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In a recent Comment, Chang et al. [Phys. Plasmas 29, 114703 (2022)] have studied the electron dynamics for an electron accelerating in a tightly focused Gaussian laser pulse with the higher order correction terms, and it is found that the initial position of the electron is the reason why the electron is pushed to the − z axis at the end. In this Reply, the electron dynamics and its nonlinear Thomson backscattering in a tightly focused Gaussian laser pulse with the higher order correction terms are presented, and it is found that the result is consistent with the lowest order approximation case in our paper [Hong et al., Phys. Plasmas 29, 043102 (2022)]. Meanwhile, it is also found that when the longitudinal deceleration effect of the ponderomotive force on the electron introduced by the falling part of the tightly focused laser pulse is greater than the longitudinal acceleration effect of the rising part, the electron that is initially stationary will be slightly pushed to the − z axis at the end, which can well explain the “return” phenomenon of the electron in the longitudinal direction both in our paper and in the Comment.

The electron dynamics and the Thomson backscattering spectra for an electron accelerating in a tightly focused Gaussian laser pulse are first investigated in detail. It is found that for a tightly focused Gaussian laser pulse, the ponderomotive force introduced due to the non-uniform intensity distribution of the laser pulse has the tendency to push out the electron from the laser pulse, which leads to the trajectory symmetry-breaking of the electron and then the generation of the even-order harmonics at the same time. Further, for the tightly focused Gaussian laser pulse, changes in several laser parameters, such as the increase of the laser peak amplitude, lengthening of the pulse width, and decrease of the beam waist, lead earlier to the relative ejected position of the electron to the laser pulse, which causes the more obvious trajectory symmetry-breaking of the electron, and then the more intensive peak intensity of the even-order harmonics. It is different from the well-known results of the plane waves and the Gaussian laser pulse with uniform transverse intensity distribution and provides a possible way for the generation of the even-order harmonics in nonlinear Thomson backscattering.

We translate three-dimensional magnetohydrodynamic equations describing the bounded plasma into a one-dimensional case and obtain an equivalent damping force that resulted from both the bounded geometry and the viscosity of the plasma by averaging all the physical quantities on the cross section, which is perpendicular to the wave propagation direction. A damping solitary wave propagating in a viscous bounded plasma is also verified by the particle-in-cell simulation method. The results in the present paper may be useful in the study of charged beam and particle acceleration, etc. Moreover, we can devise an experiment to obtain the viscosity coefficient of the plasma by measuring the ratio of two amplitudes at two different points.

By using the equation of the state of P = α d + β d T d, we studied a shock wave propagation in a strongly coupled complex plasma. A Korteweg-de Vries–Burgers equation is obtained to describe a shock wave in strongly coupled complex plasma. Dependence of the shock wave speed on the piston velocity and the plasma parameters such as the screening parameter of the strongly coupled complex plasma are given analytically for a weak shock wave. It is in good agreement with previous results. It shows in the present paper that there are density oscillations in the postshock region which is similar to that found in the previous works. Dependence of the length between two first peaks of the density oscillation on the piston velocity and the plasma parameter are also given analytically which is also in agreement qualitatively with previous results.

The combined effect of the cylindrical boundary and the adiabatic variation in dust charges on the spatiotemporal evolution of the overlapping soliton in a dusty plasma is studied in detail. We derive the mathematical expression of the overlapping soliton and investigate the effect of dust charging and the influence of its adiabatic variation on the evolution process of the soliton structure. Numerical results indicate that the basic properties of the merged pulse are partially similar to the recent experimental results reported for the interaction of planar solitons in strongly coupled dusty plasmas by Harvey et al., Phys. Rev. E 81, 057401 (2010) and Sharma et al. Phys. Rev. E 89, 013110 (2014). Moreover, it is found that the soliton amplitude and the occurrence time of its peak value increase with the increase in Rn and RT, and the increasing rate of the peak amplitude decreases with the increase in Rn and increases with the increase in RT. As time t increases, the overlapping soliton moves to the inside-traveling direction (i.e., r → 0); before reaching the peak amplitude, the merged pulse gradually increases its amplitude and decreases its width and traveling velocity; after reaching the peak amplitude, the soliton gradually decreases its amplitude and increases its width and velocity. It is also noted that when dust charge variation is considered, solitons with bigger values of Rn (or RT) experience longer phase delays. Comparatively speaking, Rn has a more remarkable effect on the physical properties of the overlapping soliton.

The properties of a high energy short pulse electron beam in a magnetic mirror field are studied numerically by the Particle-in-Cell method. The complex nature of processes studied, and also the need for the calculation of the positions, velocities, and trajectories of billions of particles, required the use of a scalable parallel algorithm. The use of modern supercomputers has allowed us to calculate the plasma dynamics, to determine the electron beam in the magnetic mirror field. Mathematical modeling of non-neutral plasma dynamics at the trap is carried out. The axially integrated radial density profiles, electric field distribution, and phase space distribution of velocity are measured. The axial and radial oscillations of a confined non-neutral plasma are also observed.

One-dimensional (1-D) particle-in-cell simulation is used to study the propagation of dark envelop solitons described by the nonlinear Schrodinger equation (NLSE) in electron-ion plasmas. The rational solution of the NLSE is presented, which is proposed as an effective tool for studying the dark envelope soliton in plasma. It is demonstrated by our numerical simulation that there is dark envelope soliton in electron-ion plasmas. The numerical results are in good agreements with the analytical ones from the NLSE which is obtained from the reductive perturbation method. The limitation of the amplitude of dark envelop solitons in plasma is noticed.

Several well-known nonlinear waves in the rational solutions of the nonlinear Schrodinger equation are studied in two-component plasmas consisting of ions fluid and nonextensive electrons, such as Kuznetsov–Ma breather (K-M), bright soliton, rogue wave (RW), Akhmediev breather (AB) and dark soliton, and so on. In this paper, we have investigated the characteristics of K-M, AB, and RW's propagation in plasma with nonextensive electron distribution, and the dependence of amplitude and width for ion acoustic rogue waves in this system. It is found that K-M' triplet is appearance-disappearance-appearance-disappearance. AB solitons only appear once and RW is a single wave that appears from nowhere and then disappears. It is also noted that the wave number and nonextensive parameter of electrons have a significant influence on the maximum envelope amplitude, but, the influence of the width was not significant. At the same time, the effects of the small parameter, which represent the nonlinear strength, on the a...

A Zakharov–Kuznetsov (ZK) equation, a modified ZK equation and a coupled ZK equation for small but finite amplitude dust acoustic waves in a magnetized two-ion-temperature dusty plasma with dust size distribution have been obtained in this paper. It seems that the soliton velocity for a dusty plasma with power law dust size distribution is larger than that of monosized dusty plasmas. The solitary waves with opposite polarity particles are investigated as well. It is found that rarefactive and compressive solitary waves exist in this system which depend on different conditions. On the other hand, the solitary wave is unstable at certain regions when the wave numbers of the transverse perturbations satisfies the conditions of 0

Two-dimensional hexagonal crystal is investigated in this paper. The dispersion relations for both compressional and transverse waves in different directions are studied as well. The analytical results are in agreement with the experimental ones reported previously. The small amplitude but finite long wavelength nonlinear waves propagating in the hexagonal crystal are also investigated. This investigation indicates that the solitary waves propagating in the directions of either n or m are stable.

A reasonable normalization for a dusty plasma with many different species of dust grains is adopted. By applying a reductive perturbation technique to the equations governing a dusty plasma with N different species of dust grains, a nonlinear Schrodinger equation (NSLE) is derived that governs the modulation of dust-acoustic waves. The effect of dust size and charge distribution on the modulational instability of these waves is studied. If there are positively charged dust grains, which is a possibility suggested by experimental results, the envelope soliton solutions to the NLSE may be different from the ones associated with a dusty plasma containing mono-sized dust grains. The instability properties may also be different. In the former case the instability region depends on the percentage of electrons residing on the dust grains. In particular, if the number of electrons residing on the dust grains is small enough, the envelope waves are unstable.

The higher order transverse perturbations for modulated wave packets in a dusty plasma are investigated. A Davey–Stewartson equation is obtained for this system. The instability for small amplitude linear transverse perturbations are investigated.

Damping dust acoustic waves described by the Korteweg-de Vries-type (KdV-type) equation and the nonlinear Schrodinger equation-type (quasi-NLSE) have been studied by the particle-in-cell (PIC) simulation method. The KdV-type equation and the quasi-NLSE with dust-neutral collision are analytically obtained by the reductive perturbation method. The PIC simulation methods for dust acoustic waves with damping force are shown. The PIC simulation results are compared with the analytical one. The relationship of the damping coefficient with the collision frequency is obtained. It is found that amplitudes of KdV-type solitary waves and quasienvelope solitary waves with damping force decrease exponentially.

