2. Parameters of the NF Target
Proton Beam
pulsed Hz
pulse length ms
energy GeV
average power ~4 MW
Target (not a stopping target)
mean power dissipation 1 MW
energy dissipated/pulse 20 kJ (50 Hz)
energy density kJ/cm3 (50 Hz)
2 cm
20 cm
beam

3. Schematic diagram of the RAL radiation cooled rotating toroidal tantalum target
proton beam
solenoid magnet
toroid at 2300 K radiates heat to water-cooled surroundings
toroid magnetically levitated and driven by linear motors

4. The New Programme
Since NuFact04 the R&D programme has altered significantly:
Simulate shock by passing a pulsed current through a wire.
Measure the radial motion of the wire to evaluate the constitutive equations (with 3.).
Use a commercial package, LS-DYNA to model the behaviour.
Life time/fatigue test. 50 Hz for 12 months.
Investigate the possibility of widely spaced micro- bunches of proton beam to reduce the shock impact.

5. Proposed R&D (2004)
Calculate the energy deposition, radio-activity for the target, solenoid magnet and beam dump.
Calculate the pion production (using results from HARP experiment) and calculate trajectories through the solenoid magnet.
2. Model the shock
a) Measure properties of tantalum at 2300 K.
b) Model using hydrocodes developed for explosive applications at LANL, LLNL, AWE, etc.
c) Model using dynamic codes developed by ANSYS.
3. Radiation cooled rotating toroid
a) Calculate levitation drive and stabilisation system.
b) Build a model of the levitation system.
4. Individual bars
a) Calculate mechanics of the system.
b) Model system.
5. Continue electron beam tests on thin foils, improving the vacuum.
6. In-beam test at ISOLDE pulses.
7. In-beam tests at ISIS – 107 pulses.
8. Design target station.

6. Shock, Pulse Length and Target Size
When a solid experiences a temperature rise the material expands. Because of mass inertia there will always be a slight lag in the expansion. This causes pressure waves to ripple through the material. When the temperature rise is relatively large and fast, the material can become so highly stressed that there is permanent distortion or failure - shock.
Short high intensity beam pulses will give rise to shock in a target.
The shock wave travels through matter at the speed of sound,
where E is Young's modulus of elasticity and ρ is the density.

7. The time taken for the wave to travel from the outer surface to the centre is given by
If the beam pulse (τp) is long compared to the characteristic time τs, then little energy goes into the target in this time and the shock wave in the target is reduced.
If the target is small compared to the beam pulse length the shock is reduced.
If No problem!
Must have sufficient pulsed energy input!

8. Proton beam “macro-pulses” and “micro-pulses”.
The Proton Pulse
macro-pulse
micro-pulse
Proton beam “macro-pulses” and “micro-pulses”.
Traditionally we have considered the micro-pulses as ~1 ns wide and the macro-pulses as ~1 s wide. The temperature rise per macro-pulse is ΔT ~ 100 K.
For the tantalum bar target, radius 1 cm and length 20 cm, then:
The time for the shock wave to travel a radius is 3 ms
The time for the shock wave to travel a half the length is 30 ms
However, in the RAL proton driver scheme with ~10 micro-pulses, it is likely that they could be spaced apart by ~40 s, thus reducing the effective thermal shock to only ΔT ~ 10 K.

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

10. Pulse Heating
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.

11. 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

12. The Velocity of the Shock Wave
Shock travels at the Speed of Sound.
Can only use small diameter wires of up to ~0.4 mm to get current penetration into the wire.
“Choose a better material”

13. Characteristic Times for the shock to travel across the radius and for the current to penetrate the wire (square pulse). τs τI ns
a, mm 1
0.1 10
100
10000
1000

14. The ISIS Extraction Kicker Pulsed Power Supply
Doing the Test
The ISIS Extraction Kicker Pulsed Power Supply
Exponential with 20 ns rise time fitted to the waveform
Voltage waveform
Time, 100 ns intervals
Rise time: ~100 ns Voltage peak: ~40 kV Repetition rate up to 50 Hz.
Flat Top: ~300 ns Current Peak: ~8 kA There is a spare available for use.

15. Solution for the case of an exponential rise in current

16. 1000 ns
100 ns
j/j0
30 ns
10 ns
1 ns
r/a
Current density versus radius at different times. Wire radius, a = 0.3 mm.

17. 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).

18. The average current density over the wire cross section versus time (t, s), for various wire radii, (a, mm).
0.4
0.5
0.3
1 mm
0.2
0.1

19. Goran Skoro, Sheffield University.
Effect of different pulse lengths (shown by arrows), for exponential current rise of 30 ns.
Goran Skoro, Sheffield University.

20. Goran Skoro, Sheffield University.
Effect of different pulse lengths (shown by arrows), for exponential current rise of 30 ns.
Goran Skoro, Sheffield University.

21. Energy Density in the Wire
Radius mm
Characteristic time
τs, ns
Energy density
MJ m -3
0.1 30
323
0.2 60 69
0.3 90 21
0.4
120 8
0.5
150
3.4
0.6
180
1.6
0.7
210
0.8
240
0.9
270
1.0
300
The energy density dissipated at the centre of the wire, within a time τ s
for
different wire radii, with I
= A.

22. Pulse Current Requirements
Radius mm
Characteristic time
τs, ns
Current
I0, kA
0.1 30 10
0.2 60 21
0.3 90 37
0.4
120 61
0.5
150 94
0.6
180
138
0.7
210
197
0.8
240
273
0.9
270
373
1.0
300
499
The current, I0, required to dissipate 300 MJ m-3 at the centre of the wire within a time τs, for different wire radii.

23. Schematic diagram of the test chamber and heater oven.
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.