LHCb-PUB-214-12 April 1, 214 Determination of the aperture of the LHCb VELO RF foil M. Ferro-Luzzi 1, T. Latham 2, C. Wallace 2. 1 CERN, Geneva, Switzerland 2 University of Warwick, United Kingdom LHCb-PUB-214-12 1/4/214 Abstract Hadronic interactions in the material of the LHCb Vertex Locator are used to determine the aperture that the RF foil presents to the LHC beam. The aperture is found to be 4.5 mm, to be compared with the nominal value of 5.5 mm. The difference is well within the tolerance of 2.4 mm considered for the safety of the beam.
1 Introduction Decreasing the inner radius of the Vertex Locator (VELO) is a highly desirable scenario for the impending upgrade of the detector [1], since it should lead to improved precision on the measurement of the impact parameter of tracks. Doing so, however, means also decreasing the inner radius of the RF foil from the current value of 5.5 mm. The new nominal radius being considered is 3.5 mm [2]. In order to guarantee the safety of the machine it is important to know just how well the current nominal value of 5.5 mm (see Figure 1 top) has been reproduced with the actual foil cf. the design tolerances [3]. Tomography data from hadronic interactions in the VELO material includes the entire length of the RF foil. This is made possible by using data from beam-gas interactions, which can occur at any point along the beam line. The particles emitted travel within the primary vacuum before possibly interacting with the foil material. The tracks from this secondary interaction continue on and are detected by the VELO. This allows a precise vertex to be formed and hence for the material in the foil to be precisely mapped. The data used in this analysis were taken during proton-proton running of the LHC in 211 and 212, where the single beam energy was 3.5 TeV and 4 TeV respectively. Only events determined by the software trigger to be consistent with a beam-gas interaction are considered. In addition, the event must have been recorded when bunches are not present in both beams at the interaction point, i.e. we select beam-empty, empty-beam and empty-empty but reject beam-beam configurations. Vertices are reconstructed from three or more tracks that each have hits in at least three R and Φ VELO sensors. Vertices along the beamline are removed with a cut on vertex radius. Requiring only one reconstructed vertex in each event effectively removes any remaining non-material interactions. The x and y positions of each vertex in the local VELO frame are calculated by subtracting the co-ordinate of the beamspot position (as given by the VELO motion system) from that of the vertex in the global LHCb frame. The resulting data can be used to make a determination of the aperture available to the beam due to the mechanical tolerances of the RF foil construction and positioning. 2 Results The method for the determination of the true aperture is to examine the vertices attributed to the RF foil in the z regions where it is at its smallest radius, i.e. the regions around the sensor slots. Figure 2 shows how the foil radius varies with the z position in these regions. We take windows of ±1 mm around the nominal z position of the centre of the slot in order to minimise the effect of the curvature in the rz plane on the measurement but still have a sufficiently large number of vertices to make a good fit. The radius of curvature in the rz plane is 5.8 mm (as seen in Fig 1 bottom). Using this value and the ±1 mm window we find the effect of this curvature will be of the order of.5% on the measured aperture and as such is negligible compared with the other uncertainties. Figure 3 shows the xy projection in two such regions, one where the slot is occupied by a sensor and one where it is empty. The structure of the RF foil from both halves of the VELO can be clearly 1
Figure 1: Projection in the (top) xy and (bottom) rz planes, showing the designed cross section of the current RF foil at the point where the foil approaches closest to the beam axis. seen. Requirements (indicated by the lines in Fig. 3) are placed on the positions of the vertices to select only those in the region at small radius where the shape of the foil is approximately annular. These data are then fitted to a circle with variable centre position and radius. The results for all slots on both sides, are given in Fig. 4. The variation of the x and y co-ordinates of the centre of the fitted circle and its radius are given as a 2
Vertex r [mm] 2 18 16 14 12 1 8 6 4 2 LHCb VELO - Collision Data 15 2 25 Vertex z [mm] Figure 2: The rz-plane distribution of vertices of hadronic interactions with y < 5 mm in the region of VELO module VL7C. function of the z position of the slot. One notes a dependence of the y-centre on the z position. This is partly explained by the actual box shape (as observed in metrological measurements performed on the right box before installation) and partly by tilts of the detector halves in the yz plane. The spread of the x-centre values is representative of the actual imperfections in the foil geometry. The aperture presented by each slot is overlaid on a single plot, assuming a circular shape in the fitted region and with a.15 mm reduction in the radius to account for the thickness of the foil. The value of.15 mm is half the nominal thickness of the foil before deformation into its final shape. Studies of the foil have shown that the pressing of the foil results in some areas being thinned but no parts have been found to be thicker than the original thickness. Since the determination of the true thickness at each station position from the tomography data is complicated by the varying vertex resolution, the original half thickness of.15 mm was used as a conservative upper bound of the actual half thickness. These results combine to give a value for the aperture of 4.9 mm compared with the nominal value of 5.5 mm. The welding of the foil to the RF box must also be considered. Figure 5 shows the rz projection of the reconstructed vertices in the regions at the upstream and downstream ends of the foil. The protrusion due to the weld is clearly visible, in particular in the downstream direction (positive z). Figure 6 shows the xy projections in the regions around the weld joints: 336 < z < 332 mm and 761 < z < 765 mm. As before, further selections are applied to select only the vertices where the foil shape is approximately annular and the resulting distributions of the radius are also shown in Fig. 6. It can be seen that the welding further reduces the aperture to approximately 4.5 mm. Even so, the difference with respect to the nominal value of 5.5 mm is well within the tolerance of 3
LHCb VELO - Collision Data Vertex y [mm] Vertex y [mm] 3 2 1 3 2 1-1 -1-2 -2 3-2 -3 2 Vertex x [mm] LHCb VELO - Collision Data Vertex y [mm] Vertex y [mm] -3 2 1 3-1 -1-2 -2-3 2 Vertex x [mm] 2 Vertex x [mm] LHCb VELO - Collision Data 1-2 -2 2-3 LHCb VELO - Collision Data -2 2 Vertex x [mm] Figure 3: Vertices of hadronic interactions in the LHCb VELO material. (top) Slots in the foil where a sensor is present: (right) 64 < z < 66 mm, (left) 79 < z < 81 mm. (bottom) Slots in the foil with no sensor present: (right) 384 < z < 386 mm, (left) 399 < z < 41 mm. The vertices selected for further analysis must satisfy the conditions: 4.5 < r < 6.57 mm (indicated by the two green circles), y < 4 mm (indicated by the two horizontal red lines) and x > 2 mm or x < 2 mm (indicated by the vertical blue line). 2.4 mm that was reserved for mechanical imperfections of the foil when considering the safety of the beam [3]. 4
3 Conclusion Tracks originating from hadronic interactions in the material of the VELO have been used to reconstruct the position of those interactions. These in turn have been used to determine the location of the RF foil at each point where it most closely approaches the beam. Combining this information we find that the smallest circular aperture that would fit within the two foils is 4.5 mm compared with the nominal value of 5.5 mm. This is well within the tolerance of 2.4 mm that was considered for the safety of the beam when the design radius was initially chosen. References [1] LHCb collaboration, LHCb VELO Upgrade Technical Design Report, LHCB-TDR-13. [2] R. B. Appleby et al., VELO aperture considerations for the LHCb Upgrade, LHCb- PUB-212-18. [3] Minutes of a meeting on LHC Impedance, held on 12 June 1998, http://wwwslap. cern.ch/collective/impedance.wkg/12-6-98/notes.ps. 5
x-centre [mm] 1.8.6.4.2 -.2 -.4 -.6 -.8-1 5 z [mm] y-centre [mm] 1.8.6.4.2 -.2 -.4 -.6 -.8-1 5 z [mm] radius [mm] 6.4 6.2 6 5.8 5.6 5.4 5.2 5 4.8 4.6 5 z [mm] radius + x-centre [mm] 6.4 6.2 6 5.8 5.6 5.4 5.2 5 4.8 4.6 5 z [mm] y [mm] 4 3 2 1-1 -2-3 -4-5 5 x [mm] Figure 4: Results of fitting a circle to the selected vertices at each slot position. The solid red squares (open blue triangles) indicate the foil with positive (negative) x co-ordinate. (top left) The variation in the x co-ordinate of the centre of the fitted circle. (top right) The variation in the y co-ordinate of the centre of the fitted circle. (middle left) The variation in the radius of the fitted circle. (middle right) The x co-ordinate of the foil at y =, i.e. the sum of the x co-ordinate of the centre and the radius of the fitted circle. (bottom) A visualisation of the true aperture. The solid black circle is the nominal aperture, i.e. a circle of radius 5.5 mm. The dashed blue and red semi-circles correspond to the fitted circles found at each slot position, where the fitted radius has been reduced by.15 mm to take into account the foil thickness. The dotted black circle is the true aperture of 4.9 mm given by the combination of the fitted circles. 6
Figure 5: Vertices of hadronic interactions in the LHCb VELO material. rz projection in the regions where the foil is welded to the sides of the RF box. 7
Figure 6: Vertices of hadronic interactions in the LHCb VELO material. (top) xy projection in the regions of the welding: (left) 336 < z < 332 mm and (right) 761 < z < 765 mm. (bottom) Radius plotted for each point which satisfy the conditions: 4 < r < 6.75 mm (indicated by the two green circles) and y < 4 mm (indicated by the two horizontal red lines). 8