Particle Physics and Particle Astrophysics Research

U.K. Neutrino Factory Target Studies

Introduction

There are proposals [1] to build a Neutrino Factory in the US, Europe and Japan, in order to understand some of the basic properties of neutrinos. The Neutrino Factory will consist of a proton driver accelerator delivering short pulses of beam to a heavy metal target at GeV energies at up to ~50 Hz, with a mean power of ~4 MW. As a result of the beam interaction with the target, a number of pions will be produced, as well as other secondary products. The pions decay to muons which are focussed and accelerated to tens of GeV. The muons then circulate in a large storage/decay ring with long straight sections where they decay to neutrinos. The neutrinos come off in a narrow cone along the axis of the muon beam and the arms of the decay ring are directed at suitable neutrino detectors many kilometres distant.

To learn more about U.K. Neutrino Factory project try one of the following links:

Solid Target for a Neutrino Factory

The target in the Neutrino Factory forms the most likely showstopper in the project and hence R&D in this area is particularly important. Because of the high energy density dissipated in the target and difficulties in removing the heat, it has been proposed to use moving liquid and solid metal targets. A free mercury jet [2] has the advantages of not suffering from radiation damage and being capable of dissipating in excess of 1 MW. The MERIT experiment [3] will be run at CERN to test the principle and examine any problems. In solid target case, when a pulse from the proton driver hits the target, it will cause a temperature rise of up to 200 K in a few hundred ns. This will create two main problems:

  1. Without an efficient cooling system for a stationary target or a mechanism for changing the target between pulses, the target will become very hot, very quickly. Solid targets in the form of a rotating metal band [4,5] have been suggested. In this case we bring the same section of target into the beam every 3 s and, but even though it is cooled by radiation, the band will reach a steady state temperature of 2000 K.
  2. It will create a sudden thermal expansion in the centre of the target that will in turn create a stress or shock wave to pass through the material, reflect off the outer surface and oscillate for many 10's of microseconds (Figure 1). Simple calculations suggest that the maximum stress will exceed the yield strength of tantalum at 2000 K, for example. As well as these two problems, the target will also become extremely active and suffer very serious radiation damage. The radiation damage means that using a target that depends on some special property of material is risky as this property is unlikely to last very long.
Our efforts have been concentrated on the problem of shock in solid targets. The work we have done is described in the following sections. Note that although focussed on the Neutrino Factory, much of this work is directly relevant for other projects requiring high power targets, in particular the T2K experiment (Phase I and Phase II).

Shock studies

Shock is the main issue for solid targets and an experimental programme was required to assess the lifetime of different solids in a Neutrino Factory, benchmark models of shock in solids under the appropriate conditions and gain a better theoretical understanding of this phenomenon. The main difficultly for such a programme is producing a shock equivalent to that from the Neutrino Factory proton beam in the same manner as the protons would, without building the proton driver. The energy density from this will be about 300 J/cm3 averaged over the target. As a result, we devised a technique using a high current power supply. If a sufficiently large current in a sufficiently short pulse is passed through a small enough diameter conductor, the current will penetrate to the centre of the conductor in a time which is short compared to the speed of sound in the material. In this way, a shock can be induced which looks not unlike the heating from a proton beam at the centre. Results from a study [6,7] using LS-DYNA [8] show that a 8 kA pulse at 50 kV which has a rise time of about 100 ns and a total pulse length of 800 ns will achieve our aims. A thin wire is necessary to allow the current to diffuse into the centre of the wire in a sufficiently short time for the shock to be effective. For tantalum and tungsten the wire cannot be greater than ~0.5 mm in diameter.

A power supply for the ISIS [9] kicker magnets is being used, supplying a maximum of 60 kV and 10000 A at up to 50 Hz in a pulse which rises in 100 ns and is 800 ns long. The wires, of 3-4 cm length, are supported in a vacuum chamber to avoid oxidation. One end of the wire is firmly clamped and the other end is allowed to expand (Figure 2) freely through a pair of graphite (or copper) conductors which lightly clamp the wire.

Goran_UKNF_fig1.gif

Figure 1: The shock (radial stress) wave created in a tantalum target by the Neutrino Factory proton beam. It is shown for a pulse of 10 bunches of different lengths (see the LS-DYNA Studies section below).

The wire is operated at temperatures of 1600-2000 K by adjusting the pulse repetition rate. The temperature is measured by a manually operated optical pyrometer and an electronic pyrometer, which can measure at up to 1 kHz rate, allowing the pulse temperature to be measured. The current through the wire is measured by a current transformer. By calculating the Ohmic heating the temperature rise can be cross checked to the electronic pyrometer measurement. Note that the current also produces a magnetic field which squeezes the wire, inducing an additional stress. Both the effect from the heating of the wire (the thermal shock) and the magnetic effect (the Lorenz shock) are included in the LS-DYNA simulations (Figure 3).

Goran_UKNF_fig2.jpg

Figure 2: A tantalum wire under test

The power supply was initially run at 5 kA with tantalum, giving a 100 K temperature rise per pulse. This creates a stress equivalent to 2 MW proton beam in the Neutrino Factory target. The tests with tantalum achieved a lifetime of only 2x105 pulses, much less than the 3.3x106 required for one years running with each tantalum sample being in the beam every 3 s. Repeated tests always show basically the same failure mode. A qualitative understand of this has been achieved from LS-DYNA. As a result, we have proved that tantalum is simply too weak at 2000 K and hence a sample of tungsten was tested as this known to be stronger at these high temperatures.

Goran_UKNF_fig3.gif

Figure 3: Radial stress at the axis of the wire due to thermal (dotted line) and Lorenz forces (dashed line).

The results of a number of tests with 0.5 mm diameter tantalum and tungsten wires are summarised in Table 1. As we already said, the tantalum was too weak at temperatures of 1400 K or more necessary for the radiant heat dissipation and only one typical result is shown in the table. The tungsten was much more robust and most of the failures occurred in the end connections rather than the wire. In fact the wire only failed when operated at temperatures well over ~2000 K.

Table 1. Results of some tantalum and tungsten wire tests. Only one representative tantalum wire test is shown. The "Equivalent Target" columns show the equivalent beam power for a full size target of 2 and 3 cm diameter for the same stress in the test wire. (Assumes a parabolic beam distribution, 3 micro-pulses per macro-pulse of ~20 μs and beam diameter equal to target diameter.)

#Wire Material CurrentPulse Temp Peak TempNumber of Pulses Equivalent Target
        Beam Power Target Diameter
  AK KMillionsMW cm
1TANTALUM3000 6018000.2 --
 TUNGSTEN       
2Broke when increased to 7200 A (2200 K) 4900 902000>3.4 22
       43
3Stuck to top copper conductors 6400 1501900>1.6 42
       83
4Not broken 5560 12019004.2 32
 Top connector failed 5840 1302050>9.0 63
5Stuck to top copper conductors 7000 1801950>1.2 42
       83

The "Equivalent Target" values were calculated in the following way. As well as giving the pion flux, MARS [10] has been used here to determine the energy deposition in the target as a function of position. From this the temperature rise can be calculated. The temperature rises are then used in the LS-DYNA programme to calculate the dynamic stresses in the target. The stress in the wire is calculated including both temperature and the Lorenz force from the magnetic field produced by the current on itself. Hence it is possible to relate the current in the wire that produces the same peak stress in the full sized target.

The lifetime tests currently only induce radial and longitudinal oscillations in the wire. Experience from other target tests suggest that so-called "violin modes", corresponding to the beam passing through the target at an angle, may also be very important. It has been calculated that, for example, for the Neutrino Factory target with an off axis beam (displaced by 5 mm in a 10 mm radius target) the stress is increased by ~25%. It is planned to modify the experiment to induce and study these modes as well, by using two parallel wires carrying a current. Figure 4 shows the calculated additional stress for two parallel wires separated by a distance d carrying a pulse current I.

Goran_UKNF_fig4.gif

Figure 4. Additional stress in two parallel wires carrying a pulse current I separated by a distance d.

More results and details about the shock studies can be found on the following UK Neutrino Factory web page: http://hepunx.rl.ac.uk/uknf/wp3/wiretest.

LS-DYNA Studies

As indicated in the previous section, LS-DYNA simulations have been used both to plan and to understand the experimental tests of solid target lifetime. In addition, LS-DYNA has been used to investigate methods of reducing the shock in a solid target. These studies have focussed on two items: the bunch structure of the proton beam and the size of the target with respect to the beam size. The effect of the bunch structure is shown in Figure 1 and in more detail in Figure 5.

What has been studied is the effect of splitting a single bunch from the proton driver into a number of separate bunches. If these separate bunches are in a pulse which has a length which is comparable to the characteristic time of the target, the time it takes the shock to pass through it, then there is little reduction in the shock. However, if the separation between the bunches is long with respect to this time, then the effect of each bunch becomes independent and the overall shock is reduced by the number of bunches. Note that the stress passes both radially and longitudinally through the material. Although the radial stress is the biggest, there is an interference between these two. It is this interference that leads to the peaks in the figure. With the Neutrino Factory there is a requirement for short micro-pulses of 1-2 ns length within a macro-pulse of a few micro-seconds. An odd number of micro-pulses is preferred for the muon accelerator and the more micro-pulses the easier for the proton driver with regard to space charge. As a result, a possible design is for a proton beam of 3 or 5 micro-pulses spaced apart by 5-10 μs. It should be noted that it is against this number that the experimental work described in the previous section has been compared.

Goran_UKNF_fig5.gif

Figure 5: Variation of peak stress versus macro-pulse length in targets of 2 and 3 cm diameter with 3 and 5 equally spaced micro-pulses (2 ns long).

So, designers of the proton driver have indicated that splitting the beam into 3 (5) bunches, each 2 ns long, in a pulse of 30-40 μs should be possible. In this configuration, the maximum von Mises stress, the most important for the target, is about 300 MPa for our default target configuration (2 cm in diameter, ~20 cm in length). The effect of increasing the target size with respect to the beam size has also been studied. This shows that if the target is at least twice the radius of the beam, the additional material reduces the shock. There is a problem with doing this, however: the rate of re-absorption of the pions increases due to this additional material and the pion flux drops dramatically. As a result, we are taking the alternative approach of increasing both the beam size and the target size. So, we are able to reduce a shock by simply reducing the peak energy density in the target. An increase in diameter from 2 to 3 cm (see Figure 5) would bring a factor of 2 reduction in stress. The potential problem is, again, that the increase in material would bring a reduction in pion production due to re-absorption. However, studies performed with MARS indicate that the loss is only 5% and this may be recovered by increasing the target length (let's say from 20 to 25 cm).

We have also looked for either stronger materials or materials in which the shock is smaller than in tungsten. The thermal stress in the target is determined by the coefficient of thermal expansion &alpha (i.e. the amount it expands) and the elastic modulus E (i.e. its response), as follows:

ST ~ αEΔT/(1 - &nu)

where ΔT = Ed/Cp is the temperature rise, &nu is Poisson's ratio, Ed is the density of the energy deposition in the wire and Cp is the specific heat. Note that α, E, &nu and Cp are all temperature dependent and LS-DYNA is used to model for different materials under the Neutrino Factory target conditions. If the tensile strength is used as a measure of the mechanical strength of a material, then we can use the ratio of the thermal stress to the tensile strength as a quality factor for the material. The smaller this factor is, the better the material as a target. To achieve this requires one or more of a small coefficient of thermal expansion or a small elastic modulus to reduce the stress (e.g. graphite) or a large tensile strength (for example tantalum + 10% tungsten and tungsten + 25% rhenium). We plan to study these materials to see if they are really better than tungsten under such extreme conditions. In addition to this, a type of laser interferometer called a VISAR [11] has been ordered to make measurements of the surface acceleration of the wire. This will be compared with the predictions of LS-DYNA to ensure that our interpretation of the results seen is correct. Samples of tantalum and tungsten are also currently being irradiated in the Brookhaven National Laboratory to ensure that the material properties we are relying on, in particular tensile strength, are not adversely affected too much by radiation damage. In addition, tungsten has replaced tantalum in the ISIS target at RAL. The first target has been changed recently after suffering radiation damage of 12 dpa without failing. As an individual Neutrino Factory target will receive damage at a similar level, this is further positive evidence of the feasibility of a tungsten target. More results and details about our modelling studies can be found on the following UK Neutrino Factory web page: http://hepunx.rl.ac.uk/uknf/wp3/shocksims.

Conclusions

During this initial phase of studying thermal shock in materials that are candidates for a Neutrino Factory target we have:

  1. developed a much better understanding of shock in solid targets using LS-DYNA simulations,
  2. through this, identified methods by which the shock can be reduced,
  3. built a system for delivering sufficient shock in a manner very similar to a Neutrino Factory proton beam,
  4. using this, demonstrated that our original material candidate, tantalum, is not strong enough at 2000 K,
  5. demonstrated that in our standard configuration, tungsten has a sufficient lifetime when subjected to the radial and longitudinal shock from a 4 MW beam,
  6. demonstrated that by increasing the size of the target and beam, this limit can be extended above the required 4 MW without significant loss in the captured pion flux,
  7. provided an initial demonstration of the feasibility of a solid target for a Neutrino Factory.

Although some of the checks are still to be made, our conclusion is this work has given the first ever demonstration that a solid target may have sufficient lifetime due to shock in a multi-megawatt proton beam for neutrino production.

References

[1] NuFact Proceedings from 1999 to 2006; e.g. NuFact05; Nucl. Physics B (Proc. Suppl.) 155 (2006).
[2] C. D. Johnson, Nufact99, Lyon, http://lyoinfo.in2p3.fr/nufact99/agenda.html
[3] MERIT Home Page; http://proj-hiptarget.web.cern.ch/proj-hiptarget/default.asp?meet=True
[4] B. J. King, S. S. Moser, R. J. Weggel, N. V. Mokhov, Proceedings of the 1999 IEEE Particle Accelerator Conference, New York City, NY, USA, 29 March- 2 April, 1999, 3041-3043, IEEE 99Ch36366.
[5] J. R. J. Bennett, AIP Conference Proceedings, 542 (2000) 253.
[6] J. R. J. Bennett, C. N. Booth, R. A. Brownsword, C. Densham, R. Edgecock, G. P. Skoro, Nucl. Phys. Proc. Suppl. 155:293-294 (2006).
[7] J. R. J. Bennett, C. N. Booth, R. A. Brownsword, C. Densham, R. Edgecock, A. J. McFarland, G. P. Skoro, Nucl. Phys. Proc. Suppl. 155:291-292 (2006).
[8] Livermore Software Technology Corp., http://www.lstc.com/
[9] The ISIS web site; http://www.isis.rl.ac.uk/
[10] N. Mokhov, http://www-ap.fnal.gov/MARS
[11] L. M. Barker , R. E. Hollenbach, J. Appl. Phys., 43 (1972) 4669.

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