ENG/BENE, Target Section, 16 March 2005

The New UK Programme for Shock Studies

J. R. J. Bennett

RAL

The Original Plan

1. Investigate, with RMCS, the possibilities of making off-line tests to determine the strength characteristics (the constitutive 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.

Target Studies1. Alec Milne (FGES Ltd) has done a scoping

study. It shows damage to the target!

2 cm dia

20 cm

The radius of the bar versus time for a single pulse. Temperature jump from 300 to 2300 K.

Different

models

Alec Milne, Jim Dunnett and Richard Brown, FGES Ltd.

m

“Accumulated” Plastic Strain versus Radius.

Models

Eq

uiv

ale

nt

Progress1. RMCS and FGES have been retired

from the project.

2. Laboratory tests using projectiles will not truly replicate the thermal shock in the target.

So a new plan is needed

The New PlanPulsed 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.

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.

Fast Pulse Currents in WiresHigh 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.

2

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:

r

j

rr

j

t

jzz 11

2

2

0

1 1

00

221

n nn

ntzz aJ

rJe

ajj n

= 1/0

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

r/a

Relative current density in the wire, j, versus radius at different times. Wire radius a = 0.0002 m

j

1 ns2 ns3 ns4 ns

8 ns

6 ns

10 ns

15 ns

20 ns

30 ns40 ns

60 ns

Square current pulse of infinite length

The Velocity of the Shock Wave• Shock travels at the Speed of Sound.

• It takes t = 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”

1-ns μm 3.3E

s

81491.07x1010335130000.0100

71721.38x1010155818200.0060

60311.95x1010551 9100.0030

45843.37x1010106 3000.0010

40334.36x101049.25 1820.0006

33916.16x101017.41 910.0003

30647.54x10109.48 610.0002

257710.67x10103.35 300.0001

T, Kj, A m-3I, kA, nsa, m

Wire radius, a, and characteristic time . (Wire resistivity at 2000 K)

Peak current I at ε0 = 3x108 J m-1 per pulse (SQUARE PULSE )

Current density j at ε0 = 3x108 J m-1 per pulse (SQUARE PULSE )

Temperature T at 50 Hz operation, thermal radiation cooling only

A possible power supplyThe ISIS Extraction Kicker Pulsed Power Supply

Time, 100 ns intervals

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

Exponential with 30 ns rise time fitted to the waveform

a, m εe, J m-3

0.0001 1.1x108

0.0002 3.2x107

0.0003 1.3x107

0.0006 2.3x106

0.0010 5.7x105

0.0030 2.4x104

0.0060 3.0x103

0.0100 6.6x102

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 .

, ns

30

61

91

182

300

910

1820

3000

Current pulse

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

tejtj 10

is,

n

n nn

n

n

tt

aJ

rJe

ae

aJ

rJjtrj

n

1 1

022

1

20

0

2

21,

0 0.2 0.4 0.6 0.8 10.75

0.79

0.83

0.88

0.92

0.96

1

relative current density

r/a

Current density versus radius within the wire, radius a = 0.2 mm. Exponential pulse, rise time = 30 ns.

t = 60 ns

t = 100 ns

t = 150 ns

t = 200 ns

t

Current pulse

3 x108

0 0.2 0.4 0.6 0.8 1r/a

Energy density

J m-3

0

1x108

2 x108

ε0

t = 200 ns

t = 150 ns

t = 100 ns

t = 60 ns

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.

t

Current pulse

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

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.

to vacuum pumpor helium gas cooling

heater

test wire

insulators

to pulsed power supply

to pulsed power supply

water cooled vacuum chamber

Schematic diagram of the test chamber and heater oven.

Pbar Target TestsPbar target assembly presently in use

GraphiteTantalumGraphite

Jim Morgan

FNAL

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

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)