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
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• Nufact solid target outline and the
shockwave problem
• Codes used for the study of shockwaves
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
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
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
Schematic outline of a future neutrino factory
Schematic of proposed rotating hoop solid target • Target material needs to pass through capture solenoid • Could be separate ‘bullets’ magnetically levitated
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
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
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
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
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?)
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
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)
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)
Study by Alec Milne Fluid Gravity Engineering Limited
“Cylindrical bar 1cm in radius is heated instantaneously from 300K to 2300K and left to expand”
The y axis is radius (metres)
Study by Alec Milne, Fluid Gravity Engineering Limited
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
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
ANSYS benchmark study: same conditions as Alec Milne/FGES study i.e.ΔT = 2000 K
The y axis is radial deflection (metres)
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
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
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
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:
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
Elastic shock waves in a candidate solid Ta neutrino factory target
Temperature jump after 1 ns pulse
(Initial temperature = 2000K )
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)
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?)
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
Elastic shock wave studies for draft ISOLDE proposal
Temperature jump after 2.4 μs pulse
(Initial temperature = 2000K )
Elastic shock wave studies for draft ISOLDE proposal
Temperature profile at centre of cylinder over 4 x 250 ns bunches
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
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)
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
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
Fibre optic strain gauge system for measuring stress waves in a proton beam
window
Nick Simos, H. Kirk, P. Thieberger (BNL), K. McDonald (Princeton)
2.4 TP, 100 ns pulse
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
Electron GunSteel
Beam Stop
Aperture Plate Light pipe
Aperture plate
Optical Transport
Window and bellows
To Spectrometer
Ta foils
Electron Scanning:
Static Load
Upper clamp
Lower guide
50 HzRepetition(100 Hz skip across foils)
Beam Design
Path
Target Foils25 µm Tantalum
WeightConnectors
Electron Beam Machine EB1
Electron Beam welder vacuum chamber
CNC table
c.500 nm c.1100 nm
Intensity v wavelength of light radiated by Ta foils
Time profile
20 x 0.5 ms exposures per ‘pulse’ (sweep)
0 ms 128 ms
diamond: thermal absorbers
J Butterworth (RAL)
diamond front end + crotch absorbers: synchrotron radiation => 420 W/mm2 heat flux in confined space