Double volume reflection of a proton beam by a sequence of two bent crystals

The doubling of the angle of beam deflection due to volume reflection of protons by a sequence of two bent silicon crystals was experimentally observed at the 400 GeV proton beam of the CERN SPS. A similar sequence of short bent crystals can be used as an efficient primary collimator for the Large Hadron Collider.

. Schematic top view of the experimental layout in the horizontal plane. QM1 and QM2 are two quasimosaic crystals installed on the rotational stage RS of the goniometer. The QM1 crystal is placed on the additional linear stage LS that allows to align QM1 with QM2. SD1, SD2, SD3 are silicon microstrip detectors, GC is a position sensitive gas chamber. The distances between the crystal and SD1, SD2, SD3 and GC equal to 0.5, 0.5, 64.8 and 70 m, respectively. The lines represents the trajectories of the protons after the crystals, the unperturbed beam (lower dashed) crossing the crystals both in amorphous position, the beam reflected by the first crystal only (upper dashed), and the double-reflected beam (solid). Deflection of channeled particles in a bent crystal is a wellestablished phenomenon and it is used in experiments with high-energy charged particle beams. Under certain conditions non-channeled particles can be deflected because of the reversal of their transverse momentum by the bent atomic planes in the crystal volume [1,2]. In a recent experiment at CERN it was found that volume reflection has an efficiency larger than 95% for the deflection of a 400 GeV proton beam at an angle of about 14 µrad [3].
However, larger deflection angles would be more appropriate for a realistic use of such crystals in the Large Hadron Collider (LHC) collimation system. This encouraged us to study sequential reflections of particles in short bent crystals. Using crystals similar to that described in [2] and the same beam and experimental setup described in [3,4] we have carried out an experiment on double volume reflection in two crystals, the results of which are reported in this Letter. Fig. 1 shows schematically the experimental layout [4]. Two silicon plates QM1 and QM2 with (111) atomic planes bent of ∼70 µrad along the plate thickness of ∼0.8 mm were installed on a high precision goniometer. The (111) planes of QM1 plate were fan-shaped in a way that made possible to align them with respect to the QM2 plate within the proton beam spot using the transverse linear motion of the QM1 support. The silicon strip detector SD1 before the crystals was used to select a fraction of the incident beam, the silicon strip detectors (SD2 and SD3) and position sensitive gas chamber (GC) were used to measure the angles of the particles exiting the crystals.
In Fig. 2 the angular scans performed before (a) and after (b) the fine relative alignment of the two crystals are shown. The color on the plots shows the relative beam intensity measured for the various deflection angles reported on the x-axis while on the y-axis the goniometer angle is reported.
The channeling peaks for both QM2 and QM1 crystals are visible as the two isolated spots at negative values of the beam deflection angles in Fig. 2(a). This scan was obtained before the alignment and therefore the two peaks appear at different angular positions of the goniometer. The mean deflection angles of the channeled protons are measured with the SD2 and SD3 detectors to be (68.6 ± 0.9) µrad and (78.1 ± 4.8) µrad for the QM2 and the QM1 crystal, respectively: they are equal to the bending angles of the (111) atomic planes in the crystals. The  region of the scan with the proton beam deflected to the opposite direction with respect to the channeled protons is due to the volume reflection effect. The deflection angle and efficiency of a single reflection are found to be (11.70 ± 0.51) µrad and (98.27 ± 0.50)%, respectively for QM2 and (11.90 ± 0.59) µrad and (97.80 ± 0.64 )% for QM1. The efficiency was defined as the ratio of the proton number within ±3σ around the distribution maximum for the crystal orientation corresponding to volume reflection of protons to the same value for the orientation with amorphous scattering of protons in the crystal. Both values were normalized on the same number of protons hitting the crystal. It is clear in Fig. 2(a) that the volume reflection regions corresponding to the QM2 and QM1 crystals are partly superimposed resulting in the deflection of the proton beam at larger angles than in the case of a single reflection.
The angle and efficiency of double reflection were accurately measured with finely aligned crystals, and the result is shown in Fig. 2(b). In this measurement the channeling peaks and the volume reflection regions for both crystals fully coincide. Fig. 3 shows the beam profiles for three different cases corresponding to either amorphous scattering, single or double reflections of protons in the crystals. The deflection angle of the double reflected beam is extracted with Gaussian fits to the beam profile distributions obtained with the SD2 and SD3, detectors, as shown in Fig. 4, and it is found to be equal to 23.23 ± 0.18(stat) ± 0.09(syst) µrad, that is twice larger than in single reflection. The efficiency of double reflection is equal to 96.73 ± 0.38(stat) ± 0.50(syst)%. The systematic uncertainties on the deflection angle and efficiency measurements are mainly related to the Gaussian model used to describe the beam profiles.
Thus, the experiment demonstrated a feasibility of multiple volume reflections in a sequence of short bent crystals with high efficiency and with beam deflection angle proportional to the number of reflections. This result opens new ways to develop crystal optics for the manipulation of high-energy charged particle beams.