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Line 157: − xxxxxx − [[Image:Magnetic_Field_Map.pdf|center|thumb|300px|Figure 13: Table of the electrons' positions as they pass through the Focal Plane.]]+ + + + + − + − xxxxxx+ − + − + − + − + − <ul> − <li>Select a starting energy for the photon tagging array (highest γ energy to tag)</li> − [[Image:Bundle_support_displacement.jpg|right|thumb|400px|Figure : 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.]] − <li>Using [https://halldweb.jlab.org/wiki/images/b/b6/Counterbounds2017%28b%29.xlsx hodoscope energy bin bounds] interpolate the crossing angle with respect to the focal plane (β<sub>1</sub>) of an electron associated the highest energy to be tagged (starting E<sub>γ</sub>)</li> − <ul> − <li> Interpolate the location on the X<sub>FP</sub> axis at which this electron crosses (X<sub>1</sub>)</li> − <li> These electrons will pass through the center of the first column of SciFi fibers</li> − </ul> − <li>Using β<sub>1</sub> calculate 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</li>+ − <ul> − <li>Add Δx and X<sub>1</sub> to get X<sub>6</sub>, then interpolate the value of β<sub>6</sub></li> − <li>Using the average value of β<sub>1</sub> and β<sub>6</sub> (β<sub>avg.</sub>), recalculate the X<sub>FP</sub> displacement (Δx) from the center of the first to sixth fiber column (X<sub>6</sub>)</li> − <li>Repeat the above two steps until the bundle support angle β (e.g. average between β<sub>1</sub> & β<sub>6</sub>) does not change appreciably</li> − </ul> + + + − 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 β<sub>avg</sub> 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 : 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.]]+ + + + + + + + + + + − 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 12.0<sup>o</sup>. This angle was selected as a compromise that would allow coverage through the photon energy range of 10 - 5.6 GeV. <i><u>As a side note</u> - 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).</i>+ − + − 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>.]]+ − + − 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. + − + − + − + − + − Old-Popsicle-Stick-CAD-iso.png|Figure ???: Side view of a bundle support (a.k.a. popsicle stick).+ − Old-Popsicle-Stick-CAD-top.png|Figure ???: Top view of a bundle support (a.k.a. popsicle stick).+ − Old-Popsicle-Stick-CAD-iso3.png|Figure ???: Side view of a bundle support (a.k.a. popsicle stick).+ − + − + − + − popsicle_stick_pivot_point.png|Figure ???: Dimensions of the pivot point to the front center of the first column of fibers. The three 2 mm<sup>2</sup> boxes at the end of each 5x3 bundle half are <i>only</i> included to represent the width of a fiber column and have no meaning in length in the longitudinal axis direction.+ − popsicle_stick_fiber_angle8.png|Figure ???: Dimensions of the pivot point to the front center of the first column of fibers. The three 2 mm<sup>2</sup> boxes at the 5x3 bundle half are <i>only</i> included to represent the width of a fiber column and have no meaning in length in the longitudinal axis direction.+ − popsicle_stick_inch_angle.png|Figure ???: Dimensions of the bundle support as viewed from below. This view shows the location of the bundle support mounting rods at 2.75 in. and 8 in. from the front of the bundle support.+ − + − + − [[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.]]