Tagger Microscope Placement in the Tagger Hall

Calculating Position of Each Bundle Support Mounting Rod

An Excel 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 drawing used to design the three parallel rail components needed for each unique tagging energy spectrum starting position of the TAGM and a drawing for the current setup (β = 12.5^o to 11.06^o). These files are in US standard units (inches) and to scale with a tolerance of ± 0.001 inch.

A summary of the spreadsheet calculations is a follows:

Figure 1: 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.

• Select a starting energy for the photon tagging array (highest γ energy to tag)
• Using hodoscope energy bin bounds interpolate the crossing angle with respect to the focal plane (β₁) of an electron associated the highest energy to be tagged (E_γo)
• Interpolate the location on the X_FP axis at which this electron crosses (X₁)
• These electrons will pass through the center of the first column of SciFi fibers
• Using β₁ 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
• Add Δx and X₁ to get X₆, then interpolate the value of β₆
• Using the average value of β₁ and β₆ (β_avg.), recalculate the X_FP displacement (Δx) from the center of the first to sixth fiber column (X₆)
• Repeat the above two steps until the bundle support angle β (e.g. average between β₁ & β₆) does not change appreciably

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 1 by the endpoints of Δx. Additionally, we know the β angle of the first bundle (noted as β_avg 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.

Figure 2: 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^o. 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).

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