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Moving the Tagger Microscope (view source)
Revision as of 15:48, 30 March 2021
, 15:48, 30 March 2021→Calculating Position of Each Bundle Support Mounting Rod
Each bundle has a "pivot point" that when placed on the focal plane, provides the optimal y-displacement from the focal plane for each fiber column in that bundle without encroaching too close to the tagger magnet window. If the bundle β angle ≠ 12<sup>o</sup>, then the 1<sup><u>st</u></sup> & 6<sup><u>th</u></sup>, 2<sup><u>nd</u></sup> & 5<sup><u>th</u></sup>, and 3<sup><u>rd</u></sup> & 4<sup><u>th</u></sup> fiber column pairs will have the same magnitude offset as one another from the focal plane in Y, but with opposite signs, see Figure ???. This is all provided that when the bundle support is mounted on the parallel railing system the tagger magnet's focal plane passes through the midpoint between the front and rear bundle halves (the so called pivot point).
Each bundle has a "pivot point" that when placed on the focal plane, provides the optimal y-displacement from the focal plane for each fiber column in that bundle without encroaching too close to the tagger magnet window. If the bundle β angle ≠ 12<sup>o</sup>, then the 1<sup><u>st</u></sup> & 6<sup><u>th</u></sup>, 2<sup><u>nd</u></sup> & 5<sup><u>th</u></sup>, and 3<sup><u>rd</u></sup> & 4<sup><u>th</u></sup> fiber column pairs will have the same magnitude offset as one another from the focal plane in Y, but with opposite signs, see Figure ???. This is all provided that when the bundle support is mounted on the parallel railing system the tagger magnet's focal plane passes through the midpoint between the front and rear bundle halves (the so called pivot point).
[[Image:popsicle_stick_fiber_angle_top_view.png|center|thumb|800px|Figure : Sketch showing the "pivot point" that should always sit on the focal plane to provide the optimal fiber alignment. The green line running through the pivot point represent the placement of the focal plane for a bundle support with β = 12<sup>o</sup>, while the red line shows the placement for β > 12<sup>o</sup>.]]
[[Image:popsicle_stick_fiber_angle_top_view.png|center|thumb|800px|Figure : Sketch showing the "pivot point" that should always sit on the focal plane to provide the optimal fiber alignment. The green line running through the pivot point represent the placement of the focal plane for a bundle support with β = 12<sup>o</sup>, while the red line shows the placement for β > 12<sup>o</sup>.]]
As shown in Figure ??? by the red and green lines, if β ≠ 12<sup>o</sup> then the front face of the first column of SciFi no longer sits on the focal plane. This offset must be accounted for. The Excel spreadsheet starts by finding the optimal first bundle support crossing angle (β<sub>avg</sub>) and places the front center of the first column of SciFi on the X<sub>FP</sub> location corresponding to E<sub>γ<sub>o</sub></sub>. Depending on β's departure from 12<sup>o</sup> the pivot point will be displaced from the focal plane. The spreadsheet calculates the (Δx, Δy) needed to return the pivot point to the focal plane and keep the first fiber column's longitudinal axis on the E<sub>γ<sub>o</sub></sub> electron's path. The spreadsheet's title for this is "Pivot Point Move" and the description is detailed below.
As shown in Figure ??? by the red and green lines, if β ≠ 12<sup>o</sup> then the front face of the first column of SciFi no longer sits on the focal plane. This offset must be accounted for. The Excel spreadsheet starts by finding the optimal first bundle support crossing angle (β<sub>avg</sub>) and places the front center of the first column of SciFi on the X<sub>FP</sub> location corresponding to E<sub>γ<sub>o</sub></sub>. Depending on β's departure from 12<sup>o</sup> the pivot point will be displaced from the focal plane. The spreadsheet calculates the (Δx, Δy) needed to return the pivot point to the focal plane and keep the first fiber column's longitudinal axis on the E<sub>γ<sub>o</sub></sub> electron's path. The spreadsheet's title for this is "Pivot Point Move" and the description is detailed below.
<i><u>NOTE:</u> &beta<sub>avg</sub> is used to determine this displacement. While the E<sub>γ<sub>o</sub></sub> electron's β angle differs slightly &beta<sub>avg</sub> and would keep the column's centerline on the proper electron path, this discrepancy is so small that it does not come close to the TAGM machining parts' tolerance. Additionally, the sixth column's β angle has the same magnitude difference from the bundle support's β, but with a different sign. For these reasons β<sub>avg</sub> was used.</i>
<i><u>NOTE:</u> &beta<sub>avg</sub> is used to determine this displacement. While the E<sub>γ<sub>o</sub></sub> electron's β angle differs slightly &beta<sub>avg</sub> and would keep the column's centerline on the proper electron path, this discrepancy is so small that it does not come close to the TAGM machining parts' tolerance. Additionally, the sixth column's β angle has the same magnitude difference from the bundle support's β, but with a different sign. For these reasons β<sub>avg</sub> was used.</i>
<gallery caption="Bundle Support for a 5x6 Array of Fibers" widths="350px" heights="350px" class="center">
<gallery caption="Bundle Support for a 5x6 Array of Fibers" widths="350px" heights="350px" class="center">
[[Image:Bundle_support_FP_shift.jpg|center|thumb|600px|Figure : Sketch showing the displacement needed to move the "pivot point" to the focal plane for β ≠ 12<sup>o</sup>, while maintaining the first fiber column on the E<sub>γ<sub>o</sub></sub> electron's path.]]
[[Image:Bundle_support_FP_shift.jpg|center|thumb|600px|Figure : Sketch showing the displacement needed to move the "pivot point" to the focal plane for β ≠ 12<sup>o</sup>, while maintaining the first fiber column on the E<sub>γ<sub>o</sub></sub> electron's path.]]
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<li>Assuming the center of the first fiber column's front face is on the focal plane where E<sub>γ<sub>o</sub></sub> electron passes and the bundle support is placed at angle β<sub>avg</sub>, use the difference between β<sub>avg</sub> and 19.5072<sup>o</sup> to calculate the Y<sub>FP</sub> displacement required to place the focal plane back on the bundle support's pivot point</li>
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<li>The angle made by the first fiber column's longitudinal axis and a line from (X<sub>1</sub>, 0)<sub>FP</sub> to the pivot point is 19.5072<sup>o</sup></li>
<li>The distance of the center of the first fiber column's front face to the bundle support's pivot point (in the (x, y)<sub>FP</sub> plane) is 0.5895 inches</li>
<li>Note that if Beta angle > ~19.5<sup>o</sup> (e.g. > 10.86 GeV photons being tagged), then the pivot point will be below the focal plane; therefore, Δy will be positive (bundle shifts towards the magnet, positive Y<sub>FP</sub> direction)</li>
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<li>Utilizing the y-displacement value and the tangent of β<sub>avg</sub> calculate the associated x-displacement along the focal plane to keep column #1 aligned to the electrons associated with E<sub>γ<sub>o</sub></sub></li>
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