Shock wave studies in solid targets

(1)

Chris Densham

Engineering Analysis Group

Shock wave studies in solid targets

FAIR Super-FRS production targets

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(3)

Super-FRS production targets

Slow extraction

- Ions extracted over few seconds

(4)

Super-FRS production targets

Slow extraction

- ions extracted over few seconds

- Slowly rotating graphite wheel probably OK

Fast extraction – the wish list!

– U238 _{beams of up to 10}12 _ions/pulse

– Pulse lengths 50-60 ns

– Beam spot sizes σ_x = 1 mm, σ_y = 1 mm

– Power densities 40 kJ/g

(5)

Super-FRS production targets

Slow extraction

- ions extracted over few seconds

- Slowly rotating graphite wheel probably OK

Fast extraction – the wish list!

– 238_{U beams of up to 10}12 _{ions/pulse – the ‘most challenging’ case}

– Pulse lengths 50-60 ns

– Beam spot sizes σ_x = 1 mm, σ_y = 1 mm

– Power densities 40 kJ/g

– ΔT=30,000°C

(6)

Fast-extracted beams:

Target options under consideration:

• Increase beam spot size – obvious easy option

• For low projectile Z and low intensities - use a PSI style

rotating graphite wheel (as planned for slow extraction)

• For highest intensities – windowless liquid metal jet

(7)

CCLRC work programme for FAIR

Study of:

Solid (graphite) target Liquid Li target

Beam Dump

Informal agreement between CCLRC and GSI:

Chris Densham, Mike Fitton, Matt Rooney (CCLRC), Helmut Weick, Klaus Sümmerer, Martin Winkler, Bernhard Franzke (GSI)

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CCLRC work programme for FAIR

Solid Target

• For a

238

_{U beam,}

_σ

x

= 1 mm,

σ

y

= 2 mm on a graphite

target:

• What are the maximum positive and negative stress

waves that traverse the graphite after the impact of the

ion pulse?

• What are the technical limits of these shock stresses?

• What is the expected lifetime of a graphite target?

• What U beam spot size would give a target lifetime of 1

year?

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CCLRC work programme for FAIR

Liquid target

• High intensity, high Z, highly focussed beam

• Liquid Li jet only candidate

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CCLRC work programme for FAIR

Beam Dump

• Primary beam is stopped in graphite

• Secondary beam stopped in subsequent Fe layer

• Calculate temperatures / shock waves in C/Fe interface and coolant pipes

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Paul Scherrer Institut • 5232 Villigen PSI ICFA-HB2002 / G. Heidenreich

Radiation-induced anisotropic shrinkage of polycrystalline graphite causes deformation of the shape and hence leads to a radial wobble. The radial displacement amplitude ΔR must be ≤2mm for the operation of the target. Beam axis • _Δ_R_≤_{2 mm} 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 D isp la cem e n t R a te Δ R [ mm/ A h ] 0.5 1 1.5 1.5 1.8

mean proton current [mA]

R6300P R6400P

Measured radial displacement rates for the targets made from the graphite grades R6300P and R6400P *)

*) SGL Carbon, D-53170 Bonn, Germany

LIFETIME OF THE ROTATING POLYCRYSTALLINE GRAPHITE TARGET CONES

A new design of graphite wheel. The target cone is subdivided into 12 segments separated by gaps of 1mm at an angle of 45o_{to the}

beam direction: This allows unconstrained dimensional changes of the irradiated part of the graphite.

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Super-FRS target parameter comparison with PSI

Material Beam Target

thickness g/cm2 Total power deposited kW PSI Graphite wheel Protons 10.8 54 Super-FRS Graphite wheel? 238_U _4.0 ₁₂

•Considerable experience gained at PSI, e.g. bearings,

materials

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Irradiation Effect of Graphite

• Expected radiation damage of the target

– The approximation formula used by NuMI target group : 0.25dpa/year – MARS simulation : 0.15~0.20 dpa/year

• Dimension change … shrinkage by ~5mm in length in 5 years at maximum. ~75μm in radius

• Degradation of thermal conductivity … decreased by 97% @ 200 °C

70~80% @ 400 °C

• Magnitude of the damage strongly depends on the irradiation temperature.

– It is better to keep the temperature of target around 400 ~ 800 °C

Irradiation Temperature(℃) 400 600 800 1000 2dpa 1dpa -0.5%

Dimension change

1 2 3 (dpa) 400o_C 800o_C

Thermal conductivity (After/Before) Toyo-Tanso Co Ltd. IG-11

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When might shock waves be a problem?

• In pulsed particle accelerators (protons, electrons, heavy ions) where:

)

(

dim

)

(

wave

velocity

ension

stic

characteri

pulse

t

≤

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Current / Future projects where shock waves are an issue

Material Beam Peak power

density J/cc/pulse Pulse length ESS (next generation ISIS) Hg Few GeV protons 20 1x10-6 _s GSI/Fair target + dump Li + Graphite Heavy ions 30000 5x10-9 _s T2K/JPARC target + window Graphite +Ti 30-50 GeV p 344 5x10-6 _s

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T2K experiment

Physics motivations

zDiscovery of νμ→νe appearance

zPrecise meas. of disappearance νμ→νx

zDiscovery of CP violation (Phase2)

~1GeV ν_μ beam (×100 of K2K) J-PARC 0.75MW 50GeV PS Super-K: 50 kton Water Cherenkov

Long baseline neutrino oscillation experiment from Tokai to Kamioka.

10 10--11 CHOO CHOO Z Z exclu

exclu_ded_ded

Δ

m

13 2

(eV

2

)

10 10--44 10 10--33 10 10--22 10 10--22 10 10--33 ₁₀₁₀--11 ₁₁

~20

sin

2

₂

_θ

13

>0.006

(90%) Sensitivity on ν_e appearance

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• Graphite Bar Target : r=15mm, L=900mm (2 interaction length) – Energy deposit … Total: 58kJ/spill, Max:186J/g Æ ΔT ≈ 200K

T2K target conceptual design

• Co-axial 2 layer cooling pipe.

– Cooling pipe: Graphite / Ti alloy (Ti-6Al-4V), Refrigerant: Helium (Water)

MARS Distribution of the energy deposit in the target (w/ 1 spill) J/gK degree

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Streamlines showing velocity in the helium.

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80 s

T2K graphite target temperature progression during first 80 seconds

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Primary Beam

• 50 GeV (40 at T=0)

• single turn fast extraction

• 3.3x10

14

proton/pulse

• 3.53 sec cycle

• 750kW (~2.6MJ/pulse)

• 8 (15) bunches

ε

=6

π

(7.5

π

)mm.mr @ 50 (40)

GeV

598ns 58ns 4.2μs

Default acceleration cycle for 50GeV

0.12s injection 1.96 s acce lerat ion 0.7s 0.7s idling Total ~3.53s (from TDR)

Idling time is to adjust total power.

If beam loss, power consumption allow, this can be reduced.

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T2K graphite target shock-wave progression

over 50 µs after 4.2 µs beam spill, cross-section of long target.

5 μs (end of beam spill) 7 MPa

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When can FEA be used to study shockwaves?

• Equation of state giving shockwave velocity:

2 0 p p

s

c

su

qu

u

=

+

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When can FEA be used to study shockwaves?

• Equation of state giving shockwave velocity:

2 0 p p

s

c

su

qu

u

=

+

For tantalum c₀ = 3414 m/s

Cf: ANSYS implicit wave propagation velocity :

s m E c 3345 / 16600 10 7 . 185 9 = × = =

ρ

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2 g/cm2 _{graphite stress wave plots from 50 GeV protons} Max Von Mises Stress: Ansys – 7MPa

LS-Dyna – 8Mpa

Max Longitudinal Stress: Ansys – 8.5MPa LS-Dyna – 10MPa Ansys (RAL) LS-Dyna (Sheffield) -20 -15 -10 -5 0 5 10 15 20 0 10 20 30 40 50 Time (µs) St re s s ( M Pa )

Von Mises (centre) Longitudinal (centre) Hoop (centre) Von Mises (radius) Hoop (radius)

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Shock wave experiment at RAL

Pulsed ohmic-heating of wires may be able to replicate pulsed

proton beam induced shock.

current

pulse

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50kV, ~8kA PSU 50Hz

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Doing the Test

The ISIS Extraction Kicker Pulsed Power Supply

Time, 100 ns intervals

Voltage

waveform

Rise time: ~50 ns Voltage peak: ~40 kV Repetition rate up to 50 Hz. + There is a spare power supply available for use.

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LS-Dyna calculations for shock-heating of different graphite wire radii using ISIS kicker magnet power supply G. Skoro Sheffield Uni

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test wire

Temperature

measurement

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Velocity Interferometry (VISAR) :

Laser Frequency ω Sample Velocity u(t) Fixed mirror Beamsplitter Etalon Length h Refractive index n Detector Fixed mirror

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Damage in tantalum wire: 1 hour x 12.5 Hz at 2200K

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Damage in tantalum wire: