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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Elastic Stress Waves in candidate Solid Targets
for a Neutrino Factory

• Nufact solid target outline and the shockwave
  problem

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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

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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

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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

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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

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• Schematic outline of a future neutrino factory

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• Schematic of proposed rotating hoop solid target
• Target material needs to pass through capture
  solenoid
• Could be separate bullets magnetically
  levitated

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• 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

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• 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

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Pulse power densities for various targets
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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

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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.
  SFma
• Should be similar to Fluid Gravity code (older
  but material models the same?)

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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.
  SFma
• Should be similar to Fluid Gravity code (older
  but material models the same?)
• ANSYS
• Uses Implicit Time Integration
• Suitable for Quasi static problems ie SF0

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Implicit vs Explicit Time Integration

• Explicit Time Integration (used by LS Dyna)
• Central Difference method used
• Accelerations (and stresses) evaluated at time t
• Accelerations -gt velocities -gt displacements
• Small time steps required to maintain stability
• Can solve non-linear problems for non-linear
  materials
• Best for dynamic problems (SFma)

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Implicit vs Explicit Time Integration

• Implicit Time Integration (used by ANSYS) -
• Finite Element method used
• Average acceleration calculated
• Displacements evaluated at time t?t
• 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 (SF0)

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Study by Alec Milne Fluid Gravity Engineering
Limited

• Cylindrical bar 1cm in radius is heated
  instantaneously from 300K to 2300K and left to
  expand

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Study by Alec Milne, Fluid Gravity Engineering
Limited
The y axis is radius (metres)
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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
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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
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ANSYS benchmark study same conditions as Alec
Milne/FGES study i.e.?T 2000 K
The y axis is radial deflection (metres)
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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
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ANSYS benchmark study same conditions as Alec
Milne/FGES study - EXCEPT ?T 100 K (not 2000 K)
Surface deflections in 1 cm radius Ta rod over 20
µs after instantaneous uniform temperature jump
of 100 K
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ANSYS benchmark study same conditions as Alec
Milne/FGES study - EXCEPT ?T 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
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ANSYS benchmark study same conditions as Alec
Milne/FGES study - EXCEPT ?T 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
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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

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Elastic shock waves in a candidate solid Ta
neutrino factory target
Temperature jump after 1 ns pulse (Initial
temperature 2000K )
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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)
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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?)

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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

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Elastic shock wave studies for draft ISOLDE
proposal
Temperature jump after 2.4 µs pulse (Initial
temperature 2000K )
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Elastic shock wave studies for draft ISOLDE
proposal
Temperature profile at centre of cylinder over 4
x 250 ns bunches
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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
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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)
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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 )
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Effect of pulse length on shockwave magnitude
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Fibre optic strain gauge system for measuring
stress waves in a proton beam windowNick Simos,
H. Kirk, P. Thieberger (BNL), K. McDonald
(Princeton)
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2.4 TP, 100 ns pulse
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• 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 ?T levels, at a similar T
• Lifetime information on candidate target
  materials

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Ta foils
Electron Gun
Steel Beam Stop
Aperture plate Optical Transport Window and
bellows
Aperture Plate
Light pipe
To Spectrometer
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Electron Scanning
Upper clamp
Beam Design Path
50 Hz Repetition (100 Hz skip across foils)
Lower guide
Static Load
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Target Foils 25 µm Tantalum
Weight Connectors
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Electron Beam Machine EB1
Electron Beam welder vacuum chamber
CNC table
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Intensity v wavelength of light radiated by Ta
foils
c.500 nm
c.1100 nm
l
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Time profile 20 x 0.5 ms exposures per pulse
(sweep)
128 ms
0 ms
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diamond thermal absorbersJ Butterworth (RAL)
diamond front end crotch absorbers synchrotron
radiation gt 420 W/mm2 heat flux in confined
space