Sieve-slit runs

In a normal spectrometer geometry without magnetic field at the target, the sieve-slit run provides the specific incident angular information for each event that reaches the focal plane through a fixed sieve-slit hole. Then using the known incident angles (in-plane and off-plane) and the measured focal plane orientation the angular optical reconstruction matrices are fitted and optimized.

In case of the HKS experimental geometry (similar to HNSS), a splitter magnetic field is present ahead of the sieve-slit plates in HKS and Enge. This causes the events that pass through each specific hole to have a strong angular and momentum correlation, i.e. each hole does not select a specific incident orientation. The usual way of obtaining the angular matrices needs to be modified.

From extensive studies and experiences from the HNSS experiment (E89-009), it was realized that the accuracy of the Splitter optics gives negligible effect to the entire optics. From the total integral of $B dl$ point of view, the Splitter contribution is only $\sim$8%. Even if the field description is known to the precision of 10$^{-3}$ level, the contribution to the resolution from the Splitter is less than 10$^{-4}$. Therefore, with a detailed TOSCA calculation of the Splitter field, we can initially treat the Splitter field as known. Using a sieve-slit simulation, a correlation of the incident angles and momentum can be found from the events passed through each sieve-slit hole, although it means a few tens of terms are needed to represent such correlations.

With the experiences from HNSS (Splitter+SOS), we found that measured events at the focal plane can be easily separated for each specific sieve-slit hole. Since we have good initial momentum matrices of Enge from the previous HNSS calibration as well as of HKS from its detailed field mapping, the initial momentum values are known with a reasonably good accuracy. Therefore, using the known functions of the incident angles vