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Moving the Tagger Microscope (view source)

Revision as of 21:46, 31 March 2021

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→‎Calculating Position of Each Bundle Support Mounting Rod

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A summary of the spreadsheet calculations is a follows:

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===A summary of the spreadsheet calculations is a follows:===

<ul>

[[Image:Bundle_support_displacement.jpg|right|thumb|425px|Figure 16: Sketch showing the X-displacement along the focal plane (Δx) from the center of the first fiber column to the center of the sixth fiber column of the first bundle support.]]

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Now we know the focal plane crossing locations for the first and sixth SciFi columns in our first bundle. Additionally, we know the β angle of the first bundle (noted as βavg above), which gives us the optimal alignment for each fiber in the bundle to their respective electron's path. The β angles for the first and sixth columns will be off by the same magnitude, but with opposite signs.

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Now we know the focal plane crossing locations for the center of the first and sixth SciFi columns in our first bundle, as depicted in Figure 16 by the endpoints of Δx. Additionally, we know the β angle of the first bundle (noted as βavg above), which gives us the optimal alignment for each fiber in the bundle to their respective electron's path. The β angles for the first and sixth columns will be off by the same magnitude, but with opposite signs.

[[Image:e_path_in_Bundle.png|center|thumb|800px|Figure 17: Sketch showing the path of electrons that pass through the center of the fiber columns near the focal plane. At the back-end of the 2 cm. SciFi a misalignment of around 0.03 mm (with respect the the fiber's axis) results from using an averaged β angle for the bundle support location.]]

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The 5x6 fiber bundle supports were designed with two 5x3 bundle halves offset such that the center of the front face of the middle column in each bundle half would sit on the magnetic focal plane for a β angle of 12.0o. This angle was selected as a compromise that would allow coverage through the photon energy range of 10 - 5.6 GeV. As a side note - If required and finances permit, the 17 bundle supports can be easily redesigned for a different β angle. This redesign would take less than an hour of CAD work, with a manufacturing turn-around time in as little as two days. Costs are estimated to be around $2k. A CAD drawing of a new bundle support design already exists, which incorporates updated locations of the threaded holes for mounting the clamps that keep the bundle straps in place. The best time to replace/modify the bundle supports, if so desired, would be during fiber replacement. This way the new fibers can be mounted to the new bundle support outside the tagger hall, before ever making it to JLab. A conservative time estimate for changing the TAGM fiber configuration would be approximately two days (16 hours).

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The 5x6 fiber bundle supports were designed with two 5x3 bundle halves offset such that the center of the front face of the middle column in each bundle half would sit on the magnetic focal plane for a β angle of 12.0o. This angle was selected as a compromise that would allow coverage through the photon energy range of 10 - 5.6 GeV.

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As a side note - If required and finances permit, the 17 bundle supports can be easily redesigned for a different β angle. This redesign would take less than an hour of CAD work, with a manufacturing turn-around time in as little as two days. Costs are estimated to be around $2k. A CAD drawing of a new bundle support design already exists, which incorporates updated locations of the threaded holes for mounting the clamps that keep the bundle straps in place. The best time to replace/modify the bundle supports, if so desired, would be during fiber replacement. This way the new fibers can be mounted to the new bundle support outside the tagger hall, before ever making it to JLab. A conservative time estimate for changing the TAGM fiber configuration would be approximately two days (16 hours).

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 ≠ 12o, then the 1st & 6th, 2nd & 5th, and 3rd & 4th fiber column pairs will have the same magnitude offset as one another from the focal plane in Y, but with opposite signs, see Figure 17. 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).

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As shown in Figure 18 by the red and green lines, if β ≠ 12o 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 (βavg) and places the front center of the first column of SciFi on the XFP location corresponding to Eγo. Depending on β's departure from 12o 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 Eγo electron's path. The spreadsheet's title for this is "Pivot Point Move" and the description is detailed below.

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NOTE: &betaavg is used to determine this displacement. While the Eγo electron's β angle differs slightly &betaavg 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 βavg was used.

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NOTE: βavg is used to determine this displacement. While the Eγo electron's β angle differs slightly βavg 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 βavg was used.

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<center>For the next part we assuming the center of the first fiber column's front face is on the focal plane where an Eγo post-bremsstrahlung electron will cross and the bundle support is placed at an angle βavg</center>

[[Image:Bundle_support_FP_shift.jpg|right|thumb|550px|Figure 22: Sketch showing the displacement needed to move the "pivot point" to the focal plane for β ≠ 12o, while maintaining the first fiber column on the Eγo 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 Eγo electron passes and the bundle support is placed at angle βavg, use the difference between βavg and 19.5072o to calculate the YFP displacement required to place the focal plane back on the bundle support's pivot point</li>

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<li>Calculate the YFP displacement required to place the focal plane back on the bundle support's pivot point, Figure 20</li>

<ul>

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<li>The angle made by the first fiber column's longitudinal axis and a line from (X1, 0)FP to the pivot point is 19.5072o</li>

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<li>The angle made by the first fiber column's longitudinal axis and a line from (X1, 0)FP to the pivot point is 19.5072o, see Figure 19</li>

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<li>Use the difference between βavg and 19.5072o</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)FP plane) is 0.5895 inches</li>

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<li>Note that if ~~Beta angle~~ > ~19.5o (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 YFP direction)</li>

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<li>Note that if β > ~19.5o (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 YFP direction)</li>

</ul>

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<li>Utilizing the y-displacement value and the tangent of βavg, calculate the associated x-displacement along the focal plane to keep column #1 aligned to the electrons associated with Eγo</li>

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<li>Utilizing the y-displacement value found above and the tangent of βavg, calculate the associated x-displacement along the focal plane to keep column #1 aligned to the electrons associated with Eγo</li>

<li>Next determine the locations of the bundle support mounting rods in focal plane coordinates</li>

<ul>

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<li>Figure 21 shows the required dimensions for these calculations</li>

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<li>For x locations, include x1 for Eγo in addition to the rods' displacement from the front center of the first fiber column</li>

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<li>For y locations, we assume y1 for Eγo lies on the focal plane y-axis</li>

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</ul>

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Changes

Moving the Tagger Microscope (view source)

Revision as of 21:46, 31 March 2021

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