Beam induced hydrodynamic tunneling in the future circular collider components

A future circular collider (FCC) has been proposed as a post-Large Hadron Collider accelerator, to explore particle physics in unprecedented energy ranges. The FCC is a circular collider in a tunnel with a circumference of 80–100 km. The FCC study puts an emphasis on proton-proton high-energy and electron-positron high-intensity frontier machines. A proton-electron interaction scenario is also examined. According to the nominal FCC parameters, each of the 50 TeV proton beams will carry an amount of 8.5 GJ energy that is equivalent to the kinetic energy of an Airbus A380 (560 t) at a typical speed of $850\mathrm{km}/\mathrm{h}$. Safety of operation with such extremely energetic beams is an important issue, as off-nominal beam loss can cause serious damage to the accelerator and detector components with a severe impact on the accelerator environment. In order to estimate the consequences of an accident with the full beam accidently deflected into equipment, we have carried out numerical simulations of interaction of a FCC beam with a solid copper target using an energy-deposition code (fluka) and a 2D hydrodynamic code (big2) iteratively. These simulations show that, although the penetration length of a single FCC proton and its shower in solid copper is about 1.5 m, the full FCC beam will penetrate up to about 350 m into the target because of the “hydrodynamic tunneling.” These simulations also show that a significant part of the target is converted into high-energy-density matter. We also discuss this interesting aspect of this study.

Figure 1

Specific energy deposition $E_s$ for a 40 TeV FCC proton in a solid copper cylinder having radius $r=2\mathrm{cm}$, length $L=500\mathrm{cm}$, with facial irradiation, beam spot size characterized with standard deviation $\sigma =0.2\mathrm{mm}$ using the fluka code (a) using a solid density of $8.93\mathrm{g}/{\mathrm{cm}}^3$; (b) using the density distribution provided by big2 at $t=450\mathrm{ns}$, (c) using the density distribution provided by big2 at $t=850\mathrm{ns}$, and (d) using the density distribution provided by big2 at $t=1150\mathrm{ns}$ (fluka calculates energy deposition in the target by the beam with a defined spot size; the result is then downscaled for a single proton to allow an easy scaling depending on the total intensity).

Figure 2

Specific energy deposition in the target calculated by big2 (a) at $t=250\mathrm{ns}$ (10 bunches delivered), (b) at $t=500\mathrm{ns}$ (20 bunches delivered), (c) at $t=1000\mathrm{ns}$ (40 bunches delivered), and (d) at $t=1250\mathrm{ns}$ (50 bunches delivered).

Figure 3

Specific energy-deposition profiles vs distance in the target at different times: (a) along the axis at $r=0$, (b) at $r=1\mathrm{mm}$, and (c) at $r=2\mathrm{mm}$.

Figure 4

Temperature distribution in the target calculated by big2 (a) at $t=250\mathrm{ns}$ (10 bunches delivered), (b) at $t=500\mathrm{ns}$ (20 bunches delivered), (c) at $t=1000\mathrm{ns}$ (40 bunches delivered), and (d) at $t=1250\mathrm{ns}$ (50 bunches delivered).

Figure 5

Target temperature profiles vs distance in the target at different times: (a) along the axis at $r=0$, (b) at $r=1\text{mm}$ and (c) $r=2\text{mm}$.

Figure 6

Magnified view of the temperature profiles presented in Fig. 5.

Figure 7

Target pressure distribution calculated by big2 (a) at $t=250\mathrm{ns}$ (10 bunches delivered), (b) at $t=500\mathrm{ns}$ (20 bunches delivered), (c) at $t=1000\mathrm{ns}$ (40 bunches delivered), and (d) at $t=1250\mathrm{ns}$ (50 bunches delivered).

Figure 8

Pressure profiles vs distance in the target at different times: (a) along the axis at $r=0$, (b) at $r=1\mathrm{mm}$, and (c) at $r=2\mathrm{mm}$.

Figure 9

Target density distribution calculated by big2 (a) at $t=250\mathrm{ns}$ (10 bunches delivered), (b) at $t=500\mathrm{ns}$ (20 bunches delivered), (c) at $t=1000\mathrm{ns}$ (40 bunches delivered), and (d) at $t=1250\mathrm{ns}$ (50 bunches delivered).

Figure 10

Density profiles vs target cylinder at different times: (a) along the axis at $r=0$, (b) at $r=1\mathrm{mm}$, and (c) at $r=2\mathrm{mm}$.

Figure 11

Target physical state calculated by big2 (a) at $t=250\mathrm{ns}$ (10 bunches delivered), (b) at $t=500\mathrm{ns}$ (20 bunches delivered), (c) at $t=1000\mathrm{ns}$ (40 bunches delivered), and (d) at $t=1250\mathrm{ns}$ (50 bunches delivered).

Figure 12

Density on the axis vs distance in the target at different times, calculation of the penetration distance of the FCC beam in a solid copper target.