1. Russian Research Center” Kurchatov Institute” Shock wave propagation near 450 GeV and 7 TeV proton beams in LHC collimator materials Alexander Ryazanov “Basic Research of General Phenomena in Irradiated Materials and Physical Mechanisms of Radiation Resistance of Materials” 12 – 16 September 2011, CERN, Geneva

2. Aims of Investigations: Development of theoretical models for the investigations of shock wave propagation in the collimator materials: Cu and C under irradiation by 450 GeV and 7 TeV proton beams taking into account ionization, electronic excitation and physical properties of materials used deposited energy from FLUKA program. Calculations of shock wave propagation in collimator materials: Cu and graphite irradiated by 450 GeV and 7 TeV proton beams taking into account deposited energy, electronic excitation and energy transfer from electronic subsystem to ionic one in these materials. Simulation and modeling of real physical processes and microstructure change in different collimator materials: Cu and C produced by shock wave propagation initiated by a 450 GeV and 7 TeV proton beams. 12-16 September 2011, CERN, Geneva

3. Development of theoretical models for the calculations of shock wave propagation near 450 GeV and 7 TeV proton beams in LHC collimator materials. Materials: Copper Graphite Copper - diamond Physical Processes: Deposited energy by 450 GeV and 7 TeV proton beams from FLUKA Electronic excitation of electronic subsystem of materials Electronic thermal conductivity of materials Electron-phonon coupling in materials Phonon thermal conductivity of ionic subsystem of material “Thermal Spike” model “Coulomb Explosion” model

4. «Thermal Spike » Model r 7 TeV, p T e T e (r,t=0) D T e (r,t=τ ep ) T i T i (r,t =τ ep ) T i (r,t=0)=T 0 2r 0 T i (r,t > τ pp ) r 7 TeV, p RTRT T0T0 Z r 0 - characteristic distance for deposited energy (r 0 > D) calculated by FLUKA, R T = (D e τ ep ) ½ D = 0.2 mm D min = 0.016 mm Electronic Temperature: Ionic Temperature: FLUKA DATA HB-2006.29.05-02.06.2006., Tsukuba, Japan

5. Characteristic times in «Thermal spike » model: τ e ~ 10 -16 s - characteristic time of the electron - electron interaction; τ e-ph ~ 10 -13 s - characteristic time of the electron - phonon interaction; τ ph-ph ~ 10 -12 ÷10 -11 s - characteristic time of phonon - phonon interaction; τ cool~ 10-12 ÷10-3 s - characteristic time of cooling HB-2006.29.05-02.06.2006., Tsukuba, Japan

6. Bunch 2808 bunches E = 350 MJ (Melting 500 kg Cu) 0,5 ns 25 ns 0,5 ns 25 ns 0,5 ns 1 bunch -protons 7 ТeV

7. Maximum beam size is equal 200 microns Minimum beam size is equal 16 microns Collimator

8. Main equations for shock wave: ρ is the density of material, u is the velocity of atoms; Ti, Te are the temperatures of ionic and electronic subsystems of material; εi, εe are the internal energies of ionic and electronic subsystems of material; Кi, Ke are the lattice and electronic thermal conductivities; pi, pe are the thermal pressure in ionic and electronic subsystems of material; g is the electron-phonon constant of material, Ae,A i are the effective energy sources in electronic and ionic subsystem ( k = i, e )

9. Initial and Boundary Conditions for Shock Wave: 1. 2., t 0 = 0.5 – 1.06 ns HB-2006.29.05-02.06.2006., Tsukuba, Japan

10. The values used in the numerical calculations of shock waves in Cu HB-2006.29.05-02.06.2006., Tsukuba, Japan

11. Electronic thermal capacity in Cu HB-2006.29.05-02.06.2006., Tsukuba, Japan

12. Behavior of electronic thermal conductivity in Cu HB-2006.29.05-02.06.2006., Tsukuba, Japan

13. Behavior of ionic thermal conductivity in Cu HB-2006.29.05-02.06.2006., Tsukuba, Japan

14. Energy deposition per 7 TeV proton in electronic subsystem of copper as a function of the depth into target and the radial coordinate. 12-16 September 2011, CERN, Geneva

