnetic field are shown to be unstable on a time scale τ ～- λ_∥/V _aφ, if the wave amplitude φ exceeds a critical value, φ _c = C _s/V _a. The slow modes generated by the modulational instability under gravity can propagate along the magnetic field with the characteristic velocity, V _ph = g/2k _∥ V _aφ. The applications of this modulational instability and slow-mode generation mechanism to a solar plasma are discussed.     

太阳黑子半影纤维尺度的一个解释

在黑子半影电流的磁场中存在扰动不稳定模式,本文认为黑子半影纤维是由这种不稳定扰动发展而形成的,利用短波近似,分别在黑子半径方向及围绕黑子方向上求解非绝热慢波色散方程。由不稳定条件可得到(1)纤维的长度与宽度的数值;(2)纤维模式在长度方向上是静止的,在宽度方向上几乎是不动的;(3)半影纤维是黑子在重力场中的磁流特征之一;(4)半影纤维的出现,表示着黑子扭转磁场的存在。     

Emission of solar radio spikes by beam-driven cyclotron resonance

The generation of bright solar radio spikes by the beam-driven cyclotron resonance maser mechanism (the resonant interaction of an electron beam with a circularly polarized wave in a background plasma under the action of a guide magnetic field) is studied. Nonlinear effects such as radiation damping and gyrophase bunching on electron energy and momentum are responsible for the enhanced direct energy conversion between the beam and the coherent wave. Factors such as beam energy spread and pitch angle distribution are analyzed. The intense maser radiation is carried at the source by the circularly polarized wave propagating along the magnetic field. Due to the magnetic field curvature, the outgoing maser radiation converts into extraordinary and ordinary modes. The extraordinary mode suffers from plasma absorption at the second harmonic layer, whereas the ordinary mode is likely to get through.     

The Effect of a Twisted Magnetic Field on the Nature of Kink MHD Waves

We consider a pressureless plasma in a thin magnetic-flux tube with a twisted magnetic field. We study the effect of twisted magnetic field on the nature of propagating kink waves. To do this, the restoring forces of oscillations in the linear ideal magnetohydrodynamics (MHD) were obtained. In the presence of a twisted magnetic field, the ratio of the magnetic-tension force to the gradient of the magnetic pressure increases for the mode with negative azimuthal wave number, but it decreases for the mode with positive azimuthal wave number. For the kink mode with positive azimuthal mode number, the ratio of the forces is more affected by the twisted magnetic field in dense loops. For the kink mode with negative azimuthal mode number, the perturbed magnetic pressure is negligible under some conditions. The magnetic twist increases (diminishes) the damping of the kink waves with positive (negative) azimuthal mode number due to resonant absorption. Our conclusion is that introducing a twisted magnetic field breaks the symmetry between the nature of the kink waves with positive and negative azimuthal wave number, and the wave can be a purely Alfvénic wave in the entire loop.     

On the Envelope Soliton – Like Fine Structure in Solar Radio Emission

Several quasi-periodic, milliseconds fine structures in the metric wave band occurring during the evolution of solar type IV bursts have been observed by Yunnan Radio Telescope, Trieste Radio Telescope and IZMIRAN dynamic spectrometer. The envelope of these quasi-period modulational fine structures have a soliton pattern, so it is called an envelope soliton-like fine structure. A modulational instability model of electromagnetic wave has been adopted here. It is found that the longitudinal modulational instability can occur only in the solar coronal region of low magnetic field and high temperature, as well as high density plasma, which will give rise to the envelope soliton-like fine structures in the solar metric and decimetric radio emission. The propagation effects of envelope soliton-like fine structure from corona to the observer on the Earth have been briefly considered. This revised version was published online in July 2006 with corrections to the Cover Date.     

Resonant interactions between cometary ions and low frequency electromagnetic waves

We explore the conditions for resonance between cometary pick-up ions and parallel propagating electromagnetic waves. A model ring—beam distribution for the pick-up H₂O⁺ ions is adopted which allows a direct comparison of the source of free energy for growth from either the beam or the gyrating ring in the limit near marginal stability. Under average solar wind conditions in the inner solar system, the gyrating ring provides the dominant contribution to wave growth. The presence of a field-aligned beam is only important to allow resonance with R-mode waves which occur in two distinct frequency bands either well above or below the pick-up ion gyrofrequency. The most unstable mode is the low frequency R-mode or fast MHD wave, though higher frequency whistlers or low frequency L-mode waves may also be excited by the same source of free energy. The nature of the unstable waves is strongly influenced by the inclination of the interplanetary field. For 3° the rate of the low frequency R-mode growth is dramatically reduced and resonant L-mode waves should experience net ion beam damping. Conversely for 75°, the ion beam velocity will be insufficient to allow resonant R-mode instability; L-mode waves should therefore predominate. The low frequency fast MHD mode should experience the most rapid amplification for intermediate inclination; 30° 75°. In the frame of the solar wind such waves must propagate along the field in the direction upstream towards the Sun with a phase speed lower than the beaming velocity of the pick-up ions. The waves are consequently blown back away from the Sun and would thus be detected with a left-hand polarization by an observer in the cometary frame. We consider this the most likely mechanism to account for the interior MHD waves observed by satellites over an extended spatial region surrounding comets Giacobini-Zinner and Halley.     

Modulational instability of a magneto-hydrodynamic jet

The effect of a magnetic field on the nonlinear capillary instability of a fluid jet is examined using the method of multiple scales. It is a well-known result that a sufficiently strong magnetic field can, in the limit of zero viscosity and resistivity, completely suppress the linear capillary instability. It turns out that while the nonlinear (modulational) instability cannot be completely suppressed, the presence of a magnetic field does greatly increase the range of stable wave numbers.     

Nonlinear Alfvén wave modulation in the solar atmosphere

Nonlinear interaction of finite-amplitude Alfvén waves with non-resonant finite-frequency electrostatic and stationary electromagnetic perturbations is considered. This interaction is governed by a pair of coupled equations consisting of nonlinear Schrödinger equation for the Alfvén wave envelope and an equation for the plasma slow response that is driven by the ponderomotive force of the Alfvén wave packets. The modulational instability of a constant amplitude Alfvén pump is investigated and some new results for the growth rate of the instability are presented. It is found that a possible stationary state of the modulated Alfvén wave packets could lead to localized structures. The relevance of our investigation to the solar atmosphere is discussed.     

Drift instabilities associated with the particles in ring current and inner edge of plasma sheet

Electromagnetic waves propagating transverse to the magnetic field, containing inhomogenous and loss cone plasma, may become unstable due to the excitation of resonant proton, resonant electron and drift cyclotron instabilities. Resonant proton instability gets excited in inhomogenous plasma, irrespective of the presence of temperature anisotropy, loss cone or temperature gradient. However, the growth rate of this instability is much smaller than the other two instabilities. The maximum growth rates of resonant electron instability are enhanced with the increase of loss cone index, gradients in transverse temperature and magnetic field, and with the decrease of temperature anisotropy and gradients in density and parallel temperature. The drift cyclotron instability exists in a bounded range of wave numbers and its growth rate increases with the increase of electron temperature, density and magnetic field gradient, and with the decrease of proton temperature and temperature anisotropy. In the region of ring current for beyond plasmapause the resonant proton and resonant electron instabilities have the characterstic frequencies around 0.1Ω_p and growth rates ~10^?6Ω_p and 10^?3Ω_p, respectively. In the ring current region the drift cyclotron instability is not excited whereas in the plasma sheet region the frequency and growth rate of this instability are around Ω_p and 10^?2Ω_p, respectively. These instabilities can accelerate the ring current particles along the magnetic field lines and dump them into the auroral region.     

Generation of 1–30 Hz waves near the plasmapause by resonant electron-instability

A generation mechanism for 1–30 Hz waves of the second category, observed near the plasmapause by Taylor and Lyons (1976), is suggested in terms of a resonant electron instability. The instability arises because of the resonant interaction between the ring current electrons outside the plasmapause and the ordinary mode drift waves. The instability can generate waves in the frequency range from 0.45 to 35.0 Hz in the region between L = 4.5 and 5.5. The instability can also explain satisfactorily the other properties such as no changes in the proton distributions, the direction of the wave magnetic field and the localization of the region of wave activity, associated with these waves.     

The Influence of Guiding Field on Low-frequency Electromagnetic Instabilities in Collisionless Current Sheets

This work investigates the effect of guiding field on low-frequency electromagnetic instabilities in collisionless current sheets using the dispersion relation obtained in the collisionless and compressible magnetohydrodynamic model. The results in the following three cases show that the guiding field can strongly affect the 3-dimensional propagating disturbed waves. (1) On the middle plane of the current sheet (z = 0), if there is no guiding field, then no instability is observed. But if there a guiding field, then instability can take place. (2) Near the middle plane of the current sheet (z = 0.2), the current sheet becomes unstable. With increasing the intensity of the guiding field, the instability grows obviously. The wave mode may be whistler or low-hybrid wave. (3) Near the edge of the current sheet (z = 0.8), the guiding field exhibits no evident effect and the unstable wave mode is a quasi-parallel whistler wave.     

Nonlinear model to study filamentation instability of circularly polarized dispersive Alfvén waves in solar wind plasmas

This paper examines the small-scale solar wind turbulence driven in view of the Alfvén waves subjected to ponderomotive nonlinearity. Filamentation instability is known to take place for the case of dispersive Alfvén wave (DAW) propagating parallel to the ambient magnetic field. The ponderomotive force associated with DAW is responsible for wave localization and these webs of filaments become more intense and irregular as one proceeds along the spatial domain. The ponderomotive force associated with pump changes with pump parameters giving rise to different evolution patterns. This paper studies in detail the nonlinear evolution of filamentation instability introduced by dispersive Alfven waves (DAWs) which becomes dispersive on account of the finite frequency of DAW i.e., pump frequency is comparable to the ion cyclotron frequency. We have explicitly obtained the perturbation dynamics and then examined the impact of pump magnitude on the driven magnetic turbulence using numerical simulation. The results show steepening at small scales with increasing pump amplitude. The compressibility associated with acoustic fluctuations may explain the variation in spectral scaling of solar wind turbulence as observed by Alexandrova et al. (Astrophys. J. 674:1157, 2008).     

Resonant character of the hall instability in protoplanetary disks

We consider nonaxisymmetric magnetosonic oscillations of a radially stratified, weakly ionized protoplanetary disk with a vertical magnetic field. The combined effect of the Hall electric field and the density and magnetic field inhomogeneities present in the disk has been previously predicted to lead to an instability of its small azimuthal perturbations. We revise the previous results and take into account the effect of inhomogeneous ionization of the protoplanetary material related to the inhomogeneity of the disk medium. We show that the instability criterion is governed by three parameters: the magnetic field and ionization fraction gradients and the plasma β. We have found that at high values of β typical of protoplanetary disks, the instability does not manifest itself if the gradients are directed oppositely. In the case of codirectional gradients, the interaction of magnetosonic fluctuations with inhomogeneities of a fixed size is resonant in character, giving rise to an instability in a narrow range of wave numbers.