1. 1 Thermal Shock Measurements and Modelling for Solid High-Power Targets at High Temperatures J. R. J. Bennett 1, G. Skoro 2, S. Brooks 1, R. Brownsword, C. J. Densham 1, R. Edgecock 1, S. Gray 1, A. J. McFarland 1 and D. Wilkins 1 roger.bennett@rl.ac.uk 1 Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, UK 2 Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, UK IWSMT-8, Taos, NM, October 2006

2. 2 Contents 1.Background 2.Shock in Solids 3.Wire Tests

3. 3  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

4. 4 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

5. 5 The Proton Pulse Structure The macro-pulse contains 3 or 5 micro-pulses micro-pulse, ~2 ns long

6. 6 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)

7. 7 Solid Target Parameters Proton Beam pulsed50 Hz pulse length~50  s energy ~10 GeV average power ~4 MW Target (not a stopping target) mean power dissipation1 MW energy dissipated/pulse20 kJ (50 Hz) energy density300 J cm -3 (50 Hz) temperature rise per pulse100-200 K (instantaneous) 2-3 cm 20 cm beam

8. 8 Bruce King Plan View of Targetry Setup shielding rollers Access port rollers protons to dump cooling solenoid channel 1 m water pipes x z

9. 9 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

10. 10 A possible alternative scheme

11. 11 Schematic diagram of the target and collector solenoid arrangement solenoids Target Bars The target bars are connected by links - like a bicycle chain.

12. 12 or

13. 13 Solenoid Target Bars Slot in solenoid Schematic diagram of the collector solenoid with a slot for the target bars.

14. 14 The main problem that is foreseen for solid targets is due to the almost instantaneous temperature rise every pulse:

15. 15 Thermal Shock

16. 16 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: 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.

17. 17 The solution is

18. 18 x = -Lx = +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.

19. 19 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!!

20. 20 Real Life is not this simple. - The Pbar target at FNAL withstands 40,000 J cm -3 ! - The NF target has only 300 J cm -3

21. 21 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.

22. 22 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, 2x10 -7 -1x10 -6 mbar Schematic circuit diagram of the wire test equipment

23. 23 turbopump Penning gauge window tantalum wireISO 63 tee bulkhead high voltage feed-throughs ct A A Schematic section of the wire test assembly Co-axial cables Top plate ISO 63 cross support rods Electrical return copper strip

24. 24 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

25. 25

26. 26

27. 27

28. 28

29. 29  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.

30. 30 Lorenz + Thermal Force Lorenz Force Thermal Force 100 ns pulse Goran Skoro

31. 31 LS-DYNA Results TUNGSTEN target operating 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 Mises Stress [MPa] 3cm x 20 cm Beam radius = Rod radius Time between successive micro-pulses [  s] 3 micro-pulses5 bunches Radial characteristic time micro-pulse macro-pulse NB. The bunches are equidistant. Goran Skoro

32. 32 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 power [MW] * - Von Mises stress Goran Skoro

33. 33 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 Mises stress [MPa] Goran Skoro

34. 34 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. 36483648 4848 2424 Beam Power MW 4.2x10 6 >9.0x10 6 >1.6x10 6 >3.4x10 6 0.2x10 6 No. of pulses to failure 1900 2050 1900 2000 1800 Max. Temp K 23232323 12.5 120 130 5560 5840 2.5 Not broken. Top connctr failed. 2323 6.2515064003 Stuck to top Cu connector 2323 12.59049003 Broke when increased to 7200A (2200K) Tungsten Tantalum is not a very good material – too weak at high temperatures. 12.56030004Tantalum Target dia cm Rep Rate Hz Pulse Temp. K Pulse Current A Lngth cm Material Equivalent Target 3.5700018019506.25>1.2x10 6 Stuck to top Cu connector

35. 35  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.

36. 36 The Number of Bars and the Number of Pulses (1 year is taken as 10 7 s)

37. 37  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 (10 7 s) is plotted against the pulse temperature.

38. 38  = 0.27  = 0.7 2 cm diameter target

39. 39 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.

40. 40 1400150016001700180019002000210022002300 0 100 200 300 400 500 600 700 800 900 1000 0 2  10 6 4  6 6  6 8  6 1  7 Number of Bars and Number of Pulses per year as a function of Peak Temperature and Thermal Emissivity Peak Temperature, K Number of Bars Number of Pulses in 1 year NT m 0.27   NT m 0.7   nT m 0.27   nT m 0.7   T m 3 cm diameter target ε = 0.27 ε = 0.7

41. 41 I believe that a solid tungsten target is viable from the point of view of shock and radiation damage.

42. 42