Alfven Solitons Research Articles

Alfvén solitons and generalized Darboux transformation for a variable-coefficient derivative nonlinear Schrödinger equation in an inhomogeneous plasma

Abstract Plasmas are believed to be possibly the most abundant form of visible matter in the Universe. Investigation in this paper is given to a variable-coefficient derivative nonlinear Schrodinger equation describing the propagation of the nonlinear Alfven waves in an inhomogeneous plasma. Based on the existing Lax pair, with respect to the left polarized Alfven wave, the N -fold generalized Darboux transformation, rational one/two Alfven soliton solutions and mixed two Alfven soliton solutions are derived, where N = 1 , 2 , 3 … . For those Alfven solitons, we find that (1) the solitonic width cannot be affected by the dispersion coefficient h ( τ ) and the loss/gain coefficient f ( τ ) , where τ is the stretched space variable; the solitonic amplitude grows (or decays) in the exponential rate exp [ − ∫ f ( τ ) d τ ] ; the solitonic amplitude cannot be affected by h ( τ ) ; the solitonic velocity and trajectory are related to h ( τ ) , while they cannot be affected by f ( τ ) ; (2) the rational two Alfven solitons experience no phase shift after the interaction; (3) the modulus square of mixed two Alfven solitons can be decomposed into two single Alfven solitons with the ∫ h ( τ ) d τ -dependent phase shifts; (4) the collapse of the rational one Alfven soliton is displayed.

Solitary dispersive Alfven wave in a plasma with hot electrons, cold positrons and ions

The dispersion relation and the nonlinear behaviour of dispersive Alfven waves (DAWs) in a plasma, which is composed by hot electrons, cold positrons and ions, are studied from the multi-component fluid theory. It can be indicated from the linear dispersion relation that the coupling of positron acoustic waves with shear Alfven waves results from the effect of the finite ion gyroradius. In our mode, the pressure and the inertia of the positron acoustic wave are, respectively, provided by the hot electrons and the cold positrons, which are different from the ones in a plasma consisting of two-group positrons with different temperatures. Furthermore, the existence and properties of DAW solitons are analysed from the Sagdeev pseudopotential equation, which indicates the existence of super-Alfvenic or sub-Alfvenic solitary DAWs, as well as the amplitude and width of DAW solitons depend on the positron concentration and the electron temperature. When the effects of cold positrons can’t be neglected, there may coexist the compressive and rarefactive DAW solitons. When the concentration of positron is negligibly small, the properties of DAW solitons in our model are similar to the ones of kinetic Alfven wave solitons in a plasma composed by hot electrons and cold ions.

Shear Alfvén Waves in a Magnetized Electron–Positron Plasma

A theoretical investigation of high-frequency shear Alfven waves is made in a magnetized relativistic rotating electron–positron (e–p) plasma. The derivative nonlinear Schrodinger equation (DNSE) is derived by employing the reductive perturbation technique. A stationary solitary solution of DNSE is derived, which is used to analyze the basic properties (amplitude, width, etc.) of shear e–p Alfven (SEPA) solitons. Different intrinsic plasma parameters (namely, positrons thermal energy to electrons thermal energy ratio and relativistic effects, etc.) are seen to influence the basic properties of SEPA waves significantly. It is found that the SEPAs have new features with high time and small length scales. The phase speed of the waves is seen to increase with the relativistic parameter while it decreases with the increase of positron-to-electron (p–e) thermal energy ratio. It is also observed that both the soliton’s amplitude and width increase with the increase of p–e thermal energy ratio, which are independent of rotational frequency. Our findings are useful to understand e–p plasma in the rotational astrophysical object.

Nonlinear Compressional Alfvén Waves in a Fully Relativistic Electron–Positron Plasma

A theoretical investigation has been carried out to study the nonlinear propagation of high-frequency electromagnetic (EM) waves in a magnetized relativistic rotating electron–positron plasma. The Korteweg-de Vries (K-dV) equation is derived by employing the reductive perturbation technique. The steady-state solution of K-dV equation is used to analyze the basic properties of small amplitude high-frequency compressional electron–positron Alfven (CEPA) solitons. It is observed that opposite polarity electron–positron plasma medium under consideration supports the CEPA solitons having new features with time (fast) and length (small) scales. It is also found that both the amplitude and width of the solitons increase with the increase of positron thermal energy to electron thermal energy ratio which are independent of rotational frequency. The findings of this investigation may be used in understanding the nonlinear EM waves phenomena in space, rotating astrophysical plasmas, and laboratory plasmas.

