LSDyna and ANSYS Calculations of Shocks in Solids

1

• Shock simulations in solid targets
• Chris Densham
• Rutherford Appleton Laboratory

2
Contents

• Introduction
• ANSYS results for NF Ta target
• Effect of multiple bunches on shock wave
  magnitude
• LS-Dyna results for NF Ta target - G.Skoro,
  Sheffield
• Shock heating of a thin wire target lifetime
  experiment at RAL
• LS-Dyna calculations for wire test - G.Skoro,
  Sheffield
• Graphite target for T2K experiment

3
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

4
Elastic shock waves in a candidate solid Ta
neutrino factory target
Temperature jump after 1 ns pulse (Initial
temperature 2000K )
5
Elastic shock waves in a candidate solid Ta
neutrino factory target
6
Effect of multiple bunches
7
Effect of multiple bunches
1 µs (end of beam spill)
10 µs
8
(No Transcript)
9
(No Transcript)
10
Effect of multiple bunches
11
LS-Dyna calculations Goran Skoro,
Sheffield University
12
LS-Dyna calculations Goran Skoro,
Sheffield University

• Material model
• Temperature Dependent Bilinear Isotropic
• 'Classical' inelastic model
• Nonlinear
• Uses 2 slopes (elastic, plastic) for representing
  of the stress-strain curve
• Inputs density, Young's modulus, CTE, Poisson's
  ratio, temperature dependent yield stress, ...
• Element type LS-Dyna Explicit Solid
• Material TANTALUM

13
(No Transcript)
14
(No Transcript)
15
Literature data on fatigue life of tantalum
16
Literature data on fatigue life of tantalum
fortunately this data is for low cycle (ie
slow) fatigue
17
(No Transcript)
18
The need for experiments

• Calculations are only as good as material data
  used
• Material data is sparse
• Hence, need for experiments to determine material
  model data
• Experiment at RAL Current pulse through wire
  (equivalent to 300 J/cc)
• Use VISAR to measure surface velocity
• Ideally, use results to 'extract' material
  properties at high temperatures...
• Predict lifetime of a future neutrino target

19
Shock wave experiment at RAL Pulsed ohmic-heating
of wires may be able to replicate pulsed proton
beam induced shock.
current pulse
tantalum (or graphite) wire
Energy density in the Ta wire needs to be e0
300 J cm-3 to correspond to 1 MW dissipated in a
target of 1 cm radius and 20 cm in length at 50
Hz.
20

• Transient Conditions
• Assume an electric field E is instantaneously
  applied across a conducting wire.
• Apply Maxwells equations.
• This produces a diffusion equation
• In cylindrical coordinates, where j is the
  current density.
• The solution is

? 1/?0?
21
Characteristic time for the shock to travel
across the radius
Characteristic Time for the current to penetrate
the wire
Need
22
Doing the Test The ISIS Extraction Kicker Pulsed
Power Supply
8 kA
Voltage waveform
Time, 100 ns intervals
Rise time 50 ns Voltage peak 40
kV Repetition rate up to 50 Hz. There is a
spare power supply available for use.
23
j/j0
0.1 mm
0.2 mm
0.3 mm
0.4 mm
0.6 mm
, s
Current density at r 0 versus time (t, s), for
different wire radii (a, mm).
24
LS-Dyna calculations for shock-heating of
different wire radii using ISIS kicker magnet
power supply
25
Comparison of stresses expected in neutrino
factory target (top) with stresses generated in
wire test (bottom)
26
Comparison of stresses expected in neutrino
factory target (top) with stresses generated in
wire test (bottom)
NB Peter Sievers Need to add radial pinch due to
magnetic field in wire
27
Schematic section of the wire shock-wave test
assembly
ct
ISO 63 cross
Penning gauge
Co-axial cables
window
2 copper bars
Wire support plate
tantalum wire
window
Electrical return copper strip
ISO 63 tee
bulkhead high voltage feed-throughs
turbopump
28
Temperature measurement
(Transient optical spectroscopy) see R.
Brownsword talk last UKNF meeting
tantalum wire
29
Temperature measurement
tantalum wire
VISAR (see Richard Brownswords talk next)
30
(No Transcript)
31
T2K experiment
Long baseline neutrino oscillation experiment
from Tokai to Kamioka.
Sensitivity on ne appearance
1GeV nm beam (?100 of K2K)
Super-K 50 kton Water Cherenkov
J-PARC 0.75MW 50GeV PS

