1 A.I.Ryazanov, E.V.Semenov and A.Ferrari DPA calculations in irradiated graphite collimator materials under 7 TeV and 450 GeV proton beams , CERN, Geneva, Switzerland National Research Centre” Kurchatov Institute” European Organization for Nuclear Research

2 Energy flux of secondary protons formed in graphite at different distances along the beam of 7 TeV protons , CERN, Geneva, Switzerland

3 Energy flux of secondary electrons formed in graphite at different distances along the beam of 7 TeV protons , CERN, Geneva, Switzerland

4 Energy flux of secondary charged pi-mesons formed in graphite at different distances along the beam of 7 TeV protons , CERN, Geneva, Switzerland

5 Cumulative energy flux of secondary neutrons formed in graphite at different distances along the beam 7 TeV protons , CERN, Geneva, Switzerland

6 Displacement cross-section , CERN, Geneva, Switzerland - Differential cross-section of secondary particles (neutrons and others) with kinetic energy E to interact with target graphite atom, that will have energy T. ν (T) is the cascade function (number of collisions created by primary knock-on atom with energy T), i is the index of summation over various nuclear reaction channels.

, CERN, Geneva, Switzerland

8 Cascade function , CERN, Geneva, Switzerland are atomic numbers of incident and target atoms, respectively, and - Bohr radius, and - displacement energy, are atomic masses of incident and target atoms, respectively,

The crystal structure of graphite showing the ABAB stacking sequence of graphene planes in which the carbon atoms have three fold coordination , CERN, Geneva, Switzerland The value of E d lies between 24 and 60 eV. (E d =25eV)

10 Differential cross-section of electrons and charged pions , CERN, Geneva, Switzerland McKinley and Feshbach formula for low-Z materials

11 Displacement cross-section of secondary neutrons formed in graphite under 7 TeV proton beam irradiation , CERN, Geneva, Switzerland

12 Displacement generation rate of point defect production , CERN, Geneva, Switzerland G d = n p is the total number of protons in a bunch(1.1*10 11 ), τ is the time gap between bunches (26 ns), Ф(Е) is the energy spectrum of secondary particles having energy E and interacting with graphite atoms, σ d (E) is the cross section of defect formation with the secondary particle energy E.

13 Displacement rate of DPA produced by secondary protons at different distances along the beam of 7 TeV protons per each bunch , CERN, Geneva, Switzerland

14 Displacement rate of DPA produced by secondary pions at different distances along the beam of 7 TeV protons per each bunch , CERN, Geneva, Switzerland

15 Displacement rate of DPA produced by secondary neutrons under 7 TeV proton beam irradiation per each bunch , CERN, Geneva, Switzerland

16 The spectrum of pions (π - ) produced in graphite at different distances along the beam of 450 GeV protons (FLUKA) , CERN, Geneva, Switzerland

17 Displacement cross sections for secondary pions with energies up to 450 GeV in graphite , CERN, Geneva, Switzerland

Cross section of defect formation for secondary π – mesons in graphite near 450 GeV proton beam

19 Generation rate of primary radiation point defects (DPA) in graphite versus energy of pions at different distances along the beam of 450 GeV protons per each bunch , CERN, Geneva, Switzerland

20 The spectrum of secondary relativistic electrons produced in graphite at different distances along the beam of 450 GeV protons (FLUKA) , CERN, Geneva, Switzerland

21 Displacement cross sections for secondary electrons with energies up to 450 GeV in graphite , CERN, Geneva, Switzerland

22 Generation rate of primary radiation point defects (DPA) in graphite versus energy of secondary electrons at different distances along the beam of 450 GeV protons per each bunch , CERN, Geneva, Switzerland

23 Energy spectra of secondary neutrons formed as a result of interaction of 450 GeV proton beam with graphite along beam axis , CERN, Geneva, Switzerland

24 Generation rate of point defect formation (DPA) under irradiation by secondary neutrons along axis of 450 GeV proton beam , CERN, Geneva, Switzerland

25 Conclusion Maximum of displacement rates for 7 TeV protons correspond to the following secondary particles: Protons – dpa/s per proton bunch Pions – 0.11 dpa/s per proton bunch Neutrons – dpa/s per proton bunch Maximum of displacement rates for 450 GeV protons correspond to the following secondary particles: Electrons – 4e-3 dpa/s per proton bunch Pions – 4.3e-3 dpa/s per proton bunch Neutrons – 4e-3 dpa/s per proton bunch

26 Thank you very much for your attention! Thank you very much for your attention!