15. Distribution of electronic energy in Cu at 10E-5 sec near one bunch x10E 6 erg

16. Distribution of electronic energy in Cu at 10E-4 sec near one bunch x10E 6 erg 12-16 September 2011, CERN, Geneva

17. Distribution of electronic temperature in Cu near one bunch of 7 TeV proton beam (after t=10E-5sec) x10E 8 K

18. Distribution of electronic temperature in Cu near one bunch of 7 TeV proton beam (after t=10E-4 sec) x10E 8 K

19. Distribution of ionic temperature in Cu near one bunch of 7 TeV proton beam (after t=10E-5 sec) x10E 8 K

20. Distribution of ionic temperature in Cu near one bunch of 7 TeV proton beam (after t=10E-4 sec) x10E 8 K

21. Distribution of density in Cu near one bunch of 7 TeV proton beam (after t=10E-5sec) ρ, g/cm3

22. Distribution of density in Cu near one bunch of 7 TeV proton beam (after t = 10E-4 sec) ρ, g/cm3

23. Distribution of pressure in Cu near one bunch of 7 TeV proton beam (after t=10E-5sec)

24. Data used in the numerical calculations for Graphite Temperature dependence of the thermal conductivity of ionic subsystem of high density of graphite with 0% porosity. Electronic specific heat: C e = 3/2 N e k B = 1 J cm - 3 K -1. Electronic thermal conductivity: K e = 2 J cm -1 s - 1 K -1. T,  K K i, Cal Sec -1 cm -1 K - 1 0% porosity 12-16 September 2011, CERN, Geneva

25. 20% porosity Temperature dependence of the thermal conductivity of ionic subsystem of graphite with 20% internal porosity. K i, Cal Sec -1 cm - 1 K -1 T,  K 12-16 September 2011, CERN, Geneva

26. Temperature dependence of the thermal diffusivity of ionic subsystem of graphite. 12-16 September 2011, CERN, Geneva

27. E nergy deposition per 7 TeV proton in electronic subsystem of graphite as a function of the depth into target and the radial coordinate. 12-16 September 2011, CERN, Geneva

28. Distribution of Initial Deposited Energy in Electronic Subsystem in Graphite at t = 0 sec for 10Е11 protons [length] = 10-2 сm, [energy] = 1012 erg/g

29. Distribution of Electronic Energy in Graphite at 0.25x10-6 sec for 10Е11 protons [length] = 10-2 сm, [energy] = 1012 erg/g

30. Distribution of Electronic Energy in Graphite at 0.11x10-3 sec for 10Е11 protons [length] = 10-2 сm, [energy] = 1012 erg/g

31. Distribution of Electronic Energy in Graphite at 0.57x10-3 sec for 10Е11 protons [length] = 10-2 сm, [energy] = 1012 erg/g

32. Distribution of Initial Electronic Temperature in Graphite at t = 0 sec for 10Е11 protons [length] = 10-2 сm, [Temperature] = 10E8 K

33. Distribution of Electronic Temperature in Graphite at 0.25x10-6 sec for 10Е11 protons [length] = 10-2 сm, [Temperature] = 10E8 K

34. Distribution of Electronic Temperature in Graphite at 0.11x10-3 sec for 10Е11 protons [length] = 10-2 сm, [Temperature] = 10E8 K

35. Distribution of Electronic Temperature in Graphite at 0.57x10-3 sec for 10Е11 protons [length] = 10-2 сm, [Temperature] = 10E8 K

36. Distribution of Ionic Energy in Graphite at 0.25x10-6 sec for 10Е11 protons [length] = 10-2 сm, [energy] = 1012 erg/g

37. Distribution of Ionic Energy in Graphite at 0.11x10-3 sec for 10Е11 protons [length] = 10-2 сm, [energy] = 1012 erg/g

38. Distribution of Ionic Energy in Graphite at 0.57x10-3 sec for 10Е11 protons [length] = 10-2 сm, [energy] = 1012 erg/g

39. Distribution of Ionic Temperature in Graphite at 0.25x10-6 sec for 10Е11 protons [length] = 10-2 сm, [Temperature] = 10E8 K

40. Distribution of Ionic Temperature in Graphite at 0.11x10-3 sec for 10Е11 protons [length] = 10-2 сm, [Temperature] = 10E8 K

41. Distribution of Ionic Temperature in Graphite at 0.57x10-3 sec for 10Е11 protons [length] = 10-2 сm, [Temperature] = 10E8 K

42. Distribution of Pressure near 7 TeV Proton Beam in Graphite at 0.25x10-6 sec for one Bunch [length] = 10-2 сm, [pressure] = 1012 erg/cm3

43. Distribution of Pressure near 7 TeV Proton Beam in Graphite at 0.11x10-3 sec for one Bunch [length] = 10-2 сm, [pressure] = 1012 erg/cm3

44. Distribution of Pressure near 7 TeV Proton Beam in Graphite at t = 0.57x10-3 sec for one Bunch [length] = 10-2 сm, [pressure] = 1012 erg/cm3

45. Distribution of Density near 7 TeV Proton Beam in Graphite at t = 0.25x10-6 sec for one Bunch [length] = 10-2 сm, [density] = 1g/cm3 Initial Density - 2.27g/cm3

46. Distribution of Density near 7 TeV Proton Beam in Graphite at t = 0.11x10-3 sec for one Bunch [length] = 10-2 сm, [density] = 1g/cm3 Initial Density - 2.27g/cm3

47. Distribution of Density near 7 TeV Proton Beam in Graphite at t = 0.57x10-3 sec for one Bunch [length] = 10-2 сm, [density] = 1g/cm3 Initial Density - 2.27g/cm3

48. Distribution of Ion Velocities in Graphite near 7 TeV Proton Beam at t = 0.25x10-6 sec for one Bunch [length] = 10-2 сm, [velocity] = 10E6 cm/sec Initial Density - 2.27g/cm3

49. Distribution of Ion Velocities in Graphite near 7 TeV Proton Beam at t = 0.11x10-3 sec for one Bunch [length] = 10-2 сm, [velocity] = 10E6 cm/sec Initial Density - 2.27g/cm3

50. Distribution of Ion Velocities in Graphite near 7 TeV Proton Beam at t = 0.57x10-3 sec for one Bunch [length] = 10-2 сm, [velocity] = 10E6 cm/sec Initial Density - 2.27g/cm3

51. Distribution of Sound Velocity in Graphite near 7 TeV Proton Beam at t = 0.25x10-6 sec for one Bunch [length] = 10-2 сm, [velocity] = 10E6 cm/sec Initial Density - 2.27g/cm3

52. Shock Wave Propagation in Graphite and Distribution of Atomic Velocities near 7 TeV Proton Beam for one Bunch (10E11 protons) for two times: a) t = 0.11x10-3 sec; b) t = 0.57x10-3 sec Z z RoRo Y X=150cm 7 TeV p Graphite Beam R 0 – beam radius R 0 = 0.2mm Tensile area [length] = 10-2 сm, [atomic velocity] = 10E6 cm/sec Compression area Tensile area a) t = 0.11x10-3 sec b) t = 0.57x10-3 sec

53. Shock Wave Propagation in Graphite and Distribution of Pressure near 7 TeV Proton Beam with beam radius for one Bunch (10E11 protons) for two times: a) 0.25x10-6 sec ; b) t = 0.57x10-3 sec [length] = 10-2 сm, [pressure] = 10E12 erg/cm3 Compression area Tensile area z RoRo X=150cm Graphite Beam R 0 – beam radius R 0 = 0.2mm 7 TeV p a) 0.25x10-6 sec b) t = 0.57x10-3 sec

54. Distribution of Sound Velocity in Graphite near 7 TeV Proton Beam at t = 0.11x10-3 sec for one Bunch [length] = 10-2 сm, [velocity] = 10E6 cm/sec Initial Density - 2.27g/cm3

55. Distribution of Sound Velocity in Graphite near 7 TeV Proton Beam at t = 0.57x10-3 sec for one Bunch [length] = 10-2 сm, [velocity] = 10E6 cm/sec Initial Density - 2.27g/cm3

56. Density and ionic temperature changes under shock wave propagation in assembled materials Cu – C (“sandwich structures”) under 450 GeV proton beam irradiation at different number of bunches 200 bunches (5000 нс) 1000 bunches (25000 нс) 200 bunches (5000 нс) Temperature Density 1000 bunches (25000 нс) 12-16 September 2011, CERN, Geneva

57. Internal stress changes under shock wave propagation in assembled materials Cu – C (“sandwich structures”) under 450 GeV proton beam irradiation at different number of bunches 200 bunches (5000 нс) 400 bunches (10000 нс) 600 bunches (15000 нс) 1000 bunches (25000 нс) 12-16 September 2011, CERN, Geneva

58. Modeling of shock wave propagation in (“sandwich structure materials”) Cu – C at 450 GeV proton beam at 600 bunches (15000ns) and 1000 bunches (25000ns); free surface (boundary conditions) stress Internal energy density 600 bunches stress 1000 bunches Cu C boundary conditions 12-16 September 2011, CERN, Geneva

59. Modeling of shock wave formation in assembled materials (“sandwich structures”) Cu – C at 450 GeV proton beam 600 bunches (15000ns) and at 1000 bunches (25000ns); wave reflection (boundary conditions) Internal energydensity stress 600 bunches 1000 bunches Cu C boundary conditions 12-16 September 2011, CERN, Geneva