BE-ABP-HSC Non convex chamber in PyECLOUD Electron Cloud meeting G. Iadarola, A. Romano, G. Rumolo

BE-ABP-HSC Electron Cloud meeting PS standard Chamber LHC standard Chamber SPS Drift A Chamber R = 78 mm

BE-ABP-HSC Electron Cloud meeting PS standard Chamber LHC standard Chamber SPS Drift A Chamber R = 78 mm Non convex Polygon

BE-ABP-HSC Electron Cloud meeting The chamber module in PyECLOUD  The function “IsOutside” checks if a point (x,y) is internal or external to the chamber. P lies outside the polygon if for at least one edge is verified:  The function “ImpactPointAndNormal”, computes the crossing point between the segment P in P out and the chamber’s profile These algorithms work for convex polygon !

BE-ABP-HSC Electron Cloud meeting The “IsOutside” function 1/3 Convex Chamber Non-Convex Chamber

BE-ABP-HSC Electron Cloud meeting The “IsOutside” function 2/3 Point-In-Polygon algorithm  One simple way of finding if a test- point is inside or outside a general polygon  The number of intersections for a ray, starting from the point and going in any fixed direction, says where is the point : o If it is ODD, the point lies inside o If it is EVEN, the point lies outside

BE-ABP-HSC Electron Cloud meeting The “IsOutside” function 3/3 Convex Chamber No-Convex Chamber

BE-ABP-HSC Electron Cloud meeting The “ImpactPointAndNormal” function 1/3 Convex Chamber No-Convex Chamber

BE-ABP-HSC Electron Cloud meeting The “ImpactPointAndNormal” function 2/3  If the polygon is not convex, we can have more crossing point between the segment P in P out and the chamber’s profile  The minimum value of the crossing point for a same segment shoud be taken P out P in

BE-ABP-HSC Electron Cloud meeting Convex Chamber No-Convex Chamber The “ImpactPointAndNormal” function 3/3

BE-ABP-HSC Electron Cloud meeting Convex/nonconvex switch convex polygon The specific algorithm can be applied ! if the sign of all the cross products is the same For each set of three adjacent point A,B,C find the cross product AB x BC Algorithm to detect the type of polygon

BE-ABP-HSC Electron Cloud meeting Convex/noconvex switch no-convex polygon Algorithm to detect the type of polygon For each set of three adjacent point A,B,C find the cross product AB x BC if the sign of all the cross products is the same

13 Electric Field X Electric Field Y PyPIC 1.02 : Refined interpolation BE-ABP-HSC Electron Cloud meeting Electric Field X Electric Field Y PyPIC 1.01: Extrapolation method

Document reference14 Model of the LHC beam screen The aim is to study the EC build up through the holes of the LHC beam screen with and without baffle plates BE-ABP-HSC Electron Cloud meeting

Document reference15 BE-ABP-HSC Electron Cloud meeting

Conclusion and Next Steps Document reference16  Implementation in PyECLOUD of non-convex chamber geometries  Improvement of the code in order to correctly manage : o detection of in/out particles with respect to the chamber o impact of particles against the chamber wall o Interpolation of the electric field near the boundaries  Simulations on EC build up will be carried out in order to quantify the EC threshold and the Heat Load with and without baffle plates BE-ABP-HSC Electron Cloud meeting

BE-ABP-HSC Thanks for your attention! Electron Cloud meeting