Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory Nufact solid target outline and the shockwave problem

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL 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

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL 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

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL 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

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL 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

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL Schematic outline of a future neutrino factory

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL Schematic of proposed rotating hoop solid target Target material needs to pass through capture solenoid Could be separate ‘bullets’ magnetically levitated

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL 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

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL 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 Shock wave stress intensity contours 4 µs after100 kJ, 1 ns proton pulse

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL Pulse power densities for various targets

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL 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

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL 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?)

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL 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

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL 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)

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL 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 materials can 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)

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL Study by Alec Milne Fluid Gravity Engineering Limited “Cylindrical bar 1cm in radius is heated instantaneously from 300K to 2300K and left to expand”

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL The y axis is radius (metres) Study by Alec Milne, Fluid Gravity Engineering Limited

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL Can ANSYS be used to study proton beam induced shockwaves? Equation of state giving shockwave velocity v. particle velocity: For tantalum c 0 = 3414 m/s

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL Can ANSYS be used to study proton beam induced shockwaves? Equation of state giving shockwave velocity v. particle velocity: For tantalum c 0 = 3414 m/s Cf: ANSYS implicit wave propagation velocity : ie same as EoS for low particle velocity

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL ANSYS benchmark study: same conditions as Alec Milne/FGES study i.e.ΔT = 2000 K The y axis is radial deflection (metres)

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL Comparison between Alec Milne/FGES and ANSYS results Alec Milne/ FGES ANSYS Amplitude of initial radial oscillation 100 μm120 μm Radial oscillation period 7.5 μs8.3 μs Mean (thermal) expansion 150 μm160 μm

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL 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

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL 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

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL ANSYS benchmark study: same conditions as Alec Milne/FGES study - EXCEPT ΔT = 100 K (not 2000 K) = 400 x 10 6 Pa 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:

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL 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

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL Elastic shock waves in a candidate solid Ta neutrino factory target Temperature jump after 1 ns pulse (Initial temperature = 2000K )

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL 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)

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL 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?)

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL 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

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL Elastic shock wave studies for draft ISOLDE proposal Temperature jump after 2.4 μs pulse (Initial temperature = 2000K )

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL Elastic shock wave studies for draft ISOLDE proposal Temperature profile at centre of cylinder over 4 x 250 ns bunches

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL 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

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL 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)

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL Comparison between Nufact target and ISOLDE test Temperature jump after 2.4 μs pulse (Initial temperature = 2000K ) Peak power density = 300 J/cc in both cases

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL Effect of pulse length on shockwave magnitude

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL Fibre optic strain gauge system for measuring stress waves in a proton beam window Nick Simos, H. Kirk, P. Thieberger (BNL), K. McDonald (Princeton)

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL 2.4 TP, 100 ns pulse

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL 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

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL Electron Gun Steel Beam Stop Aperture Plate Light pipe Aperture plate Optical Transport Window and bellows To Spectrometer Ta foils

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL Electron Scanning: Static Load Upper clamp Lower guide 50 Hz Repetition (100 Hz skip across foils) Beam Design Path

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL Target Foils 25 µm Tantalum Weight Connectors

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL Electron Beam Machine EB1 Electron Beam welder vacuum chamber CNC table

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL c.500 nmc.1100 nm Intensity v wavelength of light radiated by Ta foils

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL Time profile 20 x 0.5 ms exposures per ‘pulse’ (sweep) 0 ms 128 ms

Collimation for the Linear Collider 15 th Feb 2005 Chris Densham RAL diamond: thermal absorbers J Butterworth (RAL) diamond front end + crotch absorbers: synchrotron radiation => 420 W/mm 2 heat flux in confined space