ENG/BENE, ENG Plenary, 16 March 2005 The New UK Programme for Shock Studies J R J Bennett RAL

1. ENG/BENE, ENG Plenary, 16 March 2005 The New UK Programme for Shock Studies J R J Bennett RAL

2. The Original Plan 1. Investigate, with RMCS, the possibilities of making off-line tests to determine the strength characteristics (theconstitutive equations)of tantalum at 2000°C. 2. Obtain beam time at ISOLDE(or ISIS) and make measurements. This will give: a) strength characteristics of tantalum and tungsten at 2000°C. b) show if the target breaks after a few pulses. 3. Computer model the target and determine the optimum geometry.

3. Target Studies • Alec Milne (FGES Ltd) has done a scoping study. It shows damage to the target! 20 cm 2 cm dia

4. Different models m Alec Milne, Jim Dunnett and Richard Brown, FGES Ltd. The radius of the bar versus time for a single pulse. Temperature jump from 300 to 2300 K.

5. Models Equivalent “Accumulated” Plastic Strain versus Radius.

6. Progress • RMCS and FGES have been retired from the project. • Laboratory tests using projectiles will not truly replicate the thermal shock in the target. • So a new plan is needed

7. The New Plan Pulsed ohmic-heating of wires can replicate pulsed proton beam induced shock. current pulse tantalum wire Energy density in the wire needs to be ε0 = 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.

8. 1. Set up the pulse wire test and power supply. 2. Measure the surface vibrations to attempt to find the constitutive equations of state. 3. Calculate the shock.Goran Skoro using LS-DYNA and Chris Densham using ANSYS. 4. Life time/fatigue test. 50 Hz for 12 months. 5. In-Beam Tests at ISOLDE. 6. Calculate the pion yield, beam heating and activity.Stephen Brooks using MARS code.

9. Fast Pulse Currents in Wires High frequency EM fields only penetrate the surface of conductors. Skin depth for a plane surface This is the steady state situation. For a transient we have a slightly different situation.

10. Transient Conditions • Assume an electric field E is instantaneously applied across a conducting wire. • Apply Maxwell’s equations. • This produces a diffusion equation: • In cylindrical coordinates, where j is the current density. • The solution is:  = 1/0

11. 1 0.8 0.6 0.4 0.2 0 0 0.2 0.4 r/a 0.6 0.8 1 60 ns 40 ns 30 ns j 20 ns 15 ns Square current pulse of infinite length 10 ns 8 ns 6 ns 4 ns 3 ns 2 ns 1 ns Relative current density in the wire, j, versus radius at different times. Wire radius a = 0.0002 m

12. The Velocity of the Shock Wave • Shock travels at the Speed of Sound. • It takes τ = 60 ns for the shock wave to cross to the centre of the wire of radius of a = 0.2 mm. • Can only use small diameter wires of up to ~0.4 mm. • “Choose a better material”

13. a, m t, ns I, kA j, A m-3 T, K 0.0001 30 3.35 10.67x1010 2577 0.0002 61 9.48 7.54x1010 3064 0.0003 91 17.41 6.16x1010 3391 0.0006 182 49.25 4.36x1010 4033 0.0010 300 106 3.37x1010 4584 0.0030 910 551 1.95x1010 6031 0.0060 1820 1558 1.38x1010 7172 0.0100 3000 3351 1.07x1010 8149 Wire radius, a, and characteristic time t. (Wire resistivity at 2000 K) Peak current Iat ε0 = 3x108 J m-1 per pulse(SQUARE PULSE ) Current densityjat ε0 = 3x108 J m-1 per pulse(SQUARE PULSE ) Temperature T at 50 Hz operation, thermal radiation cooling only

14. A possible power supply The ISIS Extraction Kicker Pulsed Power Supply Time, 100 ns intervals Exponential with 30 ns rise time fitted to the waveform Current waveform Rise time: ~100 ns Voltage peak: ~40 kV Repetition rate up to 50 Hz. Flat Top: ~500 ns Current Peak: ~8 kV There is a spare available for use. The power supply can be modified to improve the performance

15. Current pulse t Energy densities achievable with the ISIS extract kicker magnet psu with 5000 A peak current, with exponential current rise (30 ns) and sharp fall with a pulse length t.

16. The solution for an exponential rise in the pulse at the surface of the wire of the form, is,

17. t = 200 ns 1 t = 150 ns relative current density 0.96 t = 100 ns 0.92 0.88 Current pulse 0.83 0.79 t t = 60 ns 0.75 0 0.2 0.4 0.6 0.8 1 r/a Current density versus radius within the wire, radius a = 0.2 mm. Exponential pulse, rise time = 30 ns.

18. 3 x108 ε0 Energy density J m-3 t = 200 ns 2 x108 Current pulse t = 150 ns 1x108 t t = 100 ns t = 60 ns 0 0 0.2 0.4 0.6 0.8 1 r/a Energy density in a 0.0002 m radius wire versus radius at times, t. Current pulse: 5000 A peak, exponential rise, sharp cut-off at times indicated on the graph.

19. Unfortunately the calculation goes wrong at short times and thus I can not show the case of the 0.0001 m radius wire for t = 30 ns!

20. Different Materials • Graphite has an electrical resistivity [1] at room temperature of 1356 ohm cm would be very suitable. • Sound velocity ~same as for Ta. • The rod could be 2 mm diameter and the average current in the rod would reach 94% of its long term value in only 100 ns. • [1]Values for carbon are taken from “Goodfellow Cambridge Ltd”. Graphite has very variable properties depending on the grade etc.

21. heater insulators to pulsed power supply to pulsed power supply test wire water cooled vacuum chamber to vacuum pump or helium gas cooling Schematic diagram of the test chamber and heater oven.

22. Pbar Target Tests Pbar target assembly presently in use Jim Morgan FNAL Graphite Tantalum Graphite

23. Tantalum target test summary (1)Pat Hurh • Goal was to create enough target damage to reduce pbar/π- yield • Started with a proton intensity of 1.0E11 and a spot size of σ = 0.50 mm. Maximum energy deposition was attained with a proton intensity of 6.5E12 and a spot size of σ = 0.15 mm • Target rotation was stopped so that beam pulses were accumulated in the same area • After accumulating 100 beam pulses, energy deposition was increased by a factor of 2 and process repeated • Target rotated 10° between data points

24. Tantalum target test summary (2)Pat Hurh, FNAL • Goal was to create enough target damage to reduce pbar/π- yield • Target did not show appreciable pbar/π- yield reduction up to maximum energy deposition • 1,100 pulses with proton intensities of 5.8-6.5E12 • Energy deposition estimated at 2,300 J/g(38,300 J/cc) • Tantalum target had 8% lower pbar/ π- yield as compared with nickel (model predicted a few percent higher)

25. Goran Skoro University of Sheffield LS-Dyna and ANSYS Calculations of Shocks in Solids

26. micro-pulse macro-pulse Proton beam “macro-pulses” and “micro-pulses”

27. NF Target: 1 cm radius 20 cm long t = 3 s Total temperature rise: DT = 100 K Effect of 1, 10 and 100 micro-pulses pulses within 1 s.

28. NF Target: 1 cm radius 20 cm long t = 3 s Total temperature rise: DT = 100 K Effect of 10 micro-pulses in 1 and 5 ms long macro-pulses.

29. NF Target: 1 cm radius 20 cm long t = 3 s Total temperature rise: DT = 100 K Effect of 1 ns and 3 ns long pulses.

30. NF Target: 1 cm radius 20 cm long t = 3 s Total temperature rise: DT = 100 K Effect of 1, 2, 3, 5 and 10 s long macro-pulses.

31. NF Target: 1 cm radius 20 cm long t = 3 s Total temperature rise: DT = 10 K per micro-pulse Effect of different length macro-pulses with the same energy in each micro-pulse.

32. Tantalum wire 0.3 mm radius t = 180 ns Effect of 100 ns and 1000 ns long pulses in a thin wire

33. NF Target: 1 cm radius 20 cm long τ = 3 s Total temperature rise: ΔT = 100 K per macro-pulse Tantalum wire: 0.3 mm radius τ = 180 ns Comparison of 0.2 mm and 1 cm radius targets