1 Thermal Shock Measurements and Modelling for Solid High-Power Targets at High Temperatures J. R....
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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
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.
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The Pbar target at FNAL withstands 40,000 J cmThe Pbar target at FNAL withstands 40,000 J cm-3-3!!
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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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