<p> JLAB-TN-07-053</p><p>JLAB-TN-07-053 SHMS Optics Study John J. LeRose These are the results of a SNAKE based study of the optical properties of the Hall C Super High Momentum Spectrometer (SHMS). In this study field maps calculated using TOSCA were installed in a working model of the SHMS1. The bender, Q1, Q2, Q3, and the dipole were arranged as in Figure 1. The magnetic fields were adjusted to reproduce the design 1st order transfer matrix2. The achieved 1st order terms are summarized in Table 1. </p><p>Figure 1: General layout of SHMS</p><p>(x|x0) = -1.274 (x|θ0) = -0.001 (x|δ) = 1.650</p><p>(θ|x0) = -0.053 (θ|θ0) = -0.785 (θ|δ) = 0.318</p><p>(y|y0) = -1.634 (y|φ0) = 0.000 (y|δ) = -0.038</p><p>(φ|y0) = -0.274 (φ|φ0) = -0.619 (φ|δ) = 0.018 Table 1: 1st order matrix elements achieved in the SNAKE model (units are meters and radians)</p><p>After the first order properties expected from the Transport studies were achieved, a large number (~5000) of random trajectories spanning the full acceptance of the spectrometer were traced through the spectrometer. These trajectories were then used as input to a fitting program (MUDIFI) that determines the best-fit polynomials reconstructing the target parameters (, 0, y0, and φ0) of the trajectories based on their positions and angles </p><p>(xf, yf, f, and φf) in the detectors. The sensitivity to measurement errors in the detectors can then be explored in a Monte-Carlo fashion. 1 Maps and geometric details were provided by Paul Brindza, Steve Lassiter, and Mike Fowler 2 1st order TRANSPORT from Chen Yan via Rolf Ent. JLAB-TN-07-053</p><p>σx = 111 um σθ = 0.274 mrad</p><p>σy= 154 um σφ = 0.382 mrad Table 2: SHMS detector performance specifications3 at 8 GeV/c. Figure 2 shows the results of the fitting (red, no error curves) and the achieved resolutions (blue, with 8 GeV/c errors) when the detector performance specifications of Table 2 are randomly superimposed on the fitted polynomial resolutions.</p><p>Summary:</p><p>In terms of resolution there aren’t any surprises. Optimal magnet positions were slightly different than those shown in figure 1. Most notably, Q1 was moved 3.25 cm further from the beam line in order to get the central ray on axis in Q1 after a 3° bend (no one should be upset by this). The only possible discovery of note is that the vertical, θ, acceptance (±40 mrad) is considerably less than what appears in the Transport Deck (±55 mrad) and even this sort of thing is typical when going from Transport, using idealized magnets, to raytracing with realistic magnets. </p><p>3 Provided by Tanja Horn JLAB-TN-07-053</p><p>Figure 2: Blue points and lines are the achieved resolutions (σ’s) for the SHMS using fitted reconstruction polynomials and detector performance specifications of Table 2. The red points and lines show the resolutions achieved with the fitted polynomials alone (i.e. with error free detectors).</p>