High-efficiency volume reflection of an ultrarelativistic proton beam with a bent silicon crystal

The volume reflection phenomenon was detected while investigating 400 GeV proton interactions with bent silicon crystals in the external beam H8 of the CERN Super Proton Synchrotron. Such a process was observed for a wide interval of crystal orientations relative to the beam axis, and its efficiency exceeds 95%, thereby surpassing any previously observed value. These observations suggest new perspectives for the manipulation of high-energy beams, e.g., for collimation and extraction in new-generation hadron colliders, such as the CERN Large Hadron Collider.     

Steering efficiency of a ultrarelativistic proton beam in a thin bent crystal

I apply FDR—a recently introduced four-dimensional approach to quantum field theories (QFTs)—to the computation of the NLO QCD corrections to $H \rightarrow gg$ in the large top mass limit. The calculation involves all key ingredients of QCD—namely ultraviolet, infrared, and collinear divergences, besides $\alpha _S$ renormalization—and paves the way for successful use of FDR in massless one-loop QFT computations. I show in detail how the correct result emerges in FDR, and discuss the translation rules to dimensional regularization.     

Volume reflection of 1-GeV protons by a bent silicon crystal

The volume reflection of 1-GeV protons by a bent crystal has been observed. The crystal is made of single crystal silicon. The (111) atomic planes are bent owing to the elastic quasimosaicity effect, which makes it possible to reduce the crystal length for a beam to 30 μm. It is found that the probability of the reflection effect is higher than the probability of the channeling effect (0.71 vs. 0.63), and the deflection angle of the protons reflected inside the crystal is equal to 1.39 ± 0.04 in terms of the critical angle for channeling under the conditions of the experiment (170 μrad). The width of the reflected peak is equal to 1.76 ± 0.04 in the same units. The protons that are not involved in channeling at the angular position of maximum channeling undergo volume reflection and are deflected in the direction opposite to the channeled beam by the angle 1.01 ± 0.05 in terms of the critical angle for channeling. The width of the reflected peak is equal to 1.94 ± 0.08 in the same units. Original Russian Text ? Yu.M. Ivanov, N.F. Bondar’, Yu.A. Gavrikov, A.S. Denisov, A.V. Zhelamkov, V.G. Ivochkin, S.V. Kos’yanenko, L.P. Lapina, A.A. Petrunin, V.V. Skorobogatov, V.M. Suvorov, A.I. Shchetkovsky, A.M. Taratin, W. Scandale, 2006, published in Pis’ma v Zhurnal éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2006, Vol. 84, No. 7, pp. 445–450.     

Volume reflection and volume refraction of relativistic particles in a uniformly bent crystal

The scattering of fast charged particles in a bent crystal has been analyzed in the framework of relativistic classical mechanics. The expressions obtained for the deflection function are in satisfactory agreement with the experimental data for the volume reflection of relativistic protons obtained by Yu. M. Ivanov et al., Phys. Rev. Lett. 97, 144801 (2006); Yu. M. Ivanov et al., Pis’ma Zh. Eksp. Teor. Fiz. 84, 445 (2006) [JETP Lett. 84, 372 (2006)]; and W. Scandale et al., Phys. Rev. Lett. 98, 154801 (2007). The features of the scattering of the particles on ring potentials are considered in a wide range of impact parameters.     

X-ray diffraction in a uniformly bent crystal in reflection geometry

The features of the intensity distribution over the exit surface of a uniformly bent crystal have been investigated in reflection geometry. Experiments have been performed using thin-layer heterostructures Si_(1−x)Ge _x /Si. For heterosystems, internal stresses induced in the film and substrate lead to an elastic bending of the whole system. The section topographs exhibit deformation interference fringes. It is important that the contrast of this interference pattern is almost one order of magnitude higher than the contrast in the case of Bragg scattering in a perfect crystal. The observed interference pattern depends on the radius of bending of the crystal. As the bending radius increases, all maxima shift toward the basic Bragg peak. Correspondingly, all distances between the interference fringes decrease. It has been shown that the positions of intensity maxima do not depend on the sign of the crystal bending. For a negative sign of the radius of the crystal bending (positive strain gradient), the integrated intensity increases. The results of the numerical simulation of the diffraction images agree well with the experimental topographs. A comparison of the numerical simulation of the interference pattern with the experimental topographs makes it possible to exactly determine the radius of the crystal bending (4%). The formulas describing the positions of interference maxima as a function of the bending radius of the sample have been obtained using the results of the numerical simulation of the experiment.     

