Volume Reflection Dependence of $400\mathrm{GeV}/c$ Protons on the Bent Crystal Curvature

The trend of volume reflection parameters (deflection angle and efficiency) in a bent (110) silicon crystal has been investigated as a function of the crystal curvature with $400\mathrm{GeV}/c$ protons on the H8 beam line at the CERN Super Proton Synchrotron. This Letter describes the analysis performed at six different curvatures showing that the optimal radius for volume reflection is approximately 10 times greater than the critical radius for channeling. A strong scattering of the beam by the planar potential is also observed for a bend radius close to the critical one.

Figure 1

The effective potentials for the (110) planes of a silicon crystal bent with a radius $R=35.71\mathrm{m}$ (a) and 3.76 m (b) for $400\mathrm{GeV}/c$ protons. The coordinate $x$ is measured in the direction opposite to the radial one; $d_p=1.92\AA$ is the planar channel width (distance between the two walls of each potential well) and $\Delta U_{ef}=(pv/R)d_p$ is the potential inclination along the channel. The trajectory of a particle being reflected with a turning point in the fourth channel is shown. The position of the corresponding reflecting plane is shown by a vertical dashed line at $x=4d_p$. The thicker lines show the turning point regions.

Figure 2

(a) Experimental layout on the H8 beam line at the CERN SPS. Si1-Si4 are the silicon microstrip detectors, $g$ is the goniometer. (b) View of the (110) silicon crystal strip bent along its height (principal bending). The anticlastic bending with a radius $R$ generated along the strip width has been used for the beam deflection. The beam axis line is shown and the dimensions of the crystal given in mm.

Figure 3

The deflection angle distribution of the $400\mathrm{GeV}/c$ proton beam due to VR in the (110) silicon crystal bent with $R=35.71\mathrm{m}$ (a) and $R=3.76\mathrm{m}$ (b). The parameters of the Gaussian fit: the mean deflection angle ${\theta }_{vr}=14.08\mu \mathrm{rad}$ (a) and $8.68\mu \mathrm{rad}$ (b); the rms deviation ${\sigma }_{vr}=5.70\mu \mathrm{rad}$ (a) and $7.28\mu \mathrm{rad}$ (b). The hatched histogram area with angles smaller than ${\theta }_{vr}+3{\sigma }_{vr}$ defines the VR efficiency $P_{vr}$.

Figure 4

The dependencies of the VR parameters on the crystal curvature and the bending radius $R$: (a) the deflection angle ${\theta }_{vr}$ (dots) and its rms deviation due to the potential scattering ${\overline{\sigma }}_{vr}$ (squares), (b) the VR inefficiency $\epsilon$.