Existence of the kinetic Alfvén solitons in a plasma with non-extensive electrons including complete ion nonlinearity

The existence of the shear Alfven solitons in a moderate β plasma with non-extensive electrons including complete ion nonlinearity is investigated. The characteristic of super-Alfvenic dip and hump type solitons, and the sub-Alfvenic dip solitons depends on the electrons non-extensive parameters q. The effects of the q on the kinetic Alfven solitons can be explained from the effective electron temperature and the electron distribution in a potential field modified by the non-extensive distribution.

Shear and compressional dust Alfvén solitons in a magnetized plasma medium of opposite polarity dust

Shear and compressional dust Alfven solitons propagating in a medium of opposite polarity magnetized dust fluids have been theoretically studied by using the reductive perturbation method. The derivative nonlinear Shrodinger (DNLS) and Korteweg-de Vries (K-dV) equations, and their stationary solitonic solutions have been derived to identify the basic properties of shear and compressional dust Alfven solitons. It is found that the opposite polarity dust medium under consideration supports the shear and compressional dust Alfven solitons having new features with new (slow) time and (large) length scales. The basic features (amplitude and width) of the shear dust Alfven solitons are found to be significantly different from those of the compressional ones. The importance of our results in understanding the nonlinear (localized) electromagnetic wave phenomena in space environments and laboratory devices is briefly discussed.

MICROWAVE BURSTS WITH FINE STRUCTURES IN THE DECAY PHASE OF A SOLAR FLARE

This paper presents the microwave bursts with fine structures (FSs) at 1.10-1.34 GHz in the decay phase of a solar flare observed by the Chinese Solar Broadband Radio Spectrometer in Huairou, which show a peak-to-peak correlation with 25-50 keV hard X-ray (HXR) bursts observed by RHESSI. In the microwave spectra, we have identified stripe-like bursts such as lace bursts, fiber structures, zebra patterns (ZPs), and quasi-periodic pulsations. We also have detected short narrowband bursts such as dots, type III, and spikes. The lace bursts had rarely been reported, but in this event they are observed to occur frequently in the decay phase of the flare. The similarity between 25 and 50 keV HXR light curve and microwave time profiles at 1.10-1.34 GHz suggests that these microwave FSs are related to the properties of electron acceleration. The electron velocity inferred from the frequency drift rates in short narrowband bursts is in the range of 0.13c-0.53c and the corresponding energy is about 10-85 keV, which is close to the energy of HXR-emitting electrons. From the Alfven soliton model of fiber structures, the double plasma resonance model of ZPs, and the Bernstein model of the lace bursts, we derived a similar magnetic fieldmore » strength in the range of 60-70 G. Additionally, the physical conditions of the source regions such as height, width, and velocity are estimated.« less

Alfven soliton and multisoliton dynamics perturbed by nonlinear Landau damping

The evolution of weakly dispersive nonlinear Alfven waves propagating either parallel or oblique to the ambient magnetic field is investigated through the derivative nonlinear Schrödinger equation (DNLS) perturbed by nonlinear Landau damping. The dynamics is analyzed with the aid of a numeric algorithm based on the inverse scattering transform (IST) and an adiabatic model that takes advantages of the perturbed DNLS invariants. Both techniques are applied to five types of DNLS soliton and multisoliton solutions: (i) the parallel Alfven soliton, (ii) the bright and dark one-parameter oblique, (iii) the breather two-parameter oblique, (iv) two parallel Alfven solitons, and (v) the combination of a dark and a bright oblique solitons. For the parallel solitons, the adiabatic model describes correctly the dynamics and it also recovers the well-known result given by the perturbed IST. Due to the radiation emission and the formation of dark solitons, the behavior of oblique solitons is more complicated and multisoliton solutions are required in the adiabatic model. The analysis shows that parallel solitons develop into the normal regime, whereas the oblique waves leads to the formation of dark solitons and breathers with a wavepacket form.

