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Thermal Shock Measurements and Modelling for Solid High-Power Targets at High Temperatures

J. R. J. Bennett1, G. Skoro2, S. Brooks1, R. Brownsword, C. J. Densham1, R. Edgecock1, S. Gray1, A. J. McFarland1 and D. Wilkins1

roger.bennett@rl.ac.uk

1 Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, UK2 Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, UK

IWSMT-8, Taos, NM, October 2006

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Contents

1. Background

2. Shock in Solids

3. Wire Tests

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This work is part of the R&D for a Neutrino Factory.

To study the properties of neutrinos

We are studying

Neutrino Factory Production Targets

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Proton Accelerator 2-30 GeV, 4 MW

10-20 Tesla solenoid

pions

Accelerate muons to 20-50 GeV

Decay to

muons&

cooling

neutrinos

Simple schematic diagram of the neutrino factory, as seen by the target

Muon decay ring

TARGET

1 MW dissipated

Targets for a Neutrino Factory

Pion mean life – 26 ns

Muon mean life - 2.2 s

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The Proton Pulse Structure

The macro-pulse contains 3 or 5 micro-pulses

micro-pulse, ~2 ns long

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Neutrino Factory Targets

It is difficult to cool a stationary target.

A water cooled target for dissipating 1 MW is just possible, but half the volume is water.

Small metal spheres cooled with water have also been suggested.

Current R&D is centred on

1. Moving Solid Targets

2. Moving Liquid Metal Targets - Free Mercury Jet (MERIT)

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Solid Target ParametersProton Beam pulsed 50 Hz pulse length ~50 s energy ~10 GeV average power ~4 MW

Target (not a stopping target)

mean power dissipation 1 MW energy dissipated/pulse 20 kJ (50 Hz) energy density 300 J cm-3 (50 Hz)

temperature rise per pulse 100-200 K (instantaneous)

2-3 cm

20 cm

beam

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Bruce King

Plan View of Targetry SetupPlan View of Targetry Setup

shielding

rollersAccess

port

rollers

rollers

protonsto dump

cooling

coolingcooling

solenoid channel

1 m water pipes

x

z

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Schematic diagram of the radiation cooled rotating toroidal target

rotating toroid

proton beam

solenoid magnet

toroid at 2300 K radiates heat to water-cooled surroundings

toroid magnetically levitated and driven by linear motors

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A possible alternative scheme

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Schematic diagram of the target and collector solenoid arrangement

solenoids

Target Target BarsBars

The target bars are connected by links - like a bicycle chain.

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or

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Solenoid

Target Target BarsBars

Slot in solenoid

Schematic diagram of the collector solenoid with a slot for the target bars.

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The main problem that is foreseen for solid targets is due to the almost instantaneous

temperature rise every pulse:

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Thermal Shock

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Simple Calculation of Stress Due to Shock Elastic Case

Longitudinal Stress Waves in a Thin Rod (Theory of Elasticity, SP Timoshenko & JN Goodier)

The equation of motion for the elastic stress, , in a freely suspended thin rod of length 2L, which is instantaneously and uniformly raised in temperature by T at time t = 0:

2

2

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2 ,1,

t

tx

cx

tx

E

c

Where x is the distance along the axis of the rod from the centre and c is the velocity of the axial wave. E is the modulus of elasticity, the density of the rod and the coefficient of thermal expansion.

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The solution is

L

ctn

L

xn

nTEtxn

n

212cos

212cos

12

14,

0

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x = -L x = +Lx = 0

t = 0

t = L/2c

t = L/c

t = 2L/c

t = 3L/2c

Stress at different times

The stress along the length of the rod at different times is shown below.

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TE max

The value of the peak stress is

With typical values for tungsten:

E = 300 GPa = 0.9x10-5 K-1 T = 100 K

0.2% Yield Strength = ~20 MPa at 2000 K

UTS = ~100 MPa

max = 270 MPa

Stress exceeds UTS

FAILURE EXPECTED!!

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Real Life is not this simple.

-

The Pbar target at FNAL withstands 40,000 J cmThe Pbar target at FNAL withstands 40,000 J cm-3-3!!

-

The NF target has only 300 J cm-3

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Thermal Shock Tests on Tantalum and Tungsten

The Programme

1. Simulate shock by passing a pulsed current through a thin wire.

2. Measure the radial (and longitudinal) motion of the wire to evaluate the constitutive equations (with 3.).

3. Use a commercial package, LS-DYNA to model the behaviour.

4. Life time/fatigue test.

5. In-beam tests at ISOLDE.

6. Investigate the possibility of widely spaced micro- bunches of proton beam to reduce the shock impact.

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Pulsed Power Supply.

0-60 kV; 0-10000 A

100 ns rise and fall time

800 ns flat top

Repetition rate 50 Hz or sub-multiples of 2

Coaxial wires

Test wire, 0.5 mm Φ

Vacuum chamber, Vacuum chamber, 2x102x10-7-7 -1x10 -1x10-6-6 mbar mbar

Schematic circuit diagram of the wire test equipment

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turbopump

Penning gauge

window

window

tantalum wireISO 63 tee

bulkhead high voltage feed-throughs

ctA

A

Schematic section of the wire test assembly

Co-axial cables

Top plate

ISO 63 cross

support rods

Electrical return copper strip

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Vertical Section through the Wire Test Apparatus

Current

Inner conductor of co-axial insulator feed-through.

