Difference between revisions of "Determining wire-phi correspondance"
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dist2tgt - distance from the target to the first guard wire plane along the normal of said plane | dist2tgt - distance from the target to the first guard wire plane along the normal of said plane | ||
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Using Mathematica, we can produce a 3D rendering of how the sectors for Level 1 would have to interact with a steady angle theta with respect to the beam line, as angle phi is rotated through 360 degrees. | Using Mathematica, we can produce a 3D rendering of how the sectors for Level 1 would have to interact with a steady angle theta with respect to the beam line, as angle phi is rotated through 360 degrees. |
Revision as of 16:45, 3 January 2017
![DC stereo.png](/./images/d/d4/DC_stereo.png)
![DC Geomentry Sideview.png](/./images/e/ec/DC_Geomentry_Sideview.png)
xdist - distance between the line of intersection of the two end-plate planes and the target position =8.298 cm th_min=4.694
dist2tgt - distance from the target to the first guard wire plane along the normal of said plane
![Hex.png](/./images/2/2c/Hex.png)
Using Mathematica, we can produce a 3D rendering of how the sectors for Level 1 would have to interact with a steady angle theta with respect to the beam line, as angle phi is rotated through 360 degrees.
![PhiCone.png](/./images/5/50/PhiCone.png)
Looking just at sector 1, we can see that the intersection of level 1 and the cone of constant angle theta forms a conic section.
![Projection side view.png](/./images/8/8c/Projection_side_view.png)
![Projection Rear view.png](/./images/4/48/Projection_Rear_view.png)
Following the rules of conic sections we know that the eccentricity of the conic is given by:
Where β is the angle of the plane, which in our case is 25 degrees for the sectors with respect to the beam line (axis of rotation of the cone).
This leaves α is the slant of the cone, which is the angle theta that the particle must be traveling with respect to the beamline.
If the conic is an circle, e=0
If the conic is an parabola, e=1
If the conic is an ellipse,
![Conic section.png](/./images/e/ef/Conic_section.png)
For ellipses centered at (h,k):
where
![Ellipse.png](/./images/9/9b/Ellipse.png)
Where
For a parabola:
where
p = distance from vertex to focus (or directrix)