Magnetic hole formation from the perspective of inverse scattering theory

[1] The dynamics of oblique, weakly dispersive nonlinear Alfven waves in the presence of weak resistive damping are investigated numerically through an extension of the derivative nonlinear Schrodinger (DNLS) equation. It is observed numerically that the nonlinear dynamics are organized around the dynamics and allowed interactions of the underlying DNLS soliton families. There are three types of oblique Alfven solitons: the compressive two-parameter soliton and one-parameter bright soliton along with the rarefactive one-parameter dark soliton. The damping of either of these compressive solitons is accompanied by the formation of one or more dark solitons. The implication of these processes is that any initial wave profile containing solitons in its Inverse Scattering Transformation representation, in the presence of weak resistive damping, will result in a leading train of dark solitons. These dark solitons have been identified with magnetic holes, and the results described above are discussed in the context of magnetic hole observations and theory.

Fiber Fine Structures Superposed on the Solar Continuum Emission Near 3 GHz

On April 21, 2002, a broadband solar radio burst was observed at about 01:00 – 03:00 UT with the digital spectrometers of National Astronomical Observatories of China (NAOC). Also many fiber bursts superposed on the continuum bursts were detected in the frequency range of 2.6 – 3.8 GHz during the time interval. After data processing, some parameters of the fibers such as frequency drift rate, duration, bandwidth, and relative bandwidth were determined. The mean value of the frequency drift was in the range of 42.3 – 87.4 MHz s−1 (negative). A theoretical interpretation for the fibers was presented based upon a model of the velocity of Alfven solitons. In this model, the source of the fiber emission was considered as the ducting of the solitons within the magnetic-mirror loop. Then the magnetic field strength of the fiber source was estimated to be about 130 ≤ B0 ≤ 270 G. Also a comparison of the magnetic field estimation was made with another model of whistler group velocity.

Alfven soliton created by Reynolds' stress of the lower-hybrid waves

The modulational interaction of very short wavelength lower-hybrid waves with slow density modulations associated with inertial Alfven mode is investigated. Nonlinear equations governing this interaction are derived and soliton-like solutions of these equations are discussed in the context of auroral ionosphere.

High resolution studies of intermediatedrift bursts

Abstract We report high resolution observations of the Intermediate Drift (IMD) bursts in decimetric band ( ν = 950 – 2650 MHz). With a time resolution of 20 – 50 ms and a frequency resolution of 4 – 10 MHz, we are able to estimate the characteristics of IMD bursts such as the bandwidth and duration of the emission. Frequency drift rate and its dependence on the frequency are derived for individual IMD structures. All IMD bursts analyzed show negative drift rate. The values are of the order of −28 – −274 MHz s −1 . The drift rates normalized by the mean frequency are ranged between −0.20 s −1 and −0.02 s −1 . Both the frequency drift rate and its frequency dependence provide important clues to the emission mechanisms of IMD. A comparison and a critique of the existing models based on the plasma and the maser emissions with modulation by Alfven solitons as well as the whistler wave model are presented.

Condition of Alfven Gauss wave-packet evolvement to solitons and criterion of Alfven wave modulation instability

By analyzing the integral constant C1 of Alfven solitons, the condition of Alfven Gaussian wave-packets evolvement to solitary waves is put forward as C1≤0. This hypothesis is also confirmed by numerical simulation results. Furthermore,simulation results show that the number of evolving solitons does not depend only on integral constant C0 or C1. The conclusions in Refs. ［1］ and ［2］ result from the shorter evolving time. Comparing with other papers, we find that C0≤0 can be used as a criterion of Alfven wave modulation instability.

On capture and acceleration of heavy ions (α-particle) in high-speed solar wind

The α-particles and other heavy ions, as well as a few protons are observed to be faster than the main part of protons by about the local Alfven speed in the high-speed solar wind. It is suggested that when the velocity of the solar wind is equal to the local Alfven velocity, another low-frequency kinetic Alfven wave will be excitated, and trap all the α-particles and a few protons, so these ions have a local Alfven velocity faster than the other parts of the solar wind. The undamping kinetic Alfven waves change into low-frequency Alfven solitons in the solar wind. This model can explain the observation and give the conditions of wave excitated and ions trapped.

