8/3/2006 Cellular Wire Chamber Modeling Christine Middleton FNAL

8/3/2006 Outline Construct a cell Mathematically model the wires Determine wire readouts –For a track on one side of the wire plane –For a track that passes through the wire plane 4 Cell Design Determine wire readouts –For a single track –For a multi-track event Conclusions

8/3/2006 Construct a Cell = +

8/3/2006 Construct a Cell - 2 Note that the size and number of wires is completely arbitrary Note the division and half-divisions. At a division it is the same as the top. One picture on top of another. Height, Width and #of divisions determines wire angle. Same here …and here

8/3/2006 Mathematically Describing Wires The wire planes are in the Y-Z plane, and the tracks drift in the X direction Using that orientation, the wires can be described in point-slope form: The slope of the wire is determined by the width of the cell, the height of the cell, and the number of divisions By letting the Z-axis run along the top of the wire planes, it is easy to determine the Z-intercept for each wire –It is important to note that since the wires wrap around, each wire is described by two equations- one when it is on the front of the cell, and a different one when it is on the back of the cell

8/3/2006 Determining Wire Number Each of these points can then be associated with a wire in each of the three sets of wires using the equations describing the wires in each plane. Let s be wire spacing along the Z-axis, and n be wire number: For a track defined by endpoints (a,b,c), (a’,b’,c’), you can determine points along the line segment representing the track So, if a set of wires is described by Then in that wire plane, point (a,b,c) will hit wire number

8/3/2006 Values Used Wire Spacing (d)0.005m # of Divisions (R)2 Height (H)30m Width (W)3m # of Wires1114 Drift Velocity (v)1.5mm/μs VariableValueUnits Wire Spacing (d) refers to the perpendicular wire spacing, whereas s (used in the previous slide) refers to the horizontal wire spacing 1.5mm/μs (or 1500m/s) is a drift velocity that corresponds to an electric field of 500V/cm The number of wires is dependent on the width of the panel and the horizontal wire spacing These initial values were chosen in an effort to show somewhat realistic resultant values

8/3/2006 For a track with endpoints (2,.5,-3), (.5,1.5,-10) This is an event that occurred entirely on one side of the anode Since we know that vertical wires 1 to 557 are on one side of the anode, and we know which side that is, we know on which side of the anode this event occurred.

8/3/2006 For a track with endpoints (2,2,-8), (-1,1,-16) By analyzing the vertical wire readout, you can determine which side the tracks on the angled wires came from. This is a track that passed through the anode

8/3/ Cell Layout In the X-Y plane, you can see the numbering for the 4-cell system In the X and Y directions, there are two cells side by side

8/3/2006 Determining Position Based on the X and Y values of the point, as well as the dimensions of the cells, you can determine which cell the point falls in Since the anode is centered in the cell, the x coordinate allows you to determine which side of the anode a point is on, and therefore the direction from which it will approach the anode –Points that fall between the wire planes of the anode return wire # = 0

8/3/2006 Single Track Perpendicular Wire Spacing (d)0.005 Horizontal Wire Spacing (s) m # of Divisions (D)2 Height (H) (z direction)30m Width (W) (y direction)3m # of Wires1114 Drift Velocity (v)1500m/s Slope (m)2.5 Cell Thickness (x direction)3m Cells are 3m x 3m x 30m Drift velocity of 1.5 mm/μs (or 1500 m/s) was chosen to represent drift in an electric field of 500 V/cm

8/3/2006 Graphs for a track from (5, 4.5, -3) to (2.5, 2, -7) This is an event that passed through cells 1, 3, and 4. However, you can’t see much detail with these graphs.

8/3/2006 Close-up of Cell #1 From this close-up of the wires in cell #1, you can tell that this track passed through the anode in this cell

8/3/2006 Multi-Track Events νμνμ p+p+ μ+μ+ e-e- By entering multiple track segments, you can recreate an event that is somewhat like what you would expect to see in a detector ~ 20 cm ~ 1m ~ 2m Endpoints: p + track: (3.5, 4, -3) to (3.5, 4.2, -3.15) e - track: (3.45, 3.95, -3.1) to (3, 3.5, -4) μ + track: (3.5, 4, -3) to (2.5, 3.5, -4.7) π0π0

8/3/2006 Graphs for Track from Diagram With these more macroscopic graphs, you can tell which cells the event occurred in, but you can’t see much detail about what happened

8/3/2006 Close-up of Cell #1 In this close-up of the graphs from cell #1, you can see the vertex where the p track and the π track both start, as well as the displacement of the e track from the vertex.

8/3/2006 Close-up of Cell #2 In cell #2 you can see the continuations of the μ track and the e track

8/3/2006 Conclusions We can model an event in a single wire chamber cell or through multiple cells We can model a multi-track event that is similar to a real event Next Steps: –Use the output data (cell number, wire number, time) to recreate the track –Incorporate signal strength into output