形(应)变超晶格的退道效应与系统的全局分叉

把超晶格"折沟道"对粒子的作用等效为形状相似的弱周期调制.利用正弦平方势把粒子运动方程化为具有外周期弱调制的非线性微分方程,导出了退道系数与晶格畸变的关系.利用多尺度法研究了系统的主共振和子共振,并利用Melnikov方法分析了系统的全局分叉和出现Smale马蹄的临界条件. The effect of deflected channel on particle motion is equivalent to modulation with a weak potential having a periodic same as the deflected channel has. The motion equation of a particle has been reduced to the nonlinear differential equation with a weak periodic modulation by using sine squared potential. The dechanneling fraction has been derived for a strained superlattice. The main resonance and sub resonance have been inverstigated by using multi scale method, a global bifurcation and the critic...     

Darboux Transformation with a Double Spectral Parameter for the Myrzakulov-I Equation

The Myrzakulov-I equation is a 2＋l-dimensional generalization of the Heisenberg ferromagnetic equa- tion and has a non-isospectral Lax pair. The ex- plicit solutions to the Myrzakulov-I equation have been discussed by many researchers. Darboux transformation is one of the useful methods to ob- tain explicit solutions to the nonlinear partial differ- ential equation. The Darboux transformation of de- gree 1 for this equation has been constructed and exact global ＇one-soliton＇ solutions are derived.     

正弦平方势与环形加速器的弯晶束流引出

在经典力学框架内和偶极近似下, 引入正弦平方势, 把粒子在弯晶中的运动方程化为具有固定力矩的摆方程。 利用Jacobian椭圆函数和椭圆积分分析了系统的相平面特征。 导出了弯晶的最大偏转能量、 退道系数和退道长度。 计算结果表明, 对于曲率半径为1 m, 能量为1.0 GeV的质子, Si(110)面沟道的引出效率为70%; 对于MeV范围的粒子, 退道长度大约是μm量级; 对于TeV范围的粒子, 退道长度可达1 m以上。 In the classical mechanics frame and the dipole approximation the particle motion equation in bent crystal is reduced to the pendulum equation with a constant momentum by using the sine squared potential.The phase planar properties are analysed by means of Jacobian elliptic function and the elliptic integral. The maximum deflected energy, the dechanneling factor and the dechanneled length are derived. The results show that the extrated efficiency is 70% for a proton beam with energy E=1.0 GeV moved in the channel on Si(110) if a radius of curvature R=1 m; and dechanneled length is of the order of μm for the particles with MeV energy; the dechanneled length is above 1 meter for the particle with TeV energy.     

Spatial Soliton Solutions in a Harmonic Potential

The F-expansion technique and the homogeneous nonlinear balance principle have been applied for solving a general （19-1）-dimensional nonlinear Schrodinger equation （NLSE） with varying coetficients and a harmonic potential. A family of （1＋1）D spatial solitons has been obtained. The evolution features of exact solutions have been investigated.     

A Novel Approach with Time-Splitting Spectral Technique for the Coupled Schrdinger–Boussinesq Equations Involving Riesz Fractional Derivative

In the present paper the Riesz fractional coupled Schr¨odinger–Boussinesq(S-B) equations have been solved by the time-splitting Fourier spectral(TSFS) method. This proposed technique is utilized for discretizing the Schrdinger like equation and further, a pseudospectral discretization has been employed for the Boussinesq-like equation. Apart from that an implicit finite difference approach has also been proposed to compare the results with the solutions obtained from the time-splitting technique. Furthermore, the time-splitting method is proved to be unconditionally stable. The error norms along with the graphical solutions have also been presented here.     

Modulational instability of a weakly relativistic ion acoustic wave in a warm plasma with nonthermal electrons

An investigation has been made of modulational instability of a nonlinear ion acoustic wave in a weakly relativistic warm unmagnetized nonthermal plasma whose constituents axe an inertial ion fluid and nonthermally distributed electrons. Up to the second order of the perturbation theory, a nonlinear Schr~dinger type (NST) equation for the complex amplitude of the perturbed ion density is obtained. The coefficients of this equation show that the relativistic effect, the finite ion temperature and the nonthermal electrons modify the condition of the modulational stability. The association between the small-wavenumber limit of the NST equation and the oscillatory solution of the Korteweg-de Varies equation, obtained by a reductive perturbation theory, is satisfied.     

Modulational instability of a weakly relativistic ion acoustic wave in a warm plasma with nonthermal electrons

An investigation has been made of modulational instability of a nonlinear ion acoustic wave in a weakly relativistic warm unmagnetized nonthermal plasma whose constituents are an inertial ion fluid and nonthermally distributed electrons. Up to the second order of the perturbation theory, a nonlinear Schr?dinger type (NST) equation for the complex amplitude of the perturbed ion density is obtained. The coefficients of this equation show that the relativistic effect, the finite ion temperature and the nonthermal electrons modify the condition of the modulational stability. The association between the small-wavenumber limit of the NST equation and the oscillatory solution of the Korteweg－de Varies equation, obtained by a reductive perturbation theory, is satisfied.     

Stress Wave Propagation in a Gradient Elastic Medium

The gradient elastic constitutive equation incorporating the second gradient of the strains is used to determine the monochromatic elastic plane wave propagation in a gradient infinite medium and thin rod.The equation of motion,together with the internal material length,has been derived.Various dispersion relations have been determined.We present explicit expressions for the relationship between various wave speeds,wavenumber and internal material length.     

Nonlinear Waves in a Cigar-Shaped Bose-Einstein Condensate with Dissipation

We discuss the possible nonlinear waves of atomic matter waves in a cigar-shaped Bose-Einstein condensatewith dissipation. The waves can be described by a KdV-type equation. The KdV-type equation has a solitary wave solution. The amplitude, speed, and width of the wave vary exponentially with time t. The dissipative term of ~/ plays an important role for the wave amplitude, speed, and width. Comparisons have been given between the analytical solutions and the numerical results. It is shown that both are in good agreement.     

Effect of adiabatic variation of dust charges on dust acoustic solitary waves in magnetized dusty plasmas

The effect of dust charging and the influence of its adiabatic variation on dust acoustic waves is investigated. By employing the reductive perturbation technique we derived a Zakharov－Kuznetsov (ZK) equation for small amplitude dust acoustic waves. We have analytically verified that there are only rarefactive solitary waves for this system. The instability region for one-dimensional solitary wave under transverse perturbations has also been obtained. The obliquely propagating solitary waves to the z-direction for the ZK equation are given in this paper as well.     

Quantitative theory of channeling particle diffusion in transverse energy in the presence of nuclear scattering and direct evaluation of dechanneling length

A refined equation for channeling particle diffusion in transverse energy taking into consideration large-angle scattering by nuclei is suggested. This equation is reduced to the Sturm–Liouville problem, allowing one to reveal both the origin and the limitations of the dechanneling length notion. The values of the latter are evaluated for both positively and negatively charged particles of various energies. New features of the dechanneling dynamics of positively charged particles are also revealed. First, it is demonstrated that the dechanneling length notion is completely inapplicable for their nuclear dechanneling process. Second, the effective electron dechanneling length of positively charged particle varies more than twice converging to a constant asymptotic value only at the depth exceeding the latter.     

Analytical model of axial channeling for heavy ions

The channeling of ions at small depths in crystals containing point defects of impurity atoms is investigated by means of the kinetic equation. The distribution of the ions in the channels and the dechanneling function are obtained, and also density oscillations of the ion flux are investigated. In the model considered, the elastic scattering of ions by defects at angles greater than critical have been taken into consideration, and the distribution of point defects in the channel has been assumed to be uniform. Diffusion models underestimate the influence of this effect on dechanneling at small depths (<1 ).Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 40–44, March, 1979.In conclusion, the authors thank R. V. Vedrinskii, A. S. Borovik, and S. V. Mikhailov for discussions.     

Effects of Higher-Order Terms on the Nonlinear Propagation of Electron Acoustic Waves

The contribution of higher-order terms on the nonlinear propagation of electron acoustic waves has been investigated, using the reductive perturbation technique. A modified KdV equation for the first order perturbed potential and a linear inhomogeneous equation for the second order perturbed potential have been derived. The soliton width and amplitude have been calculated.     

Influence of quantum fluctuations on the stochastic dynamics of the channeling effect of relativistic electrons and positrons

A system of equations describing multiple scattering by crystal nuclei and electrons, and also quantum fluctuations of the coordinate and momentum operators of fast charged particles has been obtained. Quantum corrections to the classical equations of motion have been determined in quasiclassical approximations. A computer simulation of 855-MeV electron and positron motion in the (110) planar channel of a Si crystal has been carried out. The inclusion of quantum fluctuations in the equation of motion affects the dynamics of the electron channeling effect in planar crystal channels considerably; in particular, intense dechanneling (heating) occurs. Intense rechanneling (cooling) occurs in the case of positrons.     

Dechanneling of MeV protons in tungsten

Abstract

A systematic investigation of the dechanneling of protons in tungsten has been completed for the <111> axial direction and also for the (110) plane. Measurements at room temperature have been made at energies of 0.5, 2.0, 3.5, 8.0 and 12.0 MeV; at 2.0 MeV, the effect of target temperature has been investigated over the range 77–873°K. In the axial case, the dechanneling rate increases strongly with the vibrational amplitude _ρ, but not as strongly as the ρ² dependence reported by the Catania group (Refs. 4–7) for silicon and germanium. Also, unlike silicon and germanium, the tungsten axial data exhibit practically no energy dependence and so cannot be fitted by the zρ²/E scaling parameter suggested by the Catania group. On the other hand, the planar dechanneling data in tungsten exhibit the predicted (E ^?1)dependence and relatively littie temperature dependence, in good agreement with previous work.     

Proton dechanneling in alkali halide mixed crystals

The effects of the lattice distortion in KCI-KBr mixed crystals on the dechanneling of 1.5 MeV protons are studied by means of backscattering. The dechanneling rate vs. the composition curve has a maximum at about 1:1 mixture of KCI and KBr. The lattice distortion in the mixed crystals is estimated from the dechanneling rate, and the result agrees well with that obtained by an X-ray measurement. The effective cross-section for the dechanneling caused by the lattice distortion is obtained, and compared with the results of a calculation based on a simple model.     

The Electromagnetic Analogue of Some Gravitational Perturbations in Cosmology

Recently attention has been drawn to the fact that perfect fluid tensor perturbations (with perturbed vorticity and acceleration vanishing) of isotropic cosmological models have a perturbed Weyl tensor with electric part satisfying a linear, homogeneous, third-order wave equation while the magnetic part satisfies a linear, homogeneous, second-order wave equation. We construct an analogous class of electromagnetic test fields in the isotropic cosmological models for which the electric vector satisfies a third-order, linear and homogeneous wave equation while the magnetic vector satisfies a second-order, linear and homogeneous wave equation. If the perfect fluid has an equation of state we give a simplified derivation of the authors' previous perturbation analysis describing gravitational waves carrying arbitrary information. We also present the analogous solutions of Maxwell's equations which contain electromagnetic waves conveying arbitrary information.     

Dechanneling of 6-MeV protons in a tungsten single crystal

The effect of energy losses of channeled particles on the results of determination of the depth dependence of the integral dechanneling function from the backscattering spectra has been investigated.     

Grounds for the application of fractional-order diffusion equations in channeling theory using the Langevin approach

Transverse-energy distribution densities in the case of ultrarelativistic proton channeling in the (100) planes of diamond-like crystals have been numerically calculated within the framework of the Langevin approach. Based on the self-similarity principle, the subdiffusion character of the motion under consideration has been established, which can be regarded as grounds for using fractional-order diffusion equations to adequately describe channeling and dechanneling processes mathematically.