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Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory

Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory. Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory. Nufact solid target outline and the shockwave problem. Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory.

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Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory

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  1. Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory Chris Densham RAL

  2. Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory • Nufact solid target outline and the shockwave problem Chris Densham RAL

  3. Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory • Nufact solid target outline and the shockwave problem • Codes used for the study of shockwaves Chris Densham RAL

  4. Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory • Nufact solid target outline and the shockwave problem • Codes used for the study of shockwaves • Calculations of proton beam induced stress waves using the ANSYS FEA Code Chris Densham RAL

  5. Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory • Nufact solid target outline and the shockwave problem • Codes used for the study of shockwaves • Calculations of proton beam induced stress waves using the ANSYS FEA Code • Measurements of proton beam induced stress waves Chris Densham RAL

  6. Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory • Nufact solid target outline and the shockwave problem • Codes used for the study of shockwaves • Calculations of proton beam induced stress waves using the ANSYS FEA Code • Measurements of proton beam induced stress waves • Experiments with electron beams Chris Densham RAL

  7. Schematic outline of a future neutrino factory Chris Densham RAL

  8. Schematic of proposed rotating hoop solid target • Target material needs to pass through capture solenoid • Could be separate ‘bullets’ magnetically levitated Chris Densham RAL

  9. Schematic of proposed rotating hoop solid target • Target material needs to pass through capture solenoid • Could be separate ‘bullets’ magnetically levitated • Section of target showing temperatures after single 100 kJ,1 ns • pulse • Radiation cooled – needs to operate at high temperatures, c.2000ºC Chris Densham RAL

  10. Schematic of proposed rotating hoop solid target • Target material needs to pass through capture solenoid • Could be separate ‘bullets’ magnetically levitated Shock wave stress intensity contours 4 µs after100 kJ, 1 ns proton pulse • Section of target showing temperatures after single 100 kJ,1 ns • pulse • Radiation cooled – needs to operate at high temperatures, c.2000ºC Chris Densham RAL

  11. Pulse power densities for various targets Chris Densham RAL

  12. Codes used for study of shock waves • Specialist codes eg used by Fluid Gravity Engineering Limited – Arbitrary Lagrangian-Eulerian (ALE) codes (developed for military) • Developed for dynamic e.g. impact problems • ALE not relevant? – Useful for large deformations where mesh would become highly distorted • Expensive and specialised Chris Densham RAL

  13. Codes used for study of shock waves • Specialist codes eg used by Fluid Gravity Engineering Limited – Arbitrary Lagrangian-Eulerian (ALE) codes (developed for military) • Developed for dynamic e.g. impact problems • ALE not relevant? – Useful for large deformations where mesh would become highly distorted • Expensive and specialised • LS-Dyna • Uses Explicit Time Integration (ALE method is included) • suitable for dynamic e.g. Impact problems i.e. ΣF=ma • Should be similar to Fluid Gravity code (older but material models the same?) Chris Densham RAL

  14. Codes used for study of shock waves • Specialist codes eg used by Fluid Gravity Engineering Limited – Arbitrary Lagrangian-Eulerian (ALE) codes (developed for military) • Developed for dynamic e.g. impact problems • ALE not relevant? – Useful for large deformations where mesh would become highly distorted • Expensive and specialised • LS-Dyna • Uses Explicit Time Integration (ALE method is included) • suitable for dynamic e.g. Impact problems i.e. ΣF=ma • Should be similar to Fluid Gravity code (older but material models the same?) • ANSYS • Uses Implicit Time Integration • Suitable for ‘Quasi static’ problems ie ΣF≈0 Chris Densham RAL

  15. Implicit vs Explicit Time Integration • Explicit Time Integration (used by LS Dyna) • Central Difference method used • Accelerations (and stresses) evaluated at time t • Accelerations -> velocities -> displacements • Small time steps required to maintain stability • Can solve non-linear problems for non-linear materials • Best for dynamic problems (ΣF=ma) Chris Densham RAL

  16. Implicit vs Explicit Time Integration • Implicit Time Integration (used by ANSYS) - • Finite Element method used • Average acceleration calculated • Displacements evaluated at time t+Δt • Always stable – but small time steps needed to capture transient response • Non-linear materialscan be used to solve static problems • Can solve non-linear (transient) problems… • …but only for linear material properties • Best for static or ‘quasi’ static problems (ΣF≈0) Chris Densham RAL

  17. Study by Alec Milne Fluid Gravity Engineering Limited • “Cylindrical bar 1cm in radius is heated instantaneously from 300K to 2300K and left to expand” Chris Densham RAL

  18. Study by Alec Milne, Fluid Gravity Engineering Limited The y axis is radius (metres) Chris Densham RAL

  19. Can ANSYS be used to study proton beam induced shockwaves? • Equation of state giving shockwave velocity v. particle velocity: For tantalum c0 = 3414 m/s Chris Densham RAL

  20. Can ANSYS be used to study proton beam induced shockwaves? • Equation of state giving shockwave velocity v. particle velocity: For tantalum c0 = 3414 m/s Cf: ANSYS implicit wave propagation velocity : • ie same as EoS for low particle velocity Chris Densham RAL

  21. ANSYS benchmark study: same conditions as Alec Milne/FGES study i.e.ΔT = 2000 K The y axis is radial deflection (metres) Chris Densham RAL

