Blanco Sancho, J.

Burkart, F.

Piriz, A. R.

Schmidt, R.

Shutov, A.

Tahir, N. A.

Wollmann, D.

GSI Repository

Numerical Simulations of Hydrodynamic Tunneling Experiments Performedat HiRadMat Facility Using SPS Proton Beam ∗N.A Tahir1, F. Burkart2, A. Shutov3, R. Schmidt2, D. Wollmann2, J. Blanco Sancho2, and A.R. Piriz41GSI, Darmstadt, Germany; 2CERN, Geneva, Switzerland; 3IPCP, Chernogolovka, Russia; 4UCLM, Ciudad Real,SpainExtensive simulations carried out over the past 10 yearsto study the full impact of the LHC beam on solid targetshas revealed substantial hydrodynamic tunneling of pro-tons and their shower [1-3]. This effect has very impor-tant implications on the LHC machine protection design.In order to confirm the validity of these simulations, exper-iments have been carried out at the HiRadMat facility using440 GeV protons impacting on solid targets. Detailed nu-merical simulations have been done to interpret the exper-iments. The experimental results together with a compari-son with the simulations has been reported elsewhere [4,5].In the present contribution we present the details about thesimulations.Figure 1: Energy distribution after 144 bunches.Figure 2: Temperature distribution after 144 bunches.The simulations have been carried out running an en-ergy deposition code FLUKA and a 2D hydrodynamic codeBIG2 iteratively using an iteration interval of 700 ns. Thebeam parameters include, proton energy = 440 GeV, bunchintensity = 1.5x1011, bunch length = 0.5 ns, bunch separa-tion = 50 ns and σ of the transverse intensity distribution =0.2 mm. In two experiments, 108 and 144 proton bunches,respectively, were used and the protons were delivered insets of 36 bunches each while a separation of 250 ns was∗Work supported by the BMBF and EuCARD2considered between the bunch packets. The target is con-sidered to be a solid copper cylinder 150 cm long having aradius of 4 cm, which is a good approximation to the targetused in the experiments [4,5].Figure 3: Pressure distribution after 144 bunches.Figure 4: Density state after 144 bunches.In Fig. 1, is plotted the specific energy deposition after144 bunches have been delivered. It is seen that a maxi-mum specific energy deposition of 6.3 kJ/g is achieved atthe target center. Fig. 2 shows a corresponding maximumtemperature of 7600 K. This high temperature generates ahigh pressure that leads to hydrodynamic motion in the tar-get material (see Fig. 3). The hydrodynamic motion leadsto substantial density depletion in the beam heated regionwhich is the cause of hydrodynamic tunneling. The sim-ulations show very good agreement with the experimentalresults [5].References[1] N.A. Tahir et al., JAP 97 (2005) 083532.[2] N.A. Tahir et al., PRE 79 (2009) 046410.[3] N.A. Tahir et al., PRSTAB 15 (2012) 051003[4] R. Schmidt et al., Proc. of IPAC13, Shanghai, China, 2013.[5] R. Schmidt et al., This year’s annual report.PNI-PP-17 GSI SCIENTIFIC REPORT 2013198 doi:10.15120/GR-2014-1-PNI-PP-17

Numerical Simulations of Hydrodynamic Tunneling Experiments Performed at HiRadMat Facility Using SPS Proton Beam

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Numerical Simulations of Hydrodynamic Tunneling Experiments Performed at HiRadMat Facility Using SPS Proton Beam

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