+ − + − + − <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>+ − <ul> − <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> − </ul> − <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> − <li></li> − <li></li> − <li></li> − <li></li> − <li></li> − − </ul> − − − − − − [[Image:popsicle_stick_pivot_point.png|center|thumb|600px|Figure : ]] − [[Image:popsicle_stick_fiber_angle9.png|center|thumb|600px|Figure : ]] − [[Image:popsicle_stick_inch_angle.png|center|thumb|600px|Figure : ]] − [[Image:popsicle_stick_fiber_angle8.png|center|thumb|600px|Figure : ]] − − − [[Image:Old-Popsicle-Stick-CAD-iso.png|center|thumb|600px|Figure : ]] − [[Image:Old-Popsicle-Stick-CAD-iso3.png|center|thumb|600px|Figure : ]] − [[Image:Old-Popsicle-Stick-CAD-top.png|center|thumb|600px|Figure : ]] − − [[Image:Fiber_Array.png|center|thumb|1200px|Figure 9: Electron view of the TAGM scintillating fiber array.]] − − <gallery caption="Transmission of scintillation light" widths="300px" heights="300px" class="center"> − Fiber_lg.jpg|Figure 10: An end view of a 2 mm<sup>2</sup> light guide fiber (BCF-98). A highly polished end such as the one shown here is required on the light guide end that interfaces with the SiPM for maximum light transmission. − Fiber.png|Figure 11: Image of the mating joint of 2 cm. of scintillating fiber BCF-20 (left) joined to 165 cm. light guide fiber BCF-98 (right). This picture was taken during the prototyping phase when optical epoxy was used to mate the fibers, the current method of joining fibers uses thermal fusing. − − − [[Image:SciFi-on-Popsicle-Stick.png|center|thumb|400px|Figure 12: CAD image of a bundle support (blue) with a mounted 5x6 fiber bundle. The 'S' bend minimizes the amount of fiber in the path of the electrons.]] + + + + + − [https://halldweb.jlab.org/wiki/images/e/e0/TaggerHodoscopeEnergy-1-2017.pdf Dan Sober Presentation] − ==Final== − xxxxxxxxxxxxx Line 240:
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Moving the Tagger Microscope (view source)
Revision as of 13:30, 27 April 2021
, 13:30, 27 April 2021→Bundle Support (aka Popsicle Stick)
<table align="right" cellpadding="3">
<table align="right" cellpadding="3">
<tr><td><b>Important Documents</b></td></tr>
<tr><td><b>Important Documents</b></td></tr>
<tr><td bgcolor="#e0e0f0">[[media:3DPrinterManual.pdf|3D Drawing ...1]]</td></tr>
<tr><td bgcolor="#e0e0f0">[https://zeus.phys.uconn.edu/halld/tagger/TAGM-4-2021/Protolabs_quote_6_2GeV_Move.pdf Protolabs Quote → 6.2 GeV Move]</td></tr>
<tr><td bgcolor="#e0e0f0">[[media:PLA_MSDS.pdf|3D Drawing ...2]]</td></tr>
<tr><td bgcolor="#e0e0f0">[https://zeus.phys.uconn.edu/halld/tagger/TAGM-4-2021/Top_Plate_6_2Gev.dwg Top-Plate<sub>(<i>3D CAD</i>)</sub> → 6.2 GeV Move]</td></tr>
<tr><td bgcolor="#e0e0f0">[[media:ABS_MSDS.pdf|3D Drawing ...3]]</td></tr>
<tr><td bgcolor="#e0e0f0">[https://zeus.phys.uconn.edu/halld/tagger/TAGM-4-2021/Upstream_Bar_6_2Gev.dwg Upstream Bar<sub>(<i>3D CAD</i>)</sub> → 6.2 GeV Move]</td></tr>
<tr><td bgcolor="#e0e0f0">[[media:Lab_419_Printer.pdf|3D Drawing ...4]]</td></tr>
<tr><td bgcolor="#e0e0f0">[https://zeus.phys.uconn.edu/halld/tagger/TAGM-4-2021/Downstream_Bar_6_2Gev.dwg Downstream Bar<sub>(<i>3D CAD</i>)</sub> → 6.2 GeV Move]</td></tr>
<tr><td bgcolor="#e0e0f0">[[https://docs.google.com/document/d/1TfcPB16d2L3PRFAXlTW4cL5QBGmv2FN2DODGC_htHYE/edit?usp=sharing | Some Logbook ...]]</td></tr>
<tr><td bgcolor="#e0e0f0">[https://zeus.phys.uconn.edu/halld/tagger/TAGM-4-2021/Bundle-Support-4-2021.xlsx TAGM Move Calculation Spreadsheet]</td></tr>
<tr><td bgcolor="#e0e0f0">[https://zeus.phys.uconn.edu/halld/tagger/TAGM-4-2021/TAGM_9_2GeV_Bundle_Rod_Fit.C C++ File → Fit mounting rod positions]</td></tr>
<tr><td bgcolor="#e0e0f0">[https://zeus.phys.uconn.edu/halld/tagger/TAGM-4-2021/TAGM_Weights.C C++ File → List of current rod positions fit eqns.]</td></tr>
</table>
</table>
=Moving the Tagger Microscope Along the Focal Plane=
==Tagger Microscope==
==Tagger Microscope==
[[Image:TAGM.png|center|thumb|500px|Figure 1: CAD image of the upper and lower enclosures of the Tagger Microscope made during the design phase.]]
[[Image:TAGM.png|center|thumb|500px|Figure 1: CAD image of the upper and lower enclosures of the Tagger Microscope made during the design phase.]]
Moving the TAGM to a new energy range not only involves the physical relocation of the microscope and its shielding along the tagger magnet's focal plane, but also requires internal realignment of the fiber, which is the subject of this page. The realignment of the scintillating fibers' longitudinal axes requires all 17 bundle supports to have new, individual crossing angles (β angle) with respect to the focal plane. These angles are derived from a table generated based on a TOSCA map of the post-bremsstrahlung crossing angles as they pass through the magnet's focal plane. Since the crossing angle changes with energy (e.g. displacement along the focal plane) each bundle support will have a slight "kick" or "tow" from the adjacent bundle support. The tow is typically on the order of 0.1<sup>o</sup>.
Moving the TAGM to a new energy range not only involves the physical relocation of the microscope and its shielding along the tagger magnet's focal plane, but also requires internal realignment of the fiber, which is the subject of this page. The realignment of the scintillating fibers' longitudinal axes requires all 17 bundle supports to have new, individual crossing angles (β angle) with respect to the focal plane. These angles are derived from a table generated based on a TOSCA map of the post-bremsstrahlung electrons' crossing angles as they pass through the magnet's focal plane. Since the crossing angle changes with energy (e.g. displacement along the focal plane) each bundle support will have a slight "kick" or "tow" from the adjacent bundle support. The tow is typically on the order of 0.1<sup>o</sup>.
Since the bundle supports have varying β angles, the parallel railing system that holds these supports in place are no longer representative of their namesake. That is, the front and rear rails of the parallel railing system are not parallel to each other and have a pitch with respect to one another. Figure 7 is a pictorial explanation of this and shows that for two equal length rails (front & rear), the length of the upstream and downstream alignment bars differ by 0.039 ± 0.001 in. at a starting photon energy (E<sub>γ</sub>) with a required tow of 0.09<sup>o</sup> between bundle supports. For each individual photon energy range covered by the microscope, or more simply stated for each energy that the microscope starts at, a new pitch for the parallel rails must be determined and three components (upstream alignment bar, downstream alignment bar, and upstream guide plate) unique to that starting energy must be fabricated. For this reason CAD drawings, an Excel spreadsheet, and this wiki page were created to provide the information needed to realign and move the TAGM to the following starting photon energies: 11, 10, 9, 8, 7, 6.5, 6, 5.5, and 5 GeV. The turnaround time for the machining components is typically two to five days, while the realignment of fibers will take no more than two days with inexperienced workers, and that's being conservative.
