1. 04.01.06G.Kurevlev - Manchester meeting1 Collimators Material Damage Study Previous results In our group - Adriana Bungau’s thesis - heat deposition on collimator from several bunches studied using Merlin code including scattering; 22 bunches melts Ti collimator without scattering; less critical with scattering included Beam Dump investigations - similar approach for different materials (C/Cu/H 2 O/Ar? – Cu/Ti/Be) they are not limited in material but probably have additional safety issues, we are limited but avoid shower damage in thin spoilers Two types of possible Collimators Energy Deposition sources - Ionization + electromagnetic shower: single particle models studied quite well by codes MARS, GEANT4, FLUKA … so we can get distributions for material damage analysis - Image current heating: important near wall effect (X.E.Lin, D.H.Whittum)

2. 04.01.06G.Kurevlev - Manchester meeting2 Collimators Material Damage Study All the possible heat deposition sources guide to instant temperature rise which can be solved by integration of the specific heat equation. Heat transfer equation can be solved separately then to get real time dependant temperature distribution between bunches. For metals we need to use all the parameters with real dependency of temperature. The results of analytical models need to be compared with simulations. ANSYS simulation can be really useful here as it can include phase transformations or melting and possible cracks of material.

3. 04.01.06G.Kurevlev - Manchester meeting3 Collimators Material Damage Study Ionization (approximations used for analytical study) Main source of heating – ionization with possible correction factor due to electromagnetic shower (1.4 - 2.5) Additional information needed for thick structures but not critical for L we can apply 2D models We can assume instant temperature rise due to a short bunch length in comparison with the heat diffusion Then we can get the temperature rise per bunch by integration

4. 04.01.06G.Kurevlev - Manchester meeting4 Collimators Material Damage Study Image current Q-particle charge, σ z -bunch length, δ-skin depth. a-particle offset from the metal surface in y axis g(u) – penetration function bigger then e -2u but could be approximated by it

5. 04.01.06G.Kurevlev - Manchester meeting5 Collimators Material Damage Study Heat transfer should be solved using Temperature rise limits: Temperature should be far enough from melting Induced thermal stress should be far enough from one leading to cracks

6. 04.01.06G.Kurevlev - Manchester meeting6 Collimators Material Damage Study Our approach to ANSYS simulation 2D geometry as we really can ignore longitudinal shower distribution for electrons in relatively thin collimators. Two test with energy generation command HGEN below.

7. 04.01.06G.Kurevlev - Manchester meeting7 Collimators Material Damage Study

8. 04.01.06G.Kurevlev - Manchester meeting8 Collimators Material Damage Study

9. 04.01.06G.Kurevlev - Manchester meeting9 Collimators Material Damage Study Still in progress - macro to create ANSYS keypoints that can reflect real bunch charge distribution received from another source Transient solution with a bunch current converted into time dependant energy deposition.