Enhanced Beam Deflection in Bent Crystals using Multiple Volume Reflection

(1) 4 (3) / 6 cm GeV R pv c ≈ Volume reflection [7] occurs when the entrance beam becomes tangential to the curved lattice within the bulk of the crystal, rather than at the entrance face, resulting in reflection off the coherent field of curved lattice planes towards alignment with the entrance face. Volume reflection has been simulated for 980 GeV protons and 100 GeV/u Au ions, producing a typical volume reflection angle of ~θc [8]. In a recent paper [9] enhanced volume reflection produced by a single bent crystal due to the repeated passage of ions in high-energy circular accelerators was studied with the aim of reducing the local background rate for beam collimation.

Volume reflection of MeV protons along the lattice curvature of thin, bent layers was recently studied [10] using Monte Carlo simulations with the code FLUX [11]. Periodic oscillations in the volume reflected angular distribution were observed when the angular scattering for randomly aligned trajectories was less than θ c . In thicker layers no oscillations were observed, instead producing a uniform reflected angle of ~0.7θ c . The observations were extended to higher energies to predict when similar oscillations in the volume reflected angular distribution and nuclear encounter probability may be present in present beam extraction and collimation experiments at GeV and TeV energies.

The use of large area bent crystals as a space shield to deflect high-energy, heavy ions (HZE ions) of all atomic numbers away from spacecraft was recently proposed [12]. When the front surface of such a bent crystal shield is aligned with HZE ions, most undergo bent crystal channeling and are deflected through the full lattice curvature angle δ. The bending efficiency is limited to about 75% by the planar channelling minimum yield of about 25%. This approach only works for ions which have an entrance angle at the surface of ±θ c to the planar bending direction.

Motivations for the present study are to provide a detailed study of the angular deflection and dispersion of high-energy ions by multiple volume reflection through several bent crystals layers and also to devise schemes capable of deflecting with high efficiency a larger range of entrance angles of HZE ions using bent crystal shields. This study is also relevant to applications on the use of bent crystals as a means of collimating and extracting beams from accelerators. Two computer codes are used to simulate 10,000 ion trajectories through several bent layers over a wide range of energies. The Monte Carlo code FLUX [11] which uses a binary collision model in conjunction with the Ziegler-Biersack-Littmark potential [13] is used to simulate ions with energies up to 100 MeV/n through thin layers. The code CATCH [14], based on a continuummodel [15] with Moliere potential and taking into account the single and multiple scattering on crystal electrons and nuclei, is used to simulate the passage of 400 and 980 GeV protons through much thicker layers. Fig. 1a shows the bent crystal coordinate system used in this paper. The beam entrance angle to the channeling planes of the entrance surface is θ and the lattice is curved through an angle δ. Ions which enter the surface planes within ±θ c undergo bent crystal channeling and most are deflected through an angle of δ. Ions which enter the front surface with an angle of -θ subtended by the lattice curvature angle undergo volume reflection and are deflected by an angle up to 2θ c to a more positive exit angle. Fig. 1b shows the coordinate system used for stacking two or more curved layers together, each of which is rotated by an angle of ∆ with respect to that above it. A value of ∆ = 0.0° is equivalent to a single continuous layer curved through an angle of

The first aspect considered is the relationship between the volume reflection angle and the radius of curvature R of the silicon lattice planes through which the beam passes. Fig. 2 shows the reflection angle θ R of the transmitted beam for 5 MeV protons and 100 MeV/nucleon Au ions for different curvature radii of the (110) planes using FLUX, and for 980 GeV protons for the (111) planes using CATCH. The curvature radii are normalized to R c and θ R normalized to θ c to show similar trends observed over a wide range of ion energies. From Fig. 2 the ratio θ R /θ c is approximately proportional to log (R/R c ). For R/R c > 30, almost a straight lattice, θ R tends to constant value of 1.4-1.6θ c . θ R decre

…(Full text truncated)…