Simulation of hydrodynamic tunneling induced by high-energy proton beam in copper by coupling computer codes

Abstract

The design of machine protection systems for high-energy accelerators with high-intensity beams requires analyzing a large number of failures leading to beam loss. One of the most serious failures is an accidental impact of a large number of bunches at one location, for example, due to a deflection of the particle beams by the extraction kicker magnets with the wrong strength. The numerical assessment of such an event requires an iterative execution of an energy-deposition code and a hydrodynamic code, in case the hydrodynamic tunneling effect plays an important role in the beam-matter interactions. Such calculations have been performed for the CERN Large Hadron Collider (LHC), since the energy stored in the LHC beams exceeds previous accelerators by 2 orders of magnitude. This was done using the particle shower code fluka and the hydrodynamic code big2 [Tahir et al., Phys. Rev. ST Accel. Beams 15, 051003 (2012)PRABFM1098-440210.1103/PhysRevSTAB.15.051003]. Later, simulations for a number of cases for other accelerators at CERN and the Future Circular Collider (FCC) were performed [Tahir et al., Phys. Rev. Accel. Beams 19, 081002 (2016)PRABCJ2469-988810.1103/PhysRevAccelBeams.19.081002]. These simulations showed that the penetration depth of the beam in copper or graphite could be an order of magnitude deeper when considering the hydrodynamic tunneling, compared to a static approximation. big2 is very efficient and used at GSI. It is always advantageous to cross-check the simulation results with different codes, because dedicated experiments are very complex or even impossible to carry out. For this purpose, it was decided to study the use of a commercial tool (Autodyn) for such calculations and to compare the results with previous work. This paper reports a benchmarking study against beam experiments performed at the HiRadMat (High-Radiation to Materials) facility using beams at 440 GeV from the Super Proton Synchrotron. Good agreement has been found between the simulation results and the experiments as well as previous simulations with fluka and big2 [Tahir et al., Phys. Rev. E 90, 063112 (2014)PRESCM1539-375510.1103/PhysRevE.90.063112], particularly in terms of the penetration depth of the beam in copper. This makes the coupling of fluka and Autodyn an alternative solution to the simulation of the hydrodynamic tunneling, at least in the parameter range of this case study. Studies with other parameters are planned for FCC and other high-beam-power accelerators.