CERN antiproton target: Hydrocode analysis of its core material dynamic response under proton beam impact

Antiprotons are produced at CERN by colliding a $26\mathrm{GeV}/\mathrm{c}$ proton beam with a fixed target made of a 3 mm diameter, 55 mm length iridium core. The inherent characteristics of antiproton production involve extremely high energy depositions inside the target when impacted by each primary proton beam, making it one of the most dynamically demanding among high energy solid targets in the world, with a rise temperature above $2000°\mathrm{C}$ after each pulse impact and successive dynamic pressure waves of the order of GPa’s. An optimized redesign of the current target is foreseen for the next 20 years of operation. As a first step in the design procedure, this numerical study delves into the fundamental phenomena present in the target material core under proton pulse impact and subsequent pressure wave propagation by the use of hydrocodes. Three major phenomena have been identified, (i) the dominance of a high frequency radial wave which produces destructive compressive-to-tensile pressure response (ii) The existence of end-of-pulse tensile waves and its relevance on the overall response (iii) A reduction of 44% in tensile pressure could be obtained by the use of a high density tantalum cladding.

Figure 1

Schematics of the water cooled antiproton target design used from 1987 to present day.

Figure 2

Scheme of the methodology employed in this study, including the two computational tools FLUKA and ANSYS AUTODYN®.

Figure 3

Half-view geometry of the different configurations studied in the present work: (a) W target surrounded by graphite matrix (b) W target with Cu cladding surrounded by graphite matrix (c) W target with Ta cladding surrounded by graphite matrix.

Figure 4

$3/4$ cut view of the temperature profile in the target core at the end of a single 26 GeV proton beam impact.

Figure 5

Pressure response at the center (gauge 7) and periphery (gauge 9) during the first $7\mu \mathrm{s}$ after the 430 ns -four bunches- proton pulse impact under infinitely elastic material assumption (reached pressures only for qualitative information). The plot clearly shows the existence of a radial wave with a $0.85\mu \mathrm{s}$ period. Note that the oscillation takes place in phase in the center and periphery, meaning that the rod material simultaneously expands and contracts within its transversal section.

Figure 6

Pressure response at the center (gauge 7) and periphery (gauge 9) during $20\mu \mathrm{s}–100\mu \mathrm{s}$ under infinitely elastic material assumption (reached pressures only for qualitative information). The plot clearly shows the presence of high frequency radial and low frequency $-24\mu \mathrm{s}$ period- longitudinal waves.

Figure 7

Plot of the axial displacement at different longitudinal positions of the target core after proton pulse impact and under infinitely elastic material assumption. The plot clearly shows how the material of the target core longitudinally expands and contracts with a period of $24\mu \mathrm{s}$.

Figure 8

Pressure response at the center (gauge 7) and periphery (gauge 9) of the target core after a 430 ns proton pulse impact. This simulation considers J-C strength model, which takes into account the material response beyond plasticity. Note the change in the pressure distribution in comparison to the pure elastic material assumption (Fig. 5).

Figure 9

Plot of the pressure response (blue) and its time derivative (green) in the center of the target core (gauge 7) during the first $1.5\mu \mathrm{s}$ after proton pulse impact. The plot clearly shows the discontinuities in the pressure derivative corresponding to the beginning and end of each of the four proton bunch impacts, the produced tensile wave at the end of the bursts, and four delayed waves, corresponding to the reflection of the four bunch impacts. This simulation is considering a J-C strength model for the tungsten target core.

Figure 10

Parametric study showing the pressure response in the center of the target core (gauge 7) for different proton pulse lengths. End-of-pulses tensile waves can be easily appreciated in the plot, as well as their amplifying effect when they are in phase with the natural radial waves. Compare $0.8\mu \mathrm{s}$ pulse length (brown) with $1.2\mu \mathrm{s}$ (purple), higher tensile pressure are reached in the former even if energy is deposited in a slower fashion.

Figure 11

Same analysis as in Fig. 10 but showing the pressure derivative for different pulse lengths. The influence of the end-of-pulse can be seen in the drop of the pressure derivative at the end of the pulses. It can be easily seen as well that, except on case of $0.1\mu \mathrm{s}$ length, these discontinuities in pressure derivative are more accentuated when the wave is going to tensile states, i.e. $DP/Dt<0$.

Figure 12

Pressure reached in the center of the target core (gauge 7) for the three scenarios of study. Assuming Johnson-Cook strength model for the tungsten core and models considering plasticity in the cladding consistently with Table 1. No failure models are considered. The plot shows the reduction of the reached tensile pressure when using Ta cladding.

Figure 13

Figure showing the state of the target core material after a proton pulse impact considering minimum hydrostatic failure model in tungsten. ($P_{\min }=-2.6\mathrm{GPa}$). The figure shows results for the three scenarios of study, demonstrating the efficacy of Ta cladding for reducing the internal core damage.