For dust acoustic waves in unmagnetized plasma comprising cold dust grains and both isothermal electrons and ions, small but finite amplitude nonlinear waves are governed by the Korteweg–de Vries equation. The weakly transverse long wavelength perturbations for nonlinear dust acoustic waves are investigated in this paper. It has been shown that the governing equation for this process is the Kadomtsev–Petviashvili equation. It suggests that the transverse perturbations for the nonlinear acoustic solitary waves in a dusty plasma are stable.

The structural and magnetic characteristics of Ho2Co17−xSix (x=0, 0.5, 1.0, 1.5, 2.0, 2.5, and 3.0) compounds have been investigated by means of x-ray diffraction and magnetic measurements. Powder x-ray diffractograms show that all samples are single phase and have the hexagonal Th2Ni17-type or the rhombohedral Th2Zn17-type structure. The substitution of Si for Co leads to a monotonous decrease in unit cell volume v and Curie temperature TC. The compensation points are observed for the samples with x=2.5 and 3.0, and the compensation temperatures shift to higher temperatures with increasing Si content. The intersublattice-molecular-field coefficient, nHo–Co, has been determined on the basis of magnetization curves at the compensation temperature. It has been found that the Si substitution for Co has little influence on Ho–Co exchange interaction. The magnetic phase diagram has been determined from the temperature dependence of magnetization and the XRD patterns of magnetically oriented powder samples. The...

A comparative study on magnetic and transport properties has been performed for B-site substituted perovskites La0.67Sr0.33Mn0.90B0.10O3 (B=Ga, Ni, and Fe). The doped samples show a notable decrease of the Curie Temperature, from 365 K of the undoped sample to 290 K (Ga), 292 K (Ni), and 265 K (Fe). Furthermore, the metal–semiconductor transition peaks in the doped samples shift to lower temperature, from above 300 K (undoped) to 212 K (Ga), 237 K (Ni), and 195 K (Fe). This considerable differences in magnetic and transport properties between doped and undoped samples and the diversity among the doped samples can be explained by the destruction of the partial double-exchange interactions and the exchange couplings between Mn and doped ions.

An investigation of the structure and the magnetic anisotropy of R2Co15Al2 (R=Y, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, and Tm) compounds has been performed by means of x-ray diffraction and magnetization measurements. X-ray diffraction shows the prepared compounds to be single phase, having the hexagonal Th2Ni17-type structure for R=Y, Ho, Er, and Tm and the rhombohedral Th2Zn17-type structure for R=Ce, Pr, Nd, Gd, Tb, and Dy. Except for the Ce compound, the unit-cell volumes of R2Co15Al2 compounds decrease in accordance with the lanthanide contraction. Substitution of Al for Co in R2Co17 leads to a decrease of the saturation magnetization at 1.5 K and Curie temperature. The exchange-coupling constants JCo–Co and JR–Co have been calculated by using the method based on magnetic ordering temperature. It is found that the JR–Co has a small dependence on the R elements and is almost not affected by the Al substitution. The Ce compound is found to exhibit an anomalous lattice parameter and magnetic characteristi...

The structure and magnetic properties of Pr2(Fe1−xCox)17−yGay compounds with 0⩽x⩽1 and 0⩽y⩽3 have been investigated using x-ray diffraction (XRD) and magnetization measurements. XRD patterns demonstrate that all samples were single phase with the rhombohedral Th2Zn17-type structure, except for Pr2Fe16.5Ga0.5 with some impurity phases. The replacement of (Fe, Co) by Ga results in an approximately linear increase in the unit cell volume, and decrease in the Curie temperature and saturation magnetization. The substitution of Co for Fe leads to a nonlinear variation in the unit cell volume, the Curie temperature and the saturation magnetization. The magnetic anisotropy phase diagrams of Pr2(Fe1−xCox)16.5Ga0.5 (0⩽x⩽1) and Pr2(Fe0.4Co0.6)17−yGay (0⩽y⩽3) compounds have been determined from the temperature dependence of magnetization and the XRD patterns of magnetically oriented powder samples. Most of the samples exhibit easy plane anisotropy. A small range exists in the magnetic anisotropy phase diagrams of Pr2...

X-ray diffraction (XRD) and magnetization measurements were performed to investigate the effect of Ga substitution for Co on the structural and magnetic properties of Gd2Co17−xGax compounds (x=0, 1, 2, 3, 4, 5, 6, 7, and 8). Crystal-structure studies indicate that all samples are single phase with the rhombohedral Th2Zn17-type structure except for the samples with x=7 and 8, which contain a small amount of Co. The Ga substitution for Co in Gd2Co17 compounds leads to a monotonic increase in the unit cell volume and an approximately linear decrease in the saturation magnetization. The Curie temperature TC is found to decrease monotonically from 1210 K for x=0 to 30 K for x=8. The compensation points are observed for the Gd2Co17−xGax samples with x=5 and 6. The value of the compensation temperature, determined from the temperature dependence of the magnetization measured in a magnetic field of 1000 Oe, is 120 and 152 K for x=5 and 6, respectively. It is noteworthy that the substitution of Ga for Co in the Gd...

The nonlinear propagations of dust ion-acoustic solitary waves in a collisionless four-component unmagnetized dusty plasma system containing nonextensive electrons, inertial negative ions, Maxwellian positive ions, and negatively charged static dust grains have been investigated by the particle-in-cell method. By comparing the simulation results with those obtained from the traditional reductive perturbation method, it is observed that the rarefactive KdV solitons propagate stably at a low amplitude, and when the amplitude is increased, the prime wave form evolves and then gradually breaks into several small amplitude solitary waves near the tail of soliton structure. The compressive KdV solitons propagate unstably and oscillation arises near the tail of soliton structure. The finite amplitude rarefactive and compressive Gardner solitons seem to propagate stably.

The paper work relates to Nesterenko’s problem to further study the solitary wave when the strong external force acts on the granular chain. We also study the problem under the long-wavelength approximation and find that such kind of solitary wave in system with the initial prestress can be described by the Korteweg-de Vries (KdV) equation. It is found that the results of analytical and numerical are in an excellent agreement. Furthermore, we study the scattering of the KdV solitary wave in different granular materials both in theoretical and numerical methods. It is found that the numbers and the amplitudes of both the reflected and the transmitted waves depend not only on the amplitude of the incident solitary wave but also on the variations of both sides of the discontinuity such as the mass, Young’s modulus or radius of the grains.

Stress-free and two-way thermoelastic shape memory, with 1.2% strain and 6 K temperature hysteresis, has been found in single crystalline Ni52Mn24Ga24. The deformation can be enhanced more than three times, up to 4.0% shrinkage with a bias field 1.2 T applied along the measurement direction, or changed to 1.5% expansion by the 1.2 T applied perpendicular to the measurement direction. For achieving a large deformation, the magnetic field exhibits a more evident contribution than an external stress on this material. These characteristics can be attributed to the low level of internal stress and the preferential orientation of the martensitic variants.

The magnetic and transport properties of Fe doped charge ordering La0.5Ca0.5MnO3 have been studied. With the increase of the Fe ion, the ground state of the sample changes from a charge ordering state (x=0) to a spin glass state (x=0.10). The sample with x=0.04 displays a middle state, while a larger magnetoresistance of 109 at 5 K and a decrease of the critical field of charge ordering melting were found. These differences can be explained by the antiferromagnetic exchange coupling between Fe and Mn ions, the destruction of the Mn-O plane and the competition between ferromagnetic and antiferromagnetic clusters.

Samples of (Pr1−xCex)6Fe13Al (x=0.1, 0.2, 0.3, 0.4, 0.5, and 0.6) were prepared by arc melting and annealed for two weeks at 973 K. The x-ray diffraction patterns show that all the samples crystallize with the Nd6Fe13Si-type structure. The unit-cell volume increases first and then decreases as the Ce content increases. The Curie temperature and the spontaneous magnetization decrease almost linearly with increasing Ce concentration, supporting the existence of a mixed valence of Ce3+ and Ce4+. The series is ferromagnetic at high temperature; however, the peak at low temperature of the M–T curve most likely corresponds to spin-glass behavior.

Large magnetic-field-induced strain (MFIS) of −2700 ppm has been obtained from the Heusler alloy Ni52Mn23Ga25 at 300 K. The temperature for structure transformation was confirmed by three types of magnetic measurements. A burst of MFIS up to 5400 ppm could be induced by rotating a steady field of 1 T. In the martensitic phase, the material have a high saturated magnetization of 66 Am2/kg and a high anisotropy of 0.8 T. The variant reorientation mainly occurred in the region of 0.2–0.8 T. The large MFIS is sensitive to temperature, suggesting that it can only be induced when martensite and parent phase are coexisted.

