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“Helmholtz” Capture Solenoid Mechanical Structure Calculations Peter Loveridge STFC Rutherford Appleton Laboratory, UK July 2008

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Peter Loveridge, July 2008 Objectives Using the magnetic forces calculated previously... Evaluate the approximate dimensions of the magnet mechanical structure components in the cases where: 1.A fully open Helmholtz gap is required (compatible for a target wheel WITH spokes) 2.The Helmholtz gap is filled with structure material with the exception of a bridging structure across two short unsupported lengths (compatible with a SPOKELESS target wheel) Is the required structure volume compatible with coil/target geometry?

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Peter Loveridge, July 2008 Recap: Magnetic Forces P R2 R1

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Peter Loveridge, July 2008 Recap: Magnetic Forces P R2 R1 Consider how to support axial loads on coil “SC01”

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Peter Loveridge, July 2008 Fully Open Gap: Plate Bending b a t P = FZ / A RbRb RaRa Hand calculation based on flat plate theory... Limit max bending stress in steel plate to, say, 150 MPa: –Plate thickness = 286 mm –Max plate deflection = 0.2 mm

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Peter Loveridge, July 2008 Fully Open Gap: Tensile Retaining Loads P = FZ / A RbRb RaRa t wo t wi L = 903 mm Envisage a retaining structure composed of two cylinders... From flat plate calculation we know: –Outer reaction (R a ) = 93.7 MN/360˚ –Inner reaction (R b ) = 70.0 MN/360˚ Limit max tensile stress in steel retaining structure to, say, 150 MPa: –t wo = 76 mm –t wi = 130 mm –Elongation

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Peter Loveridge, July 2008 Fully Open Gap: ANSYS Mechanical Simulation 180˚ Geometry ExpansionAxial Deflection Plot 0 mm1.2 mm Von-Mises Stress Plot 0 MPa270 MPa Axi-symmetic Mesh 76 mm thick outer cylinder 130 mm thick inner cylinder286 mm thick end plate

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Peter Loveridge, July 2008 Interpretation: Target wheel WITH spokes Target station geometry: –Need to maintain an open axial gap over a significant part of the circumference –Huge axial forces must be transferred out to an external structure Coils at 4.2K, external structure at room-temperature ?! Structure Calculations: –Hand calculations –confirmation by FEA Results: –The volume of structural material required looks extremely prohibitive (see right). Insufficient radial space between NC and SC coils Helmholtz gap filled with structure Coil geometry with required structure volume to maintain a fully open axial gap (drawn to scale) Comments: –Major geometry interference issues to resolve (coils, structure, target-access) –On first investigation the structure requirements for this option do not seem feasible! –NOTE: Have only considered the axial force balance. What about radial forces!

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Peter Loveridge, July 2008 Bridging Structure: Plate bending Hand Calculation for a plate bridging a short unsupported length... Consider a simply-supported rectangular plate –Dimensions W x L x t –Subject to same uniform pressure P Limit max bending stress in steel plate to, say, 150 MPa: –Plate thickness = 170 mm –Max plate deflection = 0.2 mm L W t

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Peter Loveridge, July 2008 Interpretation: SPOKELESS target wheel Coil geometry with required structure volume to bridge a short unsupported length (drawn to scale) Target station geometry: –The Helmholtz gap is filled with structure material with the exception of bridging sections across two short unsupported lengths –Huge axial forces are “internally balanced” (in same way as study-2 magnet) Structure Calculations: –Preliminary hand calculations only –Assumptions yet to be confirmed by FEA Results: –A significant volume of bridging structure material in “Helmholtz gap” region (see right) Current (400 mm) gap appears insufficient Comments: –Reoptimisation of geometry will be required (coils, structure, target-access) ~600 mm Helmholtz gap? Is this feasible? –Structure calculations for this option should be taken further –NOTE: Have only considered the axial force balance. What about radial forces!

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