Alfven Soliton and Intermediate Shock in the Solar Wind

We show in this paper that intermediate shocks are formed from kinetic Alfven waves through wave form continuous steepening. From the action of nonlinear interaction and dispersion Alfven solitons are formed and then evolve into shocks. We calculated the traveling stationary structures directly from nonlinear autonomous equations which we had derived. These traveling stationary structures correspond to intermediate shock, switch-on shock or Alfven solitary waves. Another kind of rare discontinuity was discovered in the calculation from the rarefying solitary waves. The solitary wave series remain on the front of the shocks because of no strong dissipation appears in the equation. When we added some anomalous dissipation terms to the equations, intermediate shocks with increased in entropy appeared.

One-dimensional solitary kinetic Alfvén waves in low-beta plasma

A two-dimensional homogeneous magnetohydrodynamic (MHD) model is applied to investigate one-dimensional solitary kinetic Alfvén waves (SKAWs) and their degenerated ion-acoustic solitons in a low-beta plasma, in which electron pressure and electron inertial effects are all taken into account. In contrast to the results of the one-dimensional SKAWs model obtained by Hasegawa and Mima [Phys. Rev. Lett. 37, 690 (1976)], Shukla et al. [J. Plasma Phys. 28, 125 (1982)], and Wu et al. [Phys. Plasmas 3, 2879 (1996)], both density hump and dip Alfvénic solitons are found to exist in the kinetic limit (2me/mi≪β≪1) and in the inertial limit (β≪2me/mi) (β=8πnTe/B02 denotes the ratio of the plasma thermal pressure to the magnetic pressure), while in the transition region (β−2me/mi), both super-Alfvénic and sub-Alfvénic solitons with a density hump or a dip are found to exist. Due to the finite-β effect, the Alfvénic solitons may degenerate into super-acoustic density hump solitons over all the range of plasma β. This result provides a one-dimensional SKAWs model to account for the observations from the Freja satellite, in which not only SKAWs accompanied by dip density solitons, but also SKAWs accompanied by hump density solitons, are found in the Earth’s ionospheric altitude.

The dissipative evolution of an Alfven soliton

A model equation for non-linear Alfven waves, allowing for dispersion and dissipation in magnetohydrodynamics, is derived. The evolution of an Alfven soliton is examined.

Effects of plasma rotation on alfv�n solitons in pulsar magnetospheres

Nonlinear Alfven wave in a hot rotating and strongly magnetized electron-positron plasma is considered. Using relativistic two fluid equations, the dispersion relation for Alfven wave in the rotating plasma is obtained. Large amplitude Alfven solitons are found to exist in the rotating pulsar plasma. Rotational effects on solitons are discussed.

Nonlinear Alfven waves in inhomogeneous plasmas

Nonlinear Alfvén waves, in inhomogeneous plasmas, are shown to be governed by the MDNLS (Modified Derivative Nonlinear Schrödinger) equation. The inhomogeneity leads to acceleration (deceleration) of the Alfvén solitons depending upon plasma β (kinetic pressure/magnetic pressure) and on density gradients vis‐a‐vis direction of wave propagation. Potential applications, of the model, to space and astrophysical plasmas are pointed out.

Radiation from accelerated Alfven solitons in inhomogeneous plasmas

In a weakly inhomogeneous plasma, the large-amplitude Alfven waves propagating parallel to the ambient magnetic field are shown to evolve into accelerated Alfven solitons. Nonlinear interaction of the accelerated Alfven solitons with the Langmuir waves results in the emission of coherent radiations. Analytical expression for the power radiated per unit solid angle from a soliton is derived for two inhomogeneity profiles, namely the linear profile and the parabolic profile. For the case of uniform plasmas, the emission occurs via a decay-type process or resonant modes. In the presence of inhomogeneity, nonresonant modes provide a new channel for the emission of radiation. The power radiated per unit solid angle is computed for the parameters relevant to Comet Halley's plasma environment. For the nonresonant modes it is found to be several orders of magnitude higher than that for the case of resonant modes.