Merlin ARPES elliptical KB mirror M 332 FEA

Merlin ARPES elliptical KB mirror, M 332, FEA Alexis Smith-Baumann 3/7/08

Merlin ARPES M 332 FEA • Mirror bent to elliptical shape – Primary and secondary foci • Apply unequal couples to flat mirror with side shaping – Constant thickness – Varying width to achieve proper curvature along length of mirror (varies moment of inertia)

Mirror specifications • Specification is 2 microradians RMS over central 200 mm for primary focus, best possible over central 160 mm for secondary focus • Mirror geometry: 500 mm long, 25 -30 mm wide, 4 mm thick. • Material is SSt 17 -4 PH • Source distance: 2. 74366 m – Primary image distance: 1. 61822 m. C 1 = 1. 52345 Nm, C 2 = 1. 80922 Nm – Secondary image distance: 3. 11822 m. C 1 = 1. 126 Nm, C 2 = 1. 065 Nm • Angle: 7 degrees

FEA Pre- and Postprocessing • Generated geometry using B-splines based on 1 mm increment profile from Yi-De • Applied ideal moments directly to mirror ends • Applied minimal constraints to mirror to prevent rigid motion • Post processing of data from ANSYS – Shift and rotate mirror surface for direct comparison to ideal ellipse (remove piston and tilt) – Calculate slope error – Remove power and recalculate slope error

Stress • Max stress (away from constraints) is 25 MPa for primary focus, 17 MPa for secondary focus. • Yield strength of SSt 17 -4 PH is 1000 MPa

Displacement • Displacement and slope data along a central, tangential line on the reflective surface of the mirror was further analyzed in Excel

Results: primary focus • Slope error 2. 4 urad over central 200 mm using ideal couples • After removal of power (constant curvature term), slope error of 0. 07 urad over central 200 mm

Results: secondary focus • Slope error 1. 8 urad over central 160 mm using ideal couples • After removal of power (constant curvature term), slope error of 0. 09 urad over central 160 mm

Leaf spring deflection • Leaf springs sized to 1. 65 mm to achieve target deflection of ~10 mm (at actuator)

Boundary conditions in FEA • Moments applied to ends • Gravity applied downward (counterintuitive in ANSYS WB 10. 0) at 7 degree angle • Fixed x, y on one end and y, z on the other at neutral axis