非常偏振光在单轴晶体表面的全反射分析

利用透射波函数和由菲涅尔公式求解反射相位差并对其求导的方法,分析了非常偏振光在单轴晶体表面发生的全反射现象,求解出晶体光轴在入射面内时,非常偏振光从各向同性介质入射到晶体和从晶体出射到各向同性介质两种情况的隐失波穿透深度和Goos-Hnchen位移的一般表达式。通过计算机模拟给出了单轴晶体为方解石和水晶情况时的穿透深度和Goos-Hnchen位移图像。结果表明,对于不同的晶体,光轴的取向对穿透深度和Goos-Hnchen位移的影响是明显不同的,若选取合适的晶体、光轴取向和入射角,可以得到较大的隐失波穿透深度和Goos-Hnchen位移。     

Focusing crystal device for deflecting a divergent 50-GeV proton beam

At large accelerators, bent crystals are employed to deflect weakly divergent proton beams at the stages of extraction and collimation. We demonstrate that a divergent particle beam may be efficiently deflected using a crystal with a focusing edge. A proton beam with divergence near 1 mrad, which exceeds the Lindhard angle by a factor of 30, has been experimentally deflected by 1.8 mrad with efficiency near 15%. The proposed focusing crystal may serve as an element of a novel optical system for secondary-particle beams in the TeV energy region.     

Peculiarities of light beam reflection from the boundary of a 1D-photonic crystal

Typical cases of lateral shift and deformation of the profile of two-dimensional light beams reflected from the surface of a one-dimensional photonic crystal are considered. We use harmonic modulation of the spatial dependence of dielectric permeability of a crystal, which permits one to study reflectance profiles analytically. The results of numerical calculations that were performed are presented for the cases when the angular spectrum of the incident beam is split.     

Incoherent radiation of fast electrons in a bent crystal

Incoherent bremsstrahlung of high-energy particles in a crystal is caused by the thermal scattering of atoms with regard to their equilibrium positions in the lattice. A previously developed procedure for the simulation of incoherent emission is applied to the case of electron motion in a sinusoidally bent crystal. The results of the simulation agree with the data of recent experiments at the Mainz Microtron (MAMI). The possibility for utilizing sinusoidally bent crystals as undulators is discussed.     

Bent crystal application to formation and diagnostics of proton beam

The analysis of the deflection efficiency of high-energy proton beam with a bent crystal has been made and the optimum length of the bent crystal estimated. A bent Si crystal was used in the experiments at Serpukhov circular accelerator with 70 GeV proton beam. The results of the formation of a narrow proton beam and measurements of the beam phase volume are discussed.     

Investigation of the emission of photons induced in the volume reflection of 10-GeV positrons in a bent silicon single crystal

The emission of photons in the motion of a 10-GeV positron beam in bent silicon crystals has been experimentally investigated. The experimental data are compared with the theoretical calculations.     

Investigation of the focusing of a 50-GeV proton beam using a new crystal device

Bent crystals are used at large accelerators to deflect particle beams for extraction and collimation. Not only the deflection but also the focusing of beams by bent crystals can be required for recently formulated proposals for investigations at the Large Hadron Collider (LHC) with a fixed target. The experimental results on the focusing of a 50-GeV proton beam with a new crystal device, which can be used in a circulating beam of a large accelerator such as the LHC, have been reported.     

First observation of multiple volume reflection by different planes in one bent silicon crystal for high-energy protons

Multiple volume reflection by different planes in a bent silicon crystal with its 〈111〉 axis orientation close to the beam direction was observed for the first time for 400 GeV/c protons at the CERN SPS. The proton beam was deflected to the side opposite to the crystal bend by an angle of about 67 μrad, which is five times larger than in a single volume reflection by the (110) bent planes. The registered efficiency of one side deflection was about 84%. It was shown that multiple volume reflection transforms to a single volume reflection when the orientation angle of the 〈111〉 axis relative to the beam direction is increased.     

Deflection of high-energy negative particles in a bent crystal through axial channeling and multiple volume reflection stimulated by doughnut scattering

Different kinds of deflection in a silicon crystal bent along the 〈111〉 axis was observed for 150 GeV/c   negative particles, mainly π⁻${\pi }^{-}$ mesons, at one of the secondary beams of the CERN SPS. The whole beam was deflected to one side in quasi-bound states of doughnut scattering (DSB) by atomic strings with the efficiency (95.4 ± 0.2)% and with the peak position close to the bend crystal angle, α=185 μrad$\alpha =185\text{μrad}$. It was observed volume capture of π⁻${\pi }^{-}$ mesons into the DSB states with a probability higher than 7%. A beam deflection opposite to the crystal bend was observed for some orientations of the crystal axis due to doughnut scattering and subsequent multiple volume reflections of π⁻${\pi }^{-}$ mesons by different bent planes crossing the axis.     

Negative refraction and reflection of Gaussian beam on two-dimensional photonic crystal slab

The refraction and reflection of Gaussian beam on two-dimensional photonic crystal (2DPC) slab are studied by the finite-difference time-domain (FDTD) method. It is shown that 2DPC slab enables negative refraction, which is demystified by the distribution of Poynting vector directions and values inside the 2DPC. A negative Goos-Hanchen shift is also found in the simulation.     

激光等离子体球面晶体光谱成像

 利用自聚焦原理,研制了一种新型的球面弯晶谱仪。晶体分析器采用云母材料,其弯曲半径为380 mm,布拉格角为51°。利用成像板接收光谱信号,其有效面积为30 mm×80 mm,从等离子体源经晶体到成像板的光程长为980 mm。物理实验在中国工程物理研究院激光聚变研究中心20 J激光装置上进行,入射激光能量为6.78 J,成像板获得了铝激光等离子体X射线的光谱空间分辨信号。球面云母弯晶谱仪的光谱分辨率达到1 000～1 500,在相同环境放置的PET平晶的光谱分辨率为50～100。结果表明：球面弯晶具有较高的光谱分辨率和信噪比,适合于激光等离子体X射线的光谱学研究。     

激光等离子体球面晶体光谱成像

利用自聚焦原理,研制了一种新型的球面弯晶谱仪。晶体分析器采用云母材料,其弯曲半径为380 mm,布拉格角为51°。利用成像板接收光谱信号,其有效面积为30 mm×80 mm,从等离子体源经晶体到成像板的光程长为980 mm。物理实验在中国工程物理研究院激光聚变研究中心20 J激光装置上进行,入射激光能量为6.78 J,成像板获得了铝激光等离子体X射线的光谱空间分辨信号。球面云母弯晶谱仪的光谱分辨率达到1 000～1 500,在相同环境放置的PET平晶的光谱分辨率为50～100。结果表明：球面弯晶具有较高的光谱分辨率和信噪比,适合于激光等离子体X射线的光谱学研究。     

Use of a bent crystal with a decreasing curvature to increase the efficiency of the extraction and collimation of a beam in an accelerator

It has been shown that the use of a bent crystal with a variable curvature radius makes it possible to reduce the fraction of dechanneled particles by an order of magnitude. This effect enables the strong reduction of the particle density at the edge of a collimator or the partition of a septum upon the multi-turn extraction of a beam from a ring accelerator. In particular, the beam extraction efficiency at the U-70 synchrotron and Large Hadron Collider can be increased to 95 and 99.65%, respectively.