Spectral method in axial channeling theory

The energy quantization of transverse particle motion in continuous potentials of atomic chains and planes can occur when fast charged particles travel in crystals. In the proposed paper, the energy levels of electrons moving in the mode of axial channeling in a system of parallel atomic chains have been found (Si crystal [110] chains have been used as an example). The energy eigenvalues were determined numerically using the so-called spectral method, which shows itself to good advantage in the problem of the plane channeling of charged particles in crystals.     

低能沟道效应及其应用

带电粒子在晶体中的运动会受到沟道效应和阻塞效应的强烈影响。本文评述了能量为Mev的质子和氦离子在晶体中的沟道效应及其在固体物理、半导体物理、表面物理和原子物理中的应用,同时也叙述了我们实验室在近几年来得到的各种实验结果。     

正弦平方势与小振幅近似下的弯晶沟道辐射

在理想情况下和经典力学框架内,引入正弦平方势,把粒子在弯晶中的运动方程化为具有外力矩的摆方程。并对系统的相平面特征进行了数值分析。在小振幅近似下,把粒子运动方程化为具有硬特性的弹簧-振子系统,用Jacobian椭圆函数和椭圆积分解析地给出系统的解和粒子运动周期。讨论了弯晶沟道辐射频率、无量纲偏转角和辐射谱的一般特征。指出利用沟道辐射作为激光的可能性。以正电子在碳单晶中沟道辐射为例进行了具体计算,得到了与其他工作基本一致的结果。     

正电子面沟道辐射的非线性特征

经典物理学指出,在电磁场中作加速运动的带电粒子将不断向外辐射能量.在晶体沟道中运动的带电粒子也不例外,晶格场可以使带电粒子的辐射能量达到很高.对于10MeV的正电子,辐射能量可达keV量级.粒子在沟道中的运动行为决定于粒子晶体的相互作用势,常用的相互作用势有Lindhard势、Moliere势和正弦平方势.由于粒子在沟道中的运动行为十分类似于震荡器中运动的自由电子,可望把沟道辐射改造为Χ射线激光或γ射线激光.从Lindhard势出发,将其展开到四次项,在经典力学框架内,粒子的运动方程可以化为含立方项的二阶非线性微分方程,并利用Jacobian椭圆函数和第一类全椭圆积分解析地表示了系统的解和粒子运动周期,导出了正电子面沟道辐射的瞬时辐射强度、平均辐射强度和最大辐射频率,指出了利用沟道辐射作为γ激光的可能性.     

Multicrystal microundulator

The mode of propagation of relativistic, positively charged particles through a system of mutually oriented and periodically arranged ultrathin crystals whose thicknesses are equal to the half-period of the particle trajectory during planar channeling in a thick crystal is considered. In the case of an incidence angle that is less than the critical channeling angle, a certain fraction of particles is specularly reflected from the atomic planes of the crystal. Therefore, passing through a stack of crystals, a particle moves along quasiundulator trajectories. The characteristics of the radiation of a particle passing through such a “multicrystal microundulator” are found. The radiation spectrum is discrete, and the first-harmonic frequency and the number of harmonics in the spectrum are dependent on the distance between the crystals, the particle energy, and the potential of atomic planes of the crystal. Radiation is concentrated in a narrow cone in the direction of the average velocity of particles and is mainly polarized in a plane that is orthogonal to the atomic planes of the crystal. The microundulator can be composed of separate crystals with micron thicknesses and can be fabricated using modern methods of microlithography and micromechanics with deep, for example, plasmochemical etching of the crystal surface.     

Parametric channeling and collapse of beams of charged particles with internal structure in crystals: 1. Features of parametric channeling of molecular ions in crystal channels

A new type of self-organized orientational motion of charged particles with internal energy structure (molecules, atoms, and in some cases nuclei and electrons) in crystals, i.e., parametric channeling, is proposed and studied in detail. A feature of this mode of motion is associated with the strong parametric coupling of orientational oscillations controlled by the interaction of the moving particle charge with averaged fields of crystal plane axes and vibrations caused by intraparticle processes. The features of parametric processes during channeling of molecular diatomic ions are studied. It is shown that this effect can cause “parametric collapse,” i.e., beam self-cooling, compression, and a decrease in its phase-space volume. For molecules whose axis is perpendicular to the channel axes, periodic parametric collapse occurs. For molecules oriented along the channel, beam self-cooling is an asymptotic, aperiodic, and irreversible process.     

Chaotic phenomena of charged particles in crystal lattices

In this article, we have applied the methods of chaos theory to channeling phenomena of positive charged particles in crystal lattices. In particular, we studied the transition between two ordered types of motion; i.e., motion parallel to a crystal axis (axial channeling) and to a crystal plane (planar channeling), respectively. The transition between these two regimes turns out to occur through an angular range in which the particle motion is highly disordered and the region of phase space spanned by the particle is much larger than the one swept in the two ordered motions. We have evaluated the maximum Lyapunov exponent with the method put forward by Rosenstein et al. [Physica D 65, 117 (1993)] and by Kantz [Phys. Lett. A 185, 77 (1994)]. Moreover, we estimated the correlation dimension by using the Grassberger-Procaccia method. We found that at the transition the system exhibits a very complex behavior showing an exponential divergence of the trajectories corresponding to a positive Lyapunov exponent and a noninteger value of the correlation dimension. These results turn out to be linked to a physical interpretation. The Lyapunov exponents are in agreement with the model by Akhiezer et al. [Phys. Rep. 203, 289 (1991)], based on the equivalence between the ion motion along the crystal plane described as a "string of strings" and the "kicked" rotator. The nonintegral value of the correlation dimension can be explained by the nonconservation of transverse energy at the transition.     

Dynamical chaos and stochastic mechanism of high-energy negatively charged particle deflection by bent crystals

Deflection of high-energy negatively charged particles in straight and bent crystals through multiple scattering by crystal atomic strings was considered for the case in which the initial angle between the particle momentum and one of the main crystallographic axes was approximately four critical angles of axial channeling. It was shown that in a bent crystal with a small crystal thickness, when the crystal bend was less than the beam incidence angle, the beam deflected in the direction opposite to the direction of the crystal bend. At larger crystal thicknesses, the large part of the beam starts to deflect in the direction of the crystal bend. In addition, there is a group of particles that follow the crystal axis bend in the angular region of approximately the critical angle of axial channeling with respect to the current direction of the crystal axis. It was shown that in all of these deflection processes, the periodicity of the location of atomic strings in the crystal does not influence the angular distributions of scattered particles. This fact is connected with the effect of dynamical chaos in particle motion in the periodical field of bent crystal atomic strings. It was also shown that observed in a recent CERN experiment effect of beam deflection, when the angle between the initial particle momentum and the crystal axis was approximately four critical angles of axial channeling, is due to peculiarities of the stochastic multiple scattering of particles by bent crystal atomic strings. These peculiarities are connected with the effect of dynamical chaos in particle motion in crystals.     

Channeling radiation: Past achievements and future prospects

Abstract

When a relativistic charged particle passes through a single crystal very nearly along a major crystalline plane or axis so that it is channeled in that direction, it undergoes periodic motion in the plane transverse to this direction and hence it can radiate. Quantum mechanically, this channeling radiation corresponds to a radiative transition between two eigenstates of the transverse crystalline potential; when the transition occurs between two bound states, a sharp spectral line is emitted. When there are only two bound states (for incident electrons), or when the interplaner potential is nearly harmonic (as for incident positrons), the emitted radiation is nearly monochromatic. Since the discovery of channeling radiation at the LLNL Electron-Positron Linear Accelerator, many of its properties have been delineated, both there and elsewhere. For example, channeling radiation is very intense, forward-directed, easily tunable, and for the planar case, linearly polarized. Channeling radiation has been used as a probe both of the interplanar potentials and other properties of perfect crystals and of the effects of impurities and defects in imperfect crystals. Finally, channeling radiation has great potential use as a photon source for numerous other applications in several fields of science and technology.

This paper is intended to keynote the first International Conference on Coherent Radiation Processes in Strong Fields by recalling some history of the discovery and exploitation to date of channeling radiation. Studies of channeling radiation, in addition to elucidating the physics of the process itself, its application to the determination of properties of perfect and imperfect crystals, and its potential application to a large variety of fields by its use as an intense, monochromatic, forward-directed, tunable, and polarized photon source, have spawned an entire industry of studies of other coherent radiation processes, all consisting of photon production from beams of relativistic charged particles traversing periodic structures, which constitute the principal subject matter of this Conference. This paper will be limited to the discussion of channeling radiation and some of its applications. It will be in the nature of an illustrative exposition, showing many of the features of channeling radiation and its applications in a qualitative way. Several detailed studies of channeling radiation will be presented later in the Conference.     

Subbarrier interaction of channeling particles under the self-similar excitation of correlated states in a periodically deformed crystal

It has been shown that application of the periodic modulation of parabolic potential well parameters (in the case of charged particle channeling in crystals, i.e., periodic spatial modulation of the wall height of a potential well in the crystal channel) leads to the formation of the coherent channeling state in particles in this well. The formation of this state changes the interaction process between these particles and nuclei, and increases the barrier transparency by many times. For channeling this mode can be formed using, e.g., the longitudinal acoustic wave running along the channel axis. This wave changes the distance between nuclei and, accordingly, modulates the height of channel walls.     

High-resolution nuclear track mapping in detailed cellular histology using CR-39 with the contact microscopy technique

In radiation cancer therapies using energetic charged particles such as proton/heavy-ion therapy and boron neutron capture therapy (BNCT), studies on radiation-induced biological response at cellular level are important because the radiation damage from energetic charged particles is highly localized along their paths and the radiation sensitivity is quite different in each cellular organelle. In such studies the information on the position of charged particle impact in biological cells is necessary. A novel method for high-resolution nuclear track mapping in detailed cellular histology has been developed. In this technique, biological specimens mounted on CR-39 plates are exposed to energetic charged particles. The irradiated samples are exposed to UV, and then etched for a short time. Both etch pits of nuclear tracks and relief for transmission UV image of the specimen can be observed on the CR-39 surface with an atomic force microscope (AFM) at about 100 nm resolution.     

On the electromagnetic radiation of channeled particles in a curved crystal

A simple model calculation of the channeling of charged particles in a curved crystal is presented. The characteristics of the powerful radiation from relativistic particles associated with the motion in a curved channel are discussed.     

周期弯晶作为束流控制元件的动力学稳定性

在经典力学框架内和偶极近似下,引入正弦平方势,把粒子运动方程化为具有阻尼项和受迫项的广义摆方程。利用Melnikov方法讨论了沟道运动次谐分叉及其稳定性, 导出了周期弯晶的临界条件和退道长度。结果表明, 要试图获得高的引出效率, 除了要求弯晶长度必须小于退道长度外, 还必须保证沟道粒子的运动是稳定的。对临界条件的分析表明, 系统的稳定性与它的参数有关, 只须适当调节系统参数, 就可以保证周期弯晶作为引出元件的稳定性。In the classical mechanics frame and with a dipole approximation the particle motion equation in the periodic bent crystal is reduced to the general pendulum equation with a damping term and the forced term by using the sine squared potential． This paper discusses the problem of the sub harmonic bifurcation of the periodic orbit and the stabilities of the channeling motion by using Melnikov method, so as to derive the critical condition and the dechanneling length of the periodic bent crystal. The results show that channeling motion must be stable in addition that the crystal length is smaller than the dechanneling length in order to ensure higher extracted efficiency. The analysis of the critical condition shows that the system stabilities are related to its parameters. Just by properly regulating the parameters of the system, the dynamic stabilities by the use of periodic bent crystal as beam control cell can be ensured.     

A dynamical transition of a chain of charged particles in a 2D substrate potential

The transport of a chain of charged particles with a transverse degree of freedom is investigated in a 2D asymmetric potential. Here, the energy of the periodic driving force is converted into motion in the vertical direction. The analysis exhibits a transition from stick-slip motion to periodic oscillation. The chain velocity can be controlled to an optimized value by adjusting system parameters, such as the amplitude and frequency of the periodic force. The existence of a resonance platform indicates resonance between the motion of the chain and the periodic force as coupling strength increases adiabatically. The atomic configuration and the transverse degree of freedom also play key roles in the control.     

Volume reflection of a proton beam in a bent crystal

Volume reflection predicted in the mid-1980s by Taratin and Vorobiev has been observed for the first time in the interactions of a 70 GeV proton beam with a short bent crystal. Incident protons deviate from convex atomic planes in the bulk of the crystal as a result of coherent interaction with bent lattice around the tangency point of particle trajectory with a curved atomic plane. The deflection angle 2theta(R) was found to be (39.5+/-2.0) microrad, or (1.65+/-0.08)theta(c) in terms of the critical angle for channeling. The process has a large probability with respect to channeling and takes place in the angular range equal to the bend angle of atomic planes. It could possibly open new fields of application of crystals in high-energy particle beam optics.     

沟道辐射

最近,人们发现,带电轻粒子在晶体沟道中运动发射与相干韧致辐射既有联系又有本质区别的新的辐射—沟道辐射。这种强度大、单色性好、高度定向且极化的辐射具有重要的理论和实验研究价值。本文讨论了沟道辐射的主要特征、实验进展状况、结果和装置及其可能的应用。并与其他有关辐射现象作了比较。     

Spectral method in quantum theory of channeling phenomena of fast charged particles in crystals

We show the possibility of using the spectral method to determine the quantum characteristics of interaction between fast charged particles and crystal when the channeling occurs. Basing on this method, we have developed the procedure for calculation of particles transversal motions eigenlevels for plane channeling. We considered origin of new levels with increasing of particle's energy and zone structure forming from these levels with increasing number of potential wells. We discuss also the possibility of using the spectral method in number of other problems of quantum theory of channeling.     

Structure of Regions of Regular Motion in the Phase Space of Channeled Electrons

The motion of electrons in the axial channeling mode in the [100] direction of a Si crystal can be regular and chaotic (depending on the initial conditions). The contribution of regions of regular and chaotic dynamics to the quasiclassical density of energy levels of the transverse motion of electrons is found in this paper. The obtained values are used as parameters of the Berry—Robnik distribution describing the level spacing statistics in the case of the coexistence of regions of regular and chaotic motion.     

Magnetic moment measurement of baryons with heavy-flavored quarks by planar channeling through a bent crystal

The precession angle of a polarization vector is calculated for a positively charged short-lived baryon channeling between single-crystal planes. When very energetic polarized baryons are produced such that the production plane of the baryon is almost parallel to the crystal plane, it is shown that the interaction of the polarization with inhomogeneous electric fields inside the crystal can be neglected from the equation of motion of the particle. In this case, the equation of motion of the polarization vector becomes the same as when the electric field is homogeneous. It is also shown that when the crystal is bent perpendicular to the planar direction, the precession angle of the polarization vector of short-lived baryons can be expressed ass $\text{Δθ}{}_{\mathrm{<mtext>R</mtext>}}{}^{\mathrm{\tau }}\text{=}\text{1}\text{2}\text{γ}{}^2\text{[(2 ? g + g/γ}{}^2\text{)]ντ/R}$ under the same condition as above, where γ is the Lorentz factor, g the g factor of the magnetic moment, R the bending radius of the crystal and τ the lifetime of the particle. It is also shown that in some cases this precession should be large enough to determine the magnetic moment of short-lived particles, such as the charmed baryon Λ_c⁺.     

弯晶沟道的混沌行为

本文预言了在周期场作用下,弯晶沟道的混沌行为。分析了系统的全局分叉性质和出现Smale马蹄的参数条件,指出系统通向混沌的过程就是粒子的退道过程,而相的沟道效应和沟道辐射都将表现出内在的随机性,为定量解释沟道效应和沟道辐射的某些特征提供了一种可能的理论分析。 关键词：