A giant magnetic-field-induced strain (MFIS) of −3100 ppm has been obtained in Heusler alloy Ni52Mn22.2Ga25.8 single crystal in the [001] direction at a temperature from 23 to 31 °C. This MFIS reaches saturation in an applied field about 6 kOe, and exhibits the same amplitude with an opposite sign while the field is perpendicular to the samples. According to a previous model, this MFIS associates with the twin boundary motion. The martensitic self-strain has been found to be 2%, implying a preferential orientation of martensite variants. Results related to the magnetic properties are discussed.

Samples of (Nd1−xCex)6Fe13Al (x=0.1, 0.2, 0.3, 0.4, 0.5, 0.6) were prepared by arc melting and annealed for 2 weeks at 700 °C. The x-ray diffraction patterns for the (Nd1−xCex)6Fe13Al samples show that all the above-mentioned samples crystallize with the Nd6Fe13Si-type tetragonal phase. The unit-cell volume v increases first and then decreases as the Ce content increases. The Curie temperature and the spontaneous magnetization decrease almost linearly with increasing Ce concentration. All these prove the existence of the mixed valence of Ce3+ and Ce4+. A complicated temperature dependence of magnetization is observed. Although the series is ferromagnetic at high temperature, there is a low-temperature peak in each M–T curve, which is in agreement with spin-glass behavior. This phenomena is reported in 6:13:1-type compounds.

An investigation of the structure and magnetocrystalline anisotropy of Ce2Co17-xAlx (x=0, 1, 2, and 3) compounds has been performed by means of x-ray diffraction and magnetization measurements. It is observed that the unit-cell volume, Curie temperature, and saturation magnetization of Ce2Co17-xAlx compounds are anomalously low in comparison with the values obtained from a simple extrapolation by the other R2Co17-xAlx compounds, such as R=Pr and Nd. These anomalies may be an evidence of a mixed-valence behavior of the Ce ion. X-ray diffraction measurements on magnetically aligned Ce2Co17-xAlx powders with x=0-3 exhibit an easy-axis type of magnetic anisotropy at room temperature. Substitution of Al for Co leads to a change of the magnetocrystalline anisotropy of the Co sublattice from the basal plane to c axis and strongly increases the uniaxial anisotropy of Ce2Co17-xAlx. The magnetocrystalline anisotropy field H-A is found first to increase and then decrease with increasing Al concentration, attaining a maximum value of 18 kOe at x=2. The magnetocrystalline anisotropy constant K-1 shows a small decrease with increasing temperature and K-2 is almost a constant. (C) 1999 American Institute of Physics. [S0021-8979(99)56308-1].

A new multinuclear metals condensation product (polymer C) was prepared by a condensation reaction between bis(oxamide oximato)nickel and 1,1′-dicarbaldehydeferrocene. Its structure was investigated by using elemental analysis, Fourier-transform infared, x-ray diffraction, and thermogravimetric analysis techniques. All these results show that the polymer is a three-dimensional layer, large π-conjugated part order structure and its initial decomposition temperature is about 230 °C. The magnetic susceptibility was measured from 5 to 160 K by a superconducting quantum interference device magnetometer under the applied magnetic field of 10 kOe. The plot of 1/χM vs T is linear in the range of 5–30 K, but deviates from the line above 30 K. The Weiss constant θ calculated according to the equation χM=C/(T−θ) in the 5–30 K was −2.1 K, indicating presence of a weak antiferromagnetic coupling between the most near neighboring two metal ions. The polymer C can also easily complex with metal ion Cu2+, but is difficult with Mn2+.A new multinuclear metals condensation product (polymer C) was prepared by a condensation reaction between bis(oxamide oximato)nickel and 1,1′-dicarbaldehydeferrocene. Its structure was investigated by using elemental analysis, Fourier-transform infared, x-ray diffraction, and thermogravimetric analysis techniques. All these results show that the polymer is a three-dimensional layer, large π-conjugated part order structure and its initial decomposition temperature is about 230 °C. The magnetic susceptibility was measured from 5 to 160 K by a superconducting quantum interference device magnetometer under the applied magnetic field of 10 kOe. The plot of 1/χM vs T is linear in the range of 5–30 K, but deviates from the line above 30 K. The Weiss constant θ calculated according to the equation χM=C/(T−θ) in the 5–30 K was −2.1 K, indicating presence of a weak antiferromagnetic coupling between the most near neighboring two metal ions. The polymer C can also easily complex with metal ion Cu2+, but is difficul...

Using the reductive perturbation method, the carrier wave modulation of ion acoustics waves in inhomogeneous plasma is investigated. It is shown that such a process can be described by a Nonlinear Schrodinger-type equation (NLS-type) equation.