• Physics motivations
• Discovery of nm?ne appearance
• Precise meas. of disappearance nm?nx
• Discovery of CP violation (Phase2)

32
Neutrino Beam Line for T2K Experiment

• Components
• Primary proton beam line
• Normal conducting magnets
• Superconducting arc
• Proton beam monitors
• Target/Horn system
• Decay pipe (130m)
• Beam dump
• muon monitors
• Near neutrino detector
• Special Features
• Superconducting combined function magnets
• Off-axis beam

Target Station
130m
decay volume
280m
Beam dump/m-pit
Near detector
To Super-Kamiokande
33
Jan.28, 2005
34
Primary Beam

• 50 GeV (40 at T0)
• single turn fast extraction
• 3.3x1014proton/pulse
• 3.53 sec cycle
• 750kW (2.6MJ/pulse)
• 8 (15) bunches
• e6p (7.5p)mm.mr _at_ 50 (40) GeV

Default acceleration cycle for 50GeV
0.7s
1.96s acceleration
0.12s injection
0.7s idling
598ns
Total 3.53s (from TDR) Idling time is to adjust
total power. If beam loss, power consumption
allow, this can be reduced.
4.2ms
58ns
35
T2K target conceptual design

• Graphite Bar Target r15mm, L900mm (2
  interaction length)
• Energy deposit Total 58kJ/spill, Max186J/g ?
  DT ? 200K

• Co-axial 2 layer cooling pipe.
• Cooling pipe Graphite / Ti alloy (Ti-6Al-4V),
  Refrigerant Helium (Water)

36
T2K Target outline assy. into horn
37
Streamlines showing velocity in the helium.
Calc. by John Butterworth
38
T2K graphite target temperature distribution
immediately after first spill, beam 1 cm off-axis
John Butterworth
39
T2K graphite target temperature progression
during first 80 seconds
80 s
40
T2K graphite target shock-wave progression over
50 µs after 5 µs beam spill (beam on axis).
7 MPa (OK?)
5 µs (end of beam spill)
41
Irradiation Effect of Graphite

• Expected radiation damage of the target
• The approximation formula used by NuMI target
  group 0.25dpa/year
• MARS simulation
  0.150.20 dpa/year
• Dimension change shrinkage by 5mm in length in
  5 years at maximum. 75mm in radius
• Degradation of thermal conductivity decreased
  by 97 _at_ 200 ?C
  
  7080 _at_ 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

800
1000
Irradiation Temperature(?)
400
600
JAERI report (1991)
2dpa
-0.5
1dpa
Dimension change
Toyo-Tanso Co Ltd. IG-11
42
A PSI pyrolytic graphite target after c.1.2 x
1022 protons/cm2
43
(No Transcript)
44
LS-Dyna calculations for shock-heating of
different graphite wire radii using ISIS kicker
magnet power supply
45
Summary of results so far

• Neutrino Factory
• Shock waves in Ta characterised within
  limitations of materials knowledge
• Effects of beam pulse length and multiple
  bunches/pulse understood
• Shock test of wire
• Power supply available which can supply necessary
  current (8kA) within short enough time to
  generate shocks of similar magnitude to those in
  NF
• Method of remote temperature measurement of wire
  fully tested transient optical spectroscopy
• VISAR to be purchased with sufficient time
  resolution and velocity sensitivity to measure
  surface velocity of wire and compare results with
  LS-Dyna calculations

46
Still to do

• Shock test of Ta wire
• Perform experiment
• Work out how to extract material data from
  experiment
• From lifetime test, predict lifetime of tantalum
  NF target

• Repeat experiment with graphite
• Graphite is target material of choice for CNGS
  and T2K (JPARC facility)
• Serious candidate material for a NF