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.     

Simulation of the deflection of 200- and 450-GeV protons by a bent germanium crystal

It is shown that the result obtained by numerically solving the kinetic Fokker-Planck equation in the transverse-energy space on the basis of computer simulations of channeled-particle trajectories describes well the results of an experiment that studied the deflection of 200- and 450-GeV protons by a bent germanium crystal.     

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⁺.     

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.     

High-efficiency beam extraction and collimation using channeling in very short bent crystals

A silicon crystal was used to channel and extract 70 GeV protons from the U-70 accelerator with an efficiency of 85.3+/-2.8%, as measured for a beam of approximately 10(12) protons directed towards crystals of approximately 2 mm length in spills of approximately 2 s duration. The experimental data follow very well the prediction of Monte Carlo simulations. This demonstration is important in devising a more efficient use of the U-70 accelerator in Protvino and provides crucial support for implementing crystal-assisted slow extraction and collimation in other machines, such as the Tevatron, RHIC, the AGS, the SNS, COSY, and the LHC.     

Observation of channeling and volume reflection in bent crystals for high-energy negative particles

Deflection due to planar channeling and volume reflection in short bent silicon crystals was observed for the first time for 150 GeV/c negative particles, π⁻ mesons, at one of the secondary beams of the CERN SPS. The deflection efficiency was about 30% for channeling and higher than 80% for volume reflection. Volume reflection occurs, in spite of the attractive character of the forces acting between the particles and the crystal planes, in a wide angular range of the crystal orientations determined by the crystal bend angle.     

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.     

Theory of axial channeling of protons and antiprotons at small depths

The theory of channeling of proton and antiproton beams is constructed using Newton's equations with a transverse force resulting from the statistical ensemble of atoms of the crystal. The equations of motion are linearized by expanding time in series of the transverse force fluctuation, which plays the role of the small parameter. Stochastic instability of the transverse motion of the channeled particles, characterized by an exponential growth of the second moments of the distribution function with path length, is observed.Institute of Nuclear Physics at Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 66–71, May, 1995.     

Comparison of the efficiency of the deflection of proton beams with various energies by a bent crystal with the use of planar channeling and the stochastic deflection mechanism

The efficiency of the deflection of 50-, 15-, and 1.3-GeV proton beams by means of planar channeling in a bent silicon crystal has been compared to that by means of the stochastic mechanism of the deflection of charged particles by the bent crystal. The deflection of protons at single passage through the crystal has been simulated. The results of the experiment on the deflection of a circulating beam at the U-70 accelerator (Institute for High Energy Physics, Protvino, Moscow region) are presented. It has been shown that the efficiency of the stochastic deflection mechanism increases with a decrease in the energy, whereas the efficiency of the planar channeling for deflection decreases.     

Channeling and axial to planar channeling transition of protons in magnesium oxide

The channeling of 1.7 MeV protons along 〈100〉 axial direction, (100), (110) and (111) planar directions in magnesium oxide single crystals and axial to planar channeling transitions from 〈100〉 to (100), (110) and (210) have been studied experimentally. The experimental data and preliminary analysis of results are presented.     

Surface channeling of protons and electrons on reflection by a single crystal

Computer modeling is used to investigate the reflection of 0.67-MeV protons and 1-MeV electrons by the (110) face of an Au single crystal for angles of divergence < _cr of the incident beam with the direction 110 lying in the surface. The angular distributions and reflection coefficients of protons and electrons are compared. Several maxima are found in the angular distributions. In additon to the specular-reflection maximum at = there is a maximum at > for protons and a maximum at < for electrons. The maxima in the angular distributions are attributed to multiple scattering at atomic chains of the crystal surface. An analytic approximation of the reflection coefficient for protons K_cor() is given. The great contribution to the reflected flux from particles channeled in the surface layer allows it to be used for structural analysis of crystal surfaces.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 85–90, March, 1979.     

Enhanced planar channeling of MeV protons through thin crystals

At certain tilt alignments between a MeV proton beam and a planar channeling direction, a single interface lattice rotation within a crystal can result in a lower rate of dechanneling than at planar alignment in a perfect crystal. Such planar channeling enhancement arises when the beam passes through a layer thickness which is a half-multiple of the oscillation wavelength and then encounters a small interface rotation which is matched to the beam tilt angle. The beam is projected into the center of the phase space ellipse below the interface, resulting in certain trajectories undergoing a reduction in their transverse energy, in a manner analogous to stochastic cooling or atom laser cooling.     

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.     

Influence of incoherent scattering on stochastic deflection of high-energy negative particle beams in bent crystals

An investigation on stochastic deflection of high-energy negatively charged particles in a bent crystal was carried out. On the basis of analytical calculation and numerical simulation it was shown that there is a maximum angle at which most of the beam is deflected. The existence of a maximum, which is taken in the correspondence of the optimal radius of curvature, is a novelty with respect to the case of positively charged particles, for which the deflection angle can be freely increased by increasing the crystal length. This difference has to be ascribed to the stronger contribution of incoherent scattering affecting the dynamics of negative particles that move closer to atomic nuclei and electrons. We therefore identified the ideal parameters for the exploitation of axial confinement for negatively charged particle beam manipulation in future high-energy accelerators, e.g., ILC or muon colliders.     

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.     

Response of a track-etch-based LET-spectrometer to high-energy protons

The spectrometer of linear energy transfer (LET) was developed. It is based on the chemically etched polyallyldiglycolcarbonate (PADC) track-etch detector. LET spectra are estimated through track parameter determination and analysed by an automatic optical image analyser LUCIA G. Three PADC materials were used: 0.5 mm thick Page, 0.5 and 1 mm thick Tastrak; they were exposed to protons with energies up to 1000 MeV. Such energetic protons are generally not directly registrable in any of PADCs mentioned; the tracks observed correspond mostly to secondary particles created through nuclear interactions of primary protons. LET spectra permit to calculate the dose absorbed in the detector due to these secondary particles and to compare it with the ionization collision dose of primary protons. It is observed that the dose due to secondary particles represents a few percent of the ionization collision dose. Their ratio varies slightly with proton energy, and some differences between the three PADCs used were also observed. The importance of results obtained for on-board spacecraft dosimetry is analysed and discussed.