Wide-range Precision Alignment for the Gem Muon System

The GEM muon system [1] is designed to achieve high momentum resolution by precisely measuring muon trajectories at three equidistant superlayers separated by a long lever arm in a large magnetized volume. In order to retain the desired precision at high momentum (i.e. ∆pt/pt ≈ 5% for the barrel detector at pt = 500 GeV/c), the muon system must determine the net 3-point sagitta of a muon track to σ = 55 μm in the bending plane. Chamber accuracies, fiducialization placement, alignment transfers, and alignment measurement error are included in this allotment. A set of realizable requirements on these quantities that combine to maintain this 55 μm tolerance are specified in Table 4-1 of Ref. [1], where it has been determined that the false sagitta (i.e. error in the measurement of the bending-plane misalignment of the three superlayers) must be limited to σ = 25 μm. Rather than place the drift chamber superlayers with such extreme precision (and require a similar degree of stability from the support structure), the relative positions of the superlayers are actively monitored and the reconstructed spacepoints are correspondingly compensated. A projective alignment scheme that relaxes the chamber positioning requirements in all coordinates has been proposed [2] and simulated [2,3]. Under this scheme, a set of six 3-point straightness monitors are used to measure the superlayer misalignment orthogonal to straight lines that extend along the muon path. Three straightness monitors run from the inner to outer superlayers at opposite edges of a muon alignment "tower" (as depicted in Fig. 2 of Ref. [4]), providing alignment measurements that determine a linear/quadratic interpolation function able to correct alignment-induced false sagitta errors for a projective muon track at arbitrary incidence. This alignment scheme is discussed in more detail elsewhere in these proceedings [4]; its immediate consequence is that the muon superlayers may be placed in the GEM detector relatively coarsely; the current requirements (i.e. Table 1 of Ref. [4]) dictate a placement of ±1 to ±3 mm and ±1 to ±5 milliradians (depending on the superlayer and coordinate), which should be realizable with standard survey techniques (for several practical reasons, it is desirable to avoid highly exacting positioning/stability requirements for structures approaching the size of the GEM muon system, which is 5000 m3 in volume). Current efforts indicate that it should be possible to extend this range even further by employing an optimal estimator to incorporate other information, such as muon data and sagitta-orthogonal alignment measurements, and improving the θ-coordinate track resolution; the false sagitta then could be appropriately compensated with superlayer misalignments reaching the order of a centimeter. In conclusion, the GEM muon alignment system requires a precision straightness monitor to be developed that exhibits a resolution better than σ = 25 μm across a dynamic measurement range approaching a centimeter. This system must perform at this specification in a magnetic field of order 1T and function with an optical path reaching beyond 9 meters (the maximum projective distance between inner and outer superlayers). Since many of these devices are required (i.e. the extreme all-projective alignment system baselined in Ref. [1] requires over 3000 straightness monitors), they must be inexpensive, easy to calibrate/install, and function reliably in the anticipated detector environment.