Simulations of beam-matter interaction experiments at the CERN HiRadMat facility and prospects of high-energy-density physics research

In a recent publication [Schmidt et al., Phys. Plasmas 21, 080701 (2014)], we reported results on beam-target interaction experiments that have been carried out at the CERN HiRadMat (High Radiation to Materials) facility using extended solid copper cylindrical targets that were irradiated with a 440-GeV proton beam delivered by the Super Proton Synchrotron (SPS). On the one hand, these experiments confirmed the existence of hydrodynamic tunneling of the protons that leads to substantial increase in the range of the protons and the corresponding hadron shower in the target, a phenomenon predicted by our previous theoretical investigations [Tahir et al., Phys. Rev. ST Accel. Beams 25, 051003 (2012)]. On the other hand, these experiments demonstrated that the beam heated part of the target is severely damaged and is converted into different phases of high energy density (HED) matter, as suggested by our previous theoretical studies [Tahir et al., Phys. Rev. E 79, 046410 (2009)]. The latter confirms that the HiRadMat facility can be used to study HED physics. In the present paper, we give details of the numerical simulations carried out to understand the experimental measurements. These include the evolution of the physical parameters, for example, density, temperature, pressure, and the internal energy in the target, during and after the irradiation. This information is important in order to determine the region of the HED phase diagram that can be accessed in such experiments. These simulations have been done using the energy deposition code fluka and a two–dimensional hydrodynamic code, big2, iteratively.

Figure 1

Three target assemblies used in the experiments, each comprising 15 solid Cu cylinders; every cylinder has radius, $r=4$ cm, length, $L=10$ cm, and 1 cm separation in between.

Figure 2

Time structure of the proton beam.

Figure 3

fluka calculations of energy deposition of a single 440-GeV SPS proton in a solid copper cylinder having radius, $r=4$ cm, length, $L=150$ cm, with facial irradiation, beam spot size characterized by standard deviation, $\sigma$ = 0.2 mm; (a) using solid density of 8.93 g/${\mathrm{cm}}^3$; (b) using the density distribution provided by the big2 at $t=2.73\mu \text{s}$; (c) using the density distribution provided by the big2 at $t=4.75\mu \text{s}$; (d) using the density distribution provided by the big2 at $t=6.75\mu \text{s}$.

Figure 4

Target physical conditions calculated by big2 at $t=5800$ ns time when 108 bunches of 440-GeV protons with focal spot $\sigma$ = 0.2 mm, bunch intensity = $1.5\times {10}^{11}$ protons, bunch length = 0.5 ns, and bunch separation = 50 ns, have been delivered (Experiment 2); (a) specific energy deposition distribution; (b) temperature distribution; (c) pressure distribution; (d) density distribution.

Figure 5

Same as in Fig. 4, but at $t=7850$ ns, when 144 bunches have been delivered (Experiment 3).

Figure 6

Temperature vs target length at $t=7850$ ns, when 144 bunches have been delivered; (a) at $r=0.0$ (axis), (b) at $r=1$ mm, and (c) at $r=2$ mm.

Figure 7

Density vs target length at $t=7850$ ns, when 144 bunches have been delivered; (a) at $r=0.0$ (axis), (b) at $r=1$ mm, and (c) at $r=2$ mm.

Figure 8

Target physical state at $t=7850$ ns, when 144 bunches have been delivered.

Figure 9

Picture showing gap between cylinders 4 and 5 of Target 3 (Experiment 3), holes generated on the faces of the cylinders, and the ejection of molten or evaporated copper which has been solidified at the surface, is clearly visible.

Figure 10

Top cover of the experimental setup after the irradiation. Traces of projected copper between the 10-cm-long cylinders of the targets indicate the length of the melting or evaporation zone. For Target 1 (bottom) the molten or evaporation zone ends in the sixth cylinder, i.e., the copper was molten over a length of $55\pm 5$ cm. For Target 2 (mid) the molten zone goes up to cylinder 8, i.e., $75\pm 5$ cm. For Target 3 (top) the molten zone goes up to cylinder 9, i.e., $85\pm 5$ cm.

Figure 11

(a) $\rho$ and $T$ vs target axis at $t=5800$ ns (108 bunches); (b) $\rho$ and $T$ vs target axis at $t=7850$ ns (144 bunches).