  22. Comparison between Alec Milne/FGES and ANSYS results Chris Densham RAL

  23. ANSYS benchmark study: same conditions as Alec Milne/FGES study - EXCEPT ΔT = 100 K (not 2000 K) Surface deflections in 1 cm radius Ta rod over 20 μs after ‘instantaneous’ uniform temperature jump of 100 K Chris Densham RAL

  24. ANSYS benchmark study: same conditions as Alec Milne/FGES study - EXCEPT ΔT = 100 K (not 2000 K) Elastic stress waves in 1 cm radius Ta rod over 20 μs after ‘instantaneous’ (1ns) pulse Stress (Pa) at : centre (purple) and outer radius (blue) Surface deflections in 1 cm radius Ta rod over 20 μs after ‘instantaneous’ uniform temperature jump of 100 K Chris Densham RAL

  25. ANSYS benchmark study: same conditions as Alec Milne/FGES study - EXCEPT ΔT = 100 K (not 2000 K) Elastic stress waves in 1 cm radius Ta rod over 20 μs after ‘instantaneous’ (1ns) pulse Stress (Pa) at : centre (purple) and outer radius (blue) Surface deflections in 1 cm radius Ta rod over 20 μs after ‘instantaneous’ uniform temperature jump of 100 K Cf static case: = 400 x 106 Pa Chris Densham RAL

  26. Elastic shock waves in a candidate solid Ta neutrino factory target • 10 mm diameter tantalum cylinder • 10 mm diameter proton beam (parabolic distribution for simplicity) • 300 J/cc/pulse peak power (Typ. for 4 MW proton beam depositing 1 MW in target) • Pulse length = 1 ns Chris Densham RAL

  27. Elastic shock waves in a candidate solid Ta neutrino factory target Temperature jump after 1 ns pulse (Initial temperature = 2000K ) Chris Densham RAL

  28. Elastic shock waves in a candidate solid Ta neutrino factory target Elastic stress waves in 1 cm diameter Ta cylinder over 10 μs after ‘instantaneous’ (1ns) pulse Stress (Pa) at : centre (purple) and outer radius (blue) Chris Densham RAL

  29. Material model data • At high temperatures material data is scarce… • Hence, need for experiments to determine material model data e.g. • Standard flyer-plate surface shock wave experiment (difficult at high temperatures and not representative of proton beam loading conditions) • Scanning electron beam (can achieve stress and thermal cycling ie fatigue but no ‘shock’ wave generated) • Current pulse through wire • Experiment at ISOLDE (Is it representative? Can we extract useful data?) Chris Densham RAL

  30. Chris Densham RAL

  31. Elastic shock wave studies for draft ISOLDE proposal • 3 mm diameter Ta cylinder • Beam diameter = 1 mm (parabolic distribution for simplicity) • Peak power deposited = 300 J/cc • Pulse length = 4 bunches of 250 ns in 2.4 μs Chris Densham RAL

  32. Elastic shock wave studies for draft ISOLDE proposal Temperature jump after 2.4 μs pulse (Initial temperature = 2000K ) Chris Densham RAL

  33. Elastic shock wave studies for draft ISOLDE proposal Temperature profile at centre of cylinder over 4 x 250 ns bunches Chris Densham RAL

  34. Elastic shock wave studies for draft ISOLDE proposal Temperature profile at centre of cylinder over 4 x 250 ns bunches Radial displacements of target cylinder surface during and after pulse Chris Densham RAL

  35. Elastic shock wave studies for draft ISOLDE proposal Temperature profile at centre of cylinder over 4 x 250 ns bunches Elastic stress waves target rod over 5 μs during and after pulse Stress (Pa) at : centre (blue) outer radius (purple) beam outer radius (red) Chris Densham RAL

  36. Comparison between Nufact target and ISOLDE test Peak power density = 300 J/cc in both cases Temperature jump after 2.4 μs pulse (Initial temperature = 2000K ) Chris Densham RAL

  37. Effect of pulse length on shockwave magnitude Chris Densham RAL

  38. Fibre optic strain gauge system for measuring stress waves in a proton beam windowNick Simos, H. Kirk, P. Thieberger (BNL), K. McDonald (Princeton) Chris Densham RAL

  39. 2.4 TP, 100 ns pulse Chris Densham RAL

  40. Electron Beam Thermal Cycling Tests at TWI • CJ Densham, PV Drumm, R Brownsword (RAL) • 175 keV Electron Beam at up to 60 kW beam Power (CW) • Aims: • High power density electron beam scanned at 4 km/s across foils • Mimics the thermal cycling of tantalum foils to NF target ΔT levels, at a similar T • Lifetime information on candidate target materials Chris Densham RAL

  41. Ta foils Electron Gun Steel Beam Stop Aperture plate Optical Transport Window and bellows Aperture Plate Light pipe To Spectrometer Chris Densham RAL

  42. Electron Scanning: Upper clamp Beam Design Path 50 Hz Repetition (100 Hz skip across foils) Lower guide Static Load Chris Densham RAL

  43. Target Foils 25 µm Tantalum Weight Connectors Chris Densham RAL

  44. Electron Beam Machine EB1 Electron Beam welder vacuum chamber CNC table Chris Densham RAL

  45. Chris Densham RAL

  46. Intensity v wavelength of light radiated by Ta foils c.500 nm c.1100 nm l Chris Densham RAL

  47. Time profile 20 x 0.5 ms exposures per ‘pulse’ (sweep) 128 ms 0 ms Chris Densham RAL

  48. diamond: thermal absorbersJ Butterworth (RAL) diamond front end + crotch absorbers: synchrotron radiation => 420 W/mm2 heat flux in confined space Chris Densham RAL

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