Difference between revisions of "Determining wire-theta correspondence"
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Revision as of 04:13, 21 May 2017
5.1.1 Determine a Wire-Theta Correspondence
|thstereo||6 degrees||Tilt of wires normal to sector midpoint|
|thtilt||25 degrees||Tilt relative to z|
|dist2tgt||228.078 cm||Distance from the target to the first guard wire plane along the
normal of said plane
|th_min||4.694 degrees||Polar angle to the first guard wire’s (in the first guard wire plane) midpoint
where the wire mid-point is the intersection of the wire with the chamber mid-plane
|wpdist||0.3861 cm||Distance between the wire planes|
At 25 degrees above the beam line direction, we can create a line that is perpendicular to the plane of the wires, which are at 65 degrees above the reverse beam line direction. This line will be a perpendicular line with respect to all parallel layers of wires with regards to the initial guard wire plane. We can use this geometry and dist2tgt, which is the distance from the target to the first guard wire in the first guard wire plane, to calculate other distances.
The wire planes in the DC are parallel to each other and separated by a constant distance wpdist. The parallel planes of wires are shown in the Figure 5.1.2 below.
The angle th_min is defined as the polar angle to the first guard wire’s (in the first guard wire plane) midpoint where the wire mid-point is the intersection of the wire with the chamber mid-plane. The first guard wire can be found at 4.694 degrees above the beam line. This position can be taken as the starting position for the initial guard wire plane. The planes of each wire runs 65 degrees above the reverse beam direction.
Using the law of sines, we can find the distance along the x' axis the 1st guard wire is from the beam line.
Making a right triangle, with the x' component as the hypotenuse, we find the x and z components
This gives the location of the first guard wire, in the plane of the foremost guard wires, at the midplane position to be in the frame of the target.
Examining the geometry file, we can see that each plane, not just the plane of the sense wires, is separated by a distance of D=.3861 cm. Each wire placement is half way between each wires in the adjacent planes. Each sense wire is in the center of an equilateral hexagon as a result. We can use the geometry of the wire placements to find
Finding the separation distance between two adjacent sense wires
Using the fact that the outer sides of an equalateral hexagon are equal in length, we can find that the distance from the first guard wire, in the first guard wire plane, to the first sense wire, in the first sense wire plane, is
The new x and z coordinates for wire 2 can be found using the change in the components
This can be extended to any point along the same wire plane, starting from the coordinates for wire 1 minus the difference in position to the next wire crossing on the plane.
The angle theta that the wire makes with the vertex is given by
For the values found earlier for the starting position: