McSiM Barrel Strips upgrade geometry Steve McMahon RAL

The Aim : What am I trying to do? Provide a tool for fast (minutes) visualization of the layout of the upgrade strip barrel (barrel in the first instance, end-cap may come later) to answer some rudimentary questions concerning the layout. The things I would imagine that we will be able to provide are: module overlaps (active layers), clearances (of envelopes around modules), coverage (hole maps), momentum resolution, and their sensitivity to small changes in layout (radius, tilt angle, stereo angle) or removal of various section It is NOT a replacement for a CAD model or a full detector simulation.

How : The idea, the tools The code is written in ROOT in a general way. It should be configurable in a few minutes (ie create a new geometry) and run in seconds. It should be run by anybody on a laptop. It should be stand alone (no monster external libraries). Small amount of documentation.

Basic strip barrel geometry r X Y 11

Start with the basic 2D “line” geometry Y X P 0A P 0B P 1A (0,+w/2) (0,-w/2) (0,0) 11  C1C1 C0C0 P 1B r r Template Module at Origin : P TA (0,-w/2) P TB (0,+w/2) Angle of module Centre i:  i = i. 2  / N i=0,N-1 (N=4m) m is integer Template Module at Module Centre i R (  i . P TA (0,-w/2) R (  i . P TB (0,+w/2) Module Centre (red dot) at Module Centre i x(C i ) = r cos(  i ) r(C i ) = r sin(  i ) P TA P TB 11

Co-ordinates of module corners at every point on a circumference with N modules Module Centre Rotation of template module defined at the origin Template module X,Y coordinates of two-corners of the i th module of N

Co-ordinates of module corners for modules 0 and 1

Now restrict ourselves to P 0B and P 1A Y X P 0B P 1A 00 11

Visualisation in 2 dimensions of “line” detector

Angular Overlap Y X P 0B P 1A 00 11 Note overlap is negative until there is gap when it goes positive

Let’s take a simple, but useful, example Let’s take the strip barrel: – r=407mm, N=28 (4x7), w = 97.5mm – Let’s look at the overlap and its sensitivity to  (tilt)

Fractional Overlap Overlap in # strips and mm

Angular overlap, various radii r=407mm r=762mm Tilt-Angle/degrees Overlap / deg

r=407mm Overlaps Overlap / fraction Overlap / mm (80 micron pitch) Overlap in strips Tilt angle

Extend into 3 dimensions, add an extra piece of silicon and a stereo angle. Add some nice visualization of two barrels at a single Z

Now make 2 concentric barrels

Tracking Now adding (overlaying on the detector) samples to tracks to calculate maps of “holes”. Traditional to quote results for samples of 1GeV tracks Some numbers – P T [GeV/c] = 0.3 x B[T] x R[m] – For ATLAS : B = 2T – For a 1 GeV P T track R[m] = 1/0.6 ~ 1.6m

Basic track geometry 1GeV track, radius R cylinder, radius r rR R (x 1,y 1 ) R-x y x 2 +y 2 =r 2 (R-x) 2 +y 2 =R 2 x = r 2 /2R y = ± r(1-r 2 /4R 2 ) 1/2 (x 2,y 2 ) Y X Intersection of track with cylinder

Basic geometry : rotate track 1GeV track, radius R cylinder, radius r r  (x 1,y 1 ) x y x 2 +y 2 =r 2 R X Y C’(x,y) C’(x)=Rcos(  ) C’(y) =Rsin(  ) R.cos(  )-X Y-R.sin(  ) R 2 =[y-R.sin(  )] 2 + [R.cos(  )-x] 2

After the algebra has stopped Set Z=r 2 /2R X 2 -[2.Z.cos(  )].X + [Z 2 -r 2 sin 2 (  )]=0 Solve with normal quadratic form to get two solutions. This gives the intersection of the two circles The intersections of the tracks with the silicon will be done with some rudimentary ray-tracing algorithms. Only really need to do this for ¼ in phi and ½ length in Z to get a real picture of the coverage.

Upgrade Strips: Currently using

Conclusion A general non-specialist tool is being developed to answer some rudimentary questions about layout and layout evolution or changes. If you want something added … just ask. Anyone can contribute… I have a summer student (Varun Varahamurt) working with me on this from 4 th June to 10 th August.