Since the bundle supports have varying β angles, the parallel railing system that holds these supports in place are no longer representative of their namesake. That is, the front and rear rails of the parallel railing system are not parallel to each other and have a pitch with respect to one another. Figure 7 is a pictorial explanation of this and shows that for two equal length rails (front & rear), the length of the upstream and downstream alignment bars differ by 0.039 ± 0.001 in. at a starting photon energy (E<sub>γ</sub>) with a required tow of 0.09<sup>o</sup> between bundle supports. For each individual photon energy range covered by the microscope, or more simply stated for each energy that the microscope starts at, a new pitch for the parallel rails must be determined and three components (upstream alignment bar, downstream alignment bar, and upstream guide plate) unique to that starting energy must be fabricated. For this reason CAD drawings, an Excel spreadsheet, and this wiki page were created to provide the information needed to realign and move the TAGM to any starting photon energy between 11 and 5 GeV. The turnaround time for the machining components is typically five to seven days, while the realignment of fibers will take no more than two days with inexperienced workers.
[[Image:Beta-Angle-Explanation-White.png|center|thumb|1000px|Figure 7: Pictorial representation of the alignment of the front and rear rails of the parallel railing system, which supports and aligns the optical fiber bundle supports along the tagger magnet's focal plane. The red circles represent the locations of the support rods that extend below the bundle supports and are used to secure them to the railings. This representative image was created from a 3D CAD drawing of the microscope which has a precision of ± 0.001 in.]]
[[Image:Beta-Angle-Explanation-White.png|center|thumb|1000px|Figure 7: Pictorial representation of the alignment of the front and rear rails of the parallel railing system, which supports and aligns the optical fiber bundle supports along the tagger magnet's focal plane. The red circles represent the locations of the support rods that extend below the bundle supports and are used to secure them to the railings. This representative image was created from a 3D CAD drawing of the microscope which has a precision of ± 0.001 in.]]
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<th colspan="2"; align="center" valign="top"; style="background-color:rgb(124,185,232); font-size:13px">New Coordinates</th>
<th colspan="2"; align="center" valign="top"; style="background-color:rgb(124,185,232); font-size:13px">Updated 2017 Coordinates</th>
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<td align="right" valign="top">X <sub>map</sub> = </td><td align="left" valign="top">0.73488 m</td>
<td align="right" valign="top">X<sub>map</sub> = </td><td align="left" valign="top">0.73488 m</td>
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<td align="right" valign="top">Y <sub>map</sub> = </td><td align="left" valign="top">1.22645 m</td>
<td align="right" valign="top">Y<sub>map</sub> = </td><td align="left" valign="top">1.22645 m</td>
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<td align="right" valign="top">X <sub>FP</sub> = </td><td align="left" valign="top">3.31245 m</td>
<td align="right" valign="top">X<sub>FP</sub> = </td><td align="left" valign="top">3.31245 m</td>
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<td align="right" valign="top">Y <sub>FP</sub> = </td><td align="left" valign="top">-0.00932 m</td>
<td align="right" valign="top">Y<sub>FP</sub> = </td><td align="left" valign="top">-0.00932 m</td>
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<th colspan="2"; align="center" valign="top"; style="background-color:rgb(244,143,177); font-size:15px">e<sup>-</sup> Focal Plane Crossing</th>
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<th colspan="2"; align="center" valign="top"; style="background-color:rgb(244,143,177); font-size:11px"><em>(for e<sup>-</sup> that will pass through the</em></th>
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<th colspan="2"; align="center" valign="top"; style="background-color:rgb(244,143,177); font-size:11px"><em>center of the 1<sup>st</sup> column's face)</em></th>
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<td align="right" valign="top">X<sub>FP</sub> = </td><td align="left" valign="top">3.26198 m</td>
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<td align="right" valign="top">Y<sub>FP</sub> = </td><td align="left" valign="top">0.0 m</td>
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<td align="right" valign="top">E<sub>γ</sub> = </td><td align="left" valign="top">9.201 GeV</td>
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<td align="right" valign="top">β = </td><td align="left" valign="top">12.695<sup>o</sup></td>
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==Bundle Support (aka Popsicle Stick)==
==Bundle Support (a.k.a. Popsicle Stick)==
The Tagger Microscope (TAGM) contains 17 optical fiber bundle, each consists of a 5x6 array of 30 fibers for a total of 510 fibers (5 rows, 102 columns). Figure 2 below shows the fiber array as viewed by the electrons passing through the tagger magnet focal plane. Each optical fiber consists of a 2 mm<sup>2</sup> x 2 cm BCF-20 scintillating fiber (SciFi) thermally fused to 2 mm<sup>2</sup> x 165 cm BCF-98 light guide, see Figures 3 & 4. The SciFi end of each fiber is thermally bent into an "S" shape to remove the fiber from the electrons' path soon after passing through the SciFi, see Figure 5. The fiber begins its bend out of the electrons' path after only 4.5 cm. This length provides enough material past the fused joint to minimize strain on the joint resulting from the bend and fiber mounting straps, while also reducing the material in the line-of-fire that could result in backscatter.
The Tagger Microscope (TAGM) contains 17 optical fiber bundle, each consists of a 5x6 array of 30 fibers for a total of 510 fibers (5 rows, 102 columns). Figure 2 below shows the fiber array as viewed by the electrons passing through the tagger magnet focal plane. Each optical fiber consists of a 2 mm<sup>2</sup> x 2 cm BCF-20 scintillating fiber (SciFi) thermally fused to 2 mm<sup>2</sup> x 165 cm BCF-98 light guide, see Figures 3 & 4. The SciFi end of each fiber is thermally bent into an "S" shape to remove the fiber from the electrons' path soon after passing through the SciFi, see Figure 5. The fiber begins its bend out of the electrons' path after only 4.5 cm. This length provides enough material past the fused joint to minimize strain on the joint resulting from the bend and fiber mounting straps, while also reducing the material in the line-of-fire that could result in backscatter.
<gallery caption="Bundle Support for a 5x6 Array of Fibers" widths="350px" heights="350px" class="center">
Old-Popsicle-Stick-CAD-iso.png|Figure 13: Side view of a bundle support (a.k.a. popsicle stick).
Old-Popsicle-Stick-CAD-top.png|Figure 14: Top view of a bundle support (a.k.a. popsicle stick).
Old-Popsicle-Stick-CAD-iso3.png|Figure 15: Side view of a bundle support (a.k.a. popsicle stick).
</gallery>
===<u>Popsicle Stick Limitations</u>===
Placing the "Pivot Point" on the focal plane and only allowing +0.5 cm towards the tagger magnet the maximum crossing angle for the current bundle support design is β<sub>max</sub> = 19.51<sup>o</sup>, while the minimum angle is β<sub>min</sub> = 4.05<sup>o</sup>. This does not account for the most forward bundle mounting strap clamp and bolts, but they are lower in Z<sub>FP</sub> than the fibers and should not extend significantly past the 0.5 cm limit even at lower β angles.
==Calculating Position of Each Bundle Support Mounting Rod==
==Calculating Position of Each Bundle Support Mounting Rod==
Up to 17 bundle supports can be mounted on the parallel railing system and instrumented in the TAGM. As the range of photon energies being tagged decreases (e.g. electron energy increases) the crossing angle (β angle) of the electrons with the focal plane also decreases. The smaller the β angle the more space along the X<sub>FP</sub> axis a bundle support will occupy. Below an E<sub>γ</sub> of 6.5 GeV (β = 9.5<sup>o</sup>) the length of the parallel railing system can only mount a maximum of 16 bundle supports.
Up to 17 bundle supports can be mounted on the parallel railing system and instrumented in the TAGM. As the range of photon energies being tagged decreases (e.g. electron energy increases) the crossing angle (β angle) of the electrons with the focal plane also decreases. The smaller the β angle the more space along the X<sub>FP</sub> axis a bundle support will occupy. Below an E<sub>γ</sub> of 6.5 GeV (β = 9.5<sup>o</sup>) the length of the parallel railing system can only mount a maximum of 16 bundle supports.