Stainless steel split sphere

Copper “nut”

Current

Two graphite (copper) wedges

Tungsten wire

Spring clips

Fixed connection

Sliding connection

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Need to independently vary the pulse current (energy density dissipated in the wire) and the peak temperature of the wire. (Not easy!)

1. Can vary the repetition rate (in factors of two).

2. Can vary the wire length which changes the cooling by thermal conduction to the end connections.

Must not fix both ends of the wire!

Some problems encountered with getting reliable electrical end connections, particularly the top sliding connection.

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Lorenz + Thermal Force

Lorenz ForceThermal Force

100 ns pulse

Goran Skoro

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LS-DYNA

Results TUNGSTEN targetoperating at 2000 K

Power = 4 MW, repetition rate = 50 Hz,Beam energy = 6 GeV (parabolic

distribution)2 ns long micro-pulses

Energy deposition from MARS

Peak

Von M

ises

Str

ess

[M

Pa]

3cm x 20 cmBeam radius = Rod radius

Time between successive micro-pulses [s]

3 micro-pulses

5 bunches

Radial characteristictime

micro-pulse

macro-pulse

NB.The bunches are equidistant.Goran Skoro

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LS-DYNA

Target: repetition rate = 50 Hz; beam energy = 6 GeV;

beam (parabolic) radius = target radius 3 x 2 ns long bunches;

pulse length = 20 s (2cm x 17cm), 25 s (3cm x 20cm);

energy deposition = MARS

Results

Isostress* Lines for Tungsten Target and Wire(operating at 2000 K)

Peak current [kA]

3 cm diameter target

2 cm diameter target

Wire: 0.5 mm diameter, 3 cm long;800 ns long pulse, exponential rise,

100 ns rise time

Beam

pow

er

[MW

]

* - Von Mises stress Goran Skoro

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LS-DYNA

Stress as a function of temperature jump in the tungsten target and wire (operating at

2000 K)

Target: 3cm x 20cm; repetition rate = 50 Hz; beam energy = 6 GeV; 3 x 2 ns long bunches; pulse length = 25 s; beam radius = target radius; beam offset = target radius/2; energy deposition = MARS

Temperature rise (peak value) [K]

Wire

Target

Wire: 0.5 mm diameter, 3 cm long;800 ns long pulse, exponential rise,100 ns rise time

Peak

von M

ises

stre

ss [

MPa]

Goran Skoro

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Some Results of 0.5 mm diameter wires

“Equivalent Target”: This shows the equivalent beam power (MW) and target radius (cm) in a real target for the same stress in the test wire. Assumes a parabolic beam distribution and 4 micro-pulses per macro-pulse of 60 s.

3648

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Beam Power

MW

4.2x106

>9.0x106

>1.6x106

>3.4x106

0.2x106

No. of pulses to

failure

1900 2050

1900

2000

1800

Max. Temp

K

2323

12.512.5

120130

55605840

2.5Not broken. Top connctr failed.

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6.2515064003Stuck to top Cu connector

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12.59049003Broke when increased to 7200A (2200K)

Tungsten

Tantalum is not a very good material – too weak at high temperatures.

12.56030004Tantalum

Target dia

cm

Rep RateHz

Pulse Temp

.K

Pulse Current

A

Lngth

cm

Material Equivalent Target

3.5

7000 180

1950

6.25 >1.2x106

Stuck to top Cu connector

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Tungsten is a good candidate for a solid target and should last for several years.

In this time it will receive ~10-20 dpa. This is similar to the 12 dpa suffered by the ISIS tungsten target with no problems.

Tantalum is too weak at high temperatures to withstand the stress.

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The Number of Bars

and

the Number of Pulses

(1 year is taken as 107 s)

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At equilibrium, a target bar heats up in the beam and then cools down by the same amount before entering the beam again.

A new bar enters the beam at the rate of 50 Hz. i.e. every 20 ms.

The more bars there are in the system then the fewer times any one bar goes through the beam in a year and the lower is the peak maximum temperature.

This is illustrated in the next overhead (for two different thermal emissivities) where the number of bars and the number of pulses each bar will receive in 1 yr (107 s) is plotted against the pulse temperature.

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ε = 0.27

ε = 0.27

ε = 0.7ε = 0.7

1400 1500 1600 1700 1800 1900 2000 2100 2200 23000

200

400

600

800

1000

1200

1400

1600

0

2106

4106

6106

8106

1107

1.2107

1.4107

1.6107

Number of Bars and Number of Pulses per Year as a Function of Peak Temperature and Thermal Emissivity

Peak Temperature, K

Num

ber

of B

ars

Num

ber

of P

ulse

s in

1 y

ear

N Tm 0.27 N Tm 0.7

n Tm 0.27 n Tm 0.7

Tm

2 cm diameter target

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A larger diameter target reduces the energy density dissipated by the beam (beam diameter = target diameter).

So going from 2 to 3 cm diameter reduces the energy density by a factor of 2 and the stress is also correspondingly reduced.

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1400 1500 1600 1700 1800 1900 2000 2100 2200 23000

100

200

300

400

500

600

700

800

900

1000

0

2 106

4 106

6 106

8 106

1 107

Number of Bars and Number of Pulses per year as a function of Peak Temperature and Thermal Emissivity

Peak Temperature, K

Num

ber

of B

ars

Num

ber

of P

ulse

s in

1 y

ear

N Tm 0.27 N Tm 0.7

n Tm 0.27 n Tm 0.7

Tm

3 cm diameter target

ε = 0.27

ε = 0.27

ε = 0.7

ε = 0.7

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I believe that a solid tungsten target is viable from the point of

view of

shock

and

radiation damage.

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