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