Since the β angle changes across the TAGM energy range, a universal bundle support β angle cannot be used. Starting with the most upstream bundle support (e.g. highest energy tagged photons) an initial bundle support angle is selected by taking the average of the crossing angles at the tagger magnet's focal plane for the electrons that pass through the center of the first and sixth fiber columns of that bundle. Recall that each bundle support holds an array of 5x6 fibers split into two 5x3 bundle halves. These halves are offset so that the bundle "pivot point" and the front center of each bundle half will all sit on the focal plane for a β angle = 12<sup>o</sup>. The pivot point is located at the midpoint of the bundle halves offset and the boundary point of the bundle halves along the bundle support long axis. The long axis that lies along the bundle support centerline passes through the pivot point, front mounting rod, and rear mounting rod. This fact is exploited during the calculations to follow. The pivot point is solely determined from the bundle support's design (e.g. offset distance) and is essential for fiber alignment on the focal plane. Regardless of the bundle β angle, if the focal plane passes through the bundle support's pivot point then the SciFi's will be at their optimal location with maximum fiber extension ± Y<sub>FP</sub> being the same.
Since the β angle changes across the TAGM energy range, a universal bundle support β angle cannot be used. Starting with the most upstream bundle support (e.g. highest energy tagged photons) an initial bundle support angle is selected by taking the average of the crossing angles at the tagger magnet's focal plane for the electrons that pass through the center of the first and sixth fiber columns of that bundle. Recall that each bundle support holds an array of 5x6 fibers split into two 5x3 bundle halves. These halves are offset so that the bundle "pivot point" and the front center of each bundle half will all sit on the focal plane for β = 12<sup>o</sup>. The pivot point is located at the midpoint of the bundle halves' offset and the boundary point of the two bundle halves (e.g. along the bundle support long axis). The long axis, which lies along the bundle support centerline, passes through the pivot point, front mounting rod, and rear mounting rod. This fact is exploited during the calculations to follow. The pivot point is solely determined from the bundle support's design (e.g. offset distance) and is essential for fiber alignment on the focal plane. Regardless of the bundle β angle, if the focal plane passes through the bundle support's pivot point then the SciFi's will be at their optimal location with the magnitude of maximum fiber extension (± Y<sub>FP</sub>) being the same.
Once the β angle for the first (upstream) bundle support is set, derived from the the starting photon tag energy, each subsequent bundle support has a β angle offset from the previous one by a tow angle. Thus, as we look downstream from one bundle support to the next, the β angle differ by -(tow angle). Adjacent bundle supports will come in contact with one another at the SciFi end and form a triangular gap along their adjacent sides based on the tow angle.
Once the β angle for the first (upstream) bundle support is set, derived from the the starting photon tag energy, each subsequent bundle support has a β angle offset from the previous one by a tow angle. Thus, as we look downstream from one bundle support to the next, the β angles differ by -(tow angle). Adjacent bundle supports will come in contact with one another at the SciFi end and form a triangular gap along their adjacent sides based on the tow angle.
An Excel [https://zeus.phys.uconn.edu/wiki/index.php/Student_Projects_in_Nuclear_Physics spreadsheet(placeholder)] has been created to calculate the location of the bundle supports' mounting rods with respect to the focal plane coordinate system. This spreadsheet also calculates the length of the parallel railing end supports which need to be fabricated anew for each unique TAGM location on the focal plane. One last, but very important thing that the spreadsheet calculates is the shim size needed during TAGM realignment in order to achieve the proper tow angle between bundle supports during mounting. In addition to the spreadsheet, AutoCAD drawings corresponding to a tagging energy spectrum starting at: [https://zeus.phys.uconn.edu/wiki/index.php/Student_Projects_in_Nuclear_Physics 11 GeV], [https://zeus.phys.uconn.edu/wiki/index.php/Student_Projects_in_Nuclear_Physics 10 GeV], [https://zeus.phys.uconn.edu/wiki/index.php/Student_Projects_in_Nuclear_Physics 9 GeV], [https://zeus.phys.uconn.edu/wiki/index.php/Student_Projects_in_Nuclear_Physics 8 GeV], [https://zeus.phys.uconn.edu/wiki/index.php/Student_Projects_in_Nuclear_Physics 7 GeV], [https://zeus.phys.uconn.edu/wiki/index.php/Student_Projects_in_Nuclear_Physics 6.5 GeV], [https://zeus.phys.uconn.edu/wiki/index.php/Student_Projects_in_Nuclear_Physics 6 GeV], [https://zeus.phys.uconn.edu/wiki/index.php/Student_Projects_in_Nuclear_Physics 5.5 GeV], and [https://zeus.phys.uconn.edu/wiki/index.php/Student_Projects_in_Nuclear_Physics 5 GeV] have been created. These CAD files contain the parallel railing system setup arranged for the corresponding photon energy range. These files are in US standard units (inches) and to scale with a tolerance of ± 0.001 inch.
An Excel [https://zeus.phys.uconn.edu/halld/tagger/TAGM-4-2021/Bundle-Support-4-2021.xlsx spreadsheet] has been created to calculate the location of the bundle supports' mounting rods with respect to the focal plane coordinate system. This spreadsheet also calculates the length of the parallel railing end supports which need to be fabricated anew for each unique TAGM location on the focal plane. One last, but very important thing that the spreadsheet calculates is the shim size needed, during TAGM realignment, in order to achieve the proper tow angle between bundle supports during mounting. In addition to the spreadsheet, an AutoCAD [https://zeus.phys.uconn.edu/halld/tagger/TAGM-4-2021/Parallel_Railing_Parts.dwg drawing] used to design the three parallel rail components needed for each unique tagging energy spectrum starting position of the TAGM and a [https://zeus.phys.uconn.edu/halld/tagger/TAGM-4-2021/Beta-Angle12_5-to-11_06deg_modified.dwg drawing] for the current setup (β = 12.5<sup>o</sup> to 11.06<sup>o</sup>). These files are in US standard units (inches) and to scale with a tolerance of ± 0.001 inch.
<u>A summary of the spreadsheet calculations is a follows:</u>
===<u>A summary of the spreadsheet calculations is on the following wiki page:</u>===
[https://zeus.phys.uconn.edu/wiki/index.php/Calculating_the_move Calculating the move]
[[Image:e_path_in_Bundle.png|center|thumb|800px|Figure 16: 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.]]
==TAGM Move Parameters for various E<sub>γ</sub> Starting Points==
Using the calculations explained in [https://zeus.phys.uconn.edu/wiki/index.php/Calculating_the_move "Calculating the move" wiki page], the following parameters for a 6 GeV maximum tagged photon energy were determined.
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<td align="left" valign="top">Starting E<sub>γ</sub> = </td> <td align="center" valign="top"> 6.0</td> <td align="left" valign="top"> GeV</td>
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<td align="left" valign="top">Ending E<sub>γ</sub> = </td> <td align="center" valign="top"> 4.475</td> <td align="left" valign="top"> GeV</td>
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<td align="left" valign="top">1<sup>st</sup> Bundle β<sub>o</sub> Angle = </td> <td align="center" valign="top"> 9.246</td> <td align="left" valign="top"> degrees</td>
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<td align="left" valign="top">1<sup>st</sup> Bundle Resolution = </td> <td align="center" valign="top"> 15.1</td> <td align="left" valign="top"> MeV</td>
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<td align="left" valign="top">Last Bundle β<sub>f</sub> Angle = </td> <td align="center" valign="top"> 8.51</td> <td align="left" valign="top"> degrees</td>
<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>
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<td align="left" valign="top">Last Bundle Resolution = </td> <td align="center" valign="top"> 17.1</td> <td align="left" valign="top"> MeV</td>
<gallery caption="Bundle Support for a 5x6 Array of Fibers" widths="350px" heights="350px" class="center">
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<td align="left" valign="top">No. of Bundles Used = </td> <td align="center" valign="top"> 16</td> <td align="left" valign="top">Bundles </td>
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<td align="left" valign="top">Tow Angle = </td> <td align="center" valign="top"> 0.049</td> <td align="left" valign="top"> degrees</td>
<gallery caption="Pivot Point Move for β ≠ 12 deg." widths="450px" heights="450px" class="center">
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<td align="left" valign="top">Tow Shim = </td> <td align="center" valign="top"> 0.0056</td> <td align="left" valign="top"> inches</td>
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<td align="left" valign="top">Forward Rail Pitch = </td> <td align="center" valign="top"> 0.035</td> <td align="left" valign="top"> degrees</td>
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<td align="left" valign="top">Rear Rail Pitch = </td> <td align="center" valign="top"> 0.118</td> <td align="left" valign="top"> degrees</td>
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<td align="left" valign="top">Starting E<sub>γ</sub> = </td> <td align="center" valign="top"> 11.0</td> <td align="left" valign="top"> GeV</td>
<td align="left" valign="top">Starting E<sub>γ</sub> = </td> <td align="center" valign="top"> 6.2</td> <td align="left" valign="top"> GeV</td>
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<td align="left" valign="top">Ending E<sub>γ</sub> = </td> <td align="center" valign="top"> 11.0</td> <td align="left" valign="top"> GeV</td>
<td align="left" valign="top">Ending E<sub>γ</sub> = </td> <td align="center" valign="top"> 4.703</td> <td align="left" valign="top"> GeV</td>
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<td align="left" valign="top">1<sup>st</sup> Bundle β<sub>o</sub> Angle = </td> <td align="center" valign="top"> 11.0</td> <td align="left" valign="top"> GeV</td>
<td align="left" valign="top">1<sup>st</sup> Bundle β<sub>o</sub> Angle = </td> <td align="center" valign="top"> 9.364</td> <td align="left" valign="top"> degrees</td>
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<td align="left" valign="top">Last Bundle β<sub>f</sub> Angle = </td> <td align="center" valign="top"> 11.0</td> <td align="left" valign="top"> GeV</td>
<td align="left" valign="top">1<sup>st</sup> Bundle Resolution = </td> <td align="center" valign="top"> 14.7</td> <td align="left" valign="top"> MeV</td>
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<td align="left" valign="top">No. of Bundles Used = </td> <td align="center" valign="top"> 17</td> <td align="left" valign="top">Bundles </td>
<td align="left" valign="top">Last Bundle β<sub>f</sub> Angle = </td> <td align="center" valign="top"> 8.605</td> <td align="left" valign="top"> degrees</td>
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<td align="left" valign="top">Tow Angle = </td> <td align="center" valign="top"> 11.0</td> <td align="left" valign="top"> <sup>o</sup></td>
<td align="left" valign="top">Last Bundle Resolution = </td> <td align="center" valign="top"> 16.8</td> <td align="left" valign="top"> MeV</td>
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<td align="left" valign="top">Rail Pitch = </td> <td align="center" valign="top"> 11.0</td> <td align="left" valign="top"> <sup>o</sup></td>
<td align="left" valign="top">No. of Bundles Used = </td> <td align="center" valign="top"> 16</td> <td align="left" valign="top">Bundles </td>
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<td align="left" valign="top">Tow Angle = </td> <td align="center" valign="top"> 0.051</td> <td align="left" valign="top"> degrees</td>
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<td align="left" valign="top">Tow Shim = </td> <td align="center" valign="top"> 0.0058</td> <td align="left" valign="top"> inches</td>
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<td align="left" valign="top">Forward Rail Pitch = </td> <td align="center" valign="top"> 0.036</td> <td align="left" valign="top"> degrees</td>
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<td align="left" valign="top">Rear Rail Pitch = </td> <td align="center" valign="top"> 0.123</td> <td align="left" valign="top"> degrees</td>
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