elastic stress waves in candidate solid targets for a neutrino factory
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/1.jpg)
Elastic Stress Waves in candidate Solid Targets for a
Neutrino Factory
![Page 2: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/2.jpg)
Elastic Stress Waves in candidate Solid Targets for a
Neutrino Factory• Nufact solid target outline and the
shockwave problem
![Page 3: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/3.jpg)
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
![Page 4: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/4.jpg)
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
![Page 5: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/5.jpg)
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
![Page 6: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/6.jpg)
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
![Page 7: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/7.jpg)
Schematic outline of a future neutrino factory
![Page 8: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/8.jpg)
Schematic of proposed rotating hoop solid target • Target material needs to pass through capture solenoid • Could be separate ‘bullets’ magnetically levitated
![Page 9: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/9.jpg)
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
![Page 10: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/10.jpg)
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
![Page 11: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/11.jpg)
Pulse power densities for various targets
Facility Particle
Target material Energy density per pulse J cm-3
Lif e, number
of pulses
Neutrino Factory p Ta 318 109
I SOLDE (CERN)
p Ta 279 2x106
Pbar (FNAL)
p Ni 10000 5x106 Damage
NuMI p C 600 Shock not a problem
SLC (SLAC)
e W26Re 591 6x105
RAL/ TWI e Ta thin f oil
500 106
![Page 12: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/12.jpg)
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
![Page 13: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/13.jpg)
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?)
![Page 14: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/14.jpg)
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
![Page 15: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/15.jpg)
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)
![Page 16: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/16.jpg)
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)
![Page 17: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/17.jpg)
Study by Alec Milne Fluid Gravity Engineering Limited
“Cylindrical bar 1cm in radius is heated instantaneously from 300K to 2300K and left to expand”
![Page 18: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/18.jpg)
The y axis is radius (metres)
Study by Alec Milne, Fluid Gravity Engineering Limited
![Page 19: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/19.jpg)
Can ANSYS be used to study proton beam induced shockwaves?
Equation of state giving shockwave velocity v. particle velocity:
20 pps qusucu
For tantalum c0 = 3414 m/s
![Page 20: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/20.jpg)
Can ANSYS be used to study proton beam induced shockwaves?
Equation of state giving shockwave velocity v. particle velocity:
20 pps qusucu
For tantalum c0 = 3414 m/s
Cf: ANSYS implicit wave propagation velocity :
smE
c /334516600
107.185 9
ie same as EoS for low particle velocity
![Page 21: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/21.jpg)
ANSYS benchmark study: same conditions as Alec Milne/FGES study i.e.ΔT = 2000 K
The y axis is radial deflection (metres)
![Page 22: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/22.jpg)
Comparison between Alec Milne/FGES and ANSYS results
Alec Milne/ FGES
ANSYS
Amplitude of initial radial oscillation
100 μm 120 μm
Radial oscillation period
7.5 μs 8.3 μs
Mean (thermal) expansion
150 μm 160 μm
![Page 23: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/23.jpg)
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
![Page 24: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/24.jpg)
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
![Page 25: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/25.jpg)
ANSYS benchmark study: same conditions as Alec Milne/FGES study - EXCEPT ΔT = 100 K (not 2000 K)
21
),(,,
TE
trzr
= 400 x 106 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:
![Page 26: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/26.jpg)
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
![Page 27: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/27.jpg)
Elastic shock waves in a candidate solid Ta neutrino factory target
Temperature jump after 1 ns pulse
(Initial temperature = 2000K )
![Page 28: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/28.jpg)
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)
![Page 29: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/29.jpg)
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?)
![Page 30: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/30.jpg)
![Page 31: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/31.jpg)
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
![Page 32: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/32.jpg)
Elastic shock wave studies for draft ISOLDE proposal
Temperature jump after 2.4 μs pulse
(Initial temperature = 2000K )
![Page 33: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/33.jpg)
Elastic shock wave studies for draft ISOLDE proposal
Temperature profile at centre of cylinder over 4 x 250 ns bunches
![Page 34: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/34.jpg)
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
![Page 35: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/35.jpg)
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)
![Page 36: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/36.jpg)
Comparison between Nufact target and ISOLDE test
Temperature jump after 2.4 μs pulse
(Initial temperature = 2000K )
-1.00E+09 -5.00E+08 0.00E+00 5.00E+08 1.00E+09 1.50E+09
Maximum negative stress(r=0)
Shockwave oscillationamplitude (r=0)
Maximum stress at surface
Shockwave oscillationamplitude at surface
Stress (Pa)
ISOLDE test
Nufact target
Peak power density = 300 J/cc in both cases
![Page 37: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/37.jpg)
Effect of pulse length on shockwave magnitude
-8.00E+08
-6.00E+08
-4.00E+08
-2.00E+08
0.00E+00
2.00E+08
4.00E+08
6.00E+08
8.00E+08
1.00E+09
1.20E+09
1.00E-08 1.00E-07 1.00E-06 1.00E-05Proton beam pulse length (s)
Str
ess
(Pa)
Maximum negative stress(r=0)
Shockwave oscillation amplitude (r=0)
Maximum stress at surface
Shockwave oscillation amplitude at surface
![Page 38: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/38.jpg)
Fibre optic strain gauge system for measuring stress waves in a proton beam
window
Nick Simos, H. Kirk, P. Thieberger (BNL), K. McDonald (Princeton)
![Page 39: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/39.jpg)
2.4 TP, 100 ns pulse
![Page 40: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/40.jpg)
Collimation for the Linear Collider 15th 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
![Page 41: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/41.jpg)
Electron GunSteel
Beam Stop
Aperture Plate Light pipe
Aperture plate
Optical Transport
Window and bellows
To Spectrometer
Ta foils
![Page 42: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/42.jpg)
Electron Scanning:
Static Load
Upper clamp
Lower guide
50 HzRepetition(100 Hz skip across foils)
Beam Design
Path
![Page 43: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/43.jpg)
Target Foils25 µm Tantalum
WeightConnectors
![Page 44: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/44.jpg)
Electron Beam Machine EB1
Electron Beam welder vacuum chamber
CNC table
![Page 45: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/45.jpg)
![Page 46: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/46.jpg)
c.500 nm c.1100 nm
Intensity v wavelength of light radiated by Ta foils
![Page 47: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/47.jpg)
Time profile
20 x 0.5 ms exposures per ‘pulse’ (sweep)
0 ms 128 ms
![Page 48: Elastic Stress Waves in candidate Solid Targets for a Neutrino Factory](https://reader036.vdocuments.net/reader036/viewer/2022062315/56814dce550346895dbb2856/html5/thumbnails/48.jpg)
diamond: thermal absorbers
J Butterworth (RAL)
diamond front end + crotch absorbers: synchrotron radiation => 420 W/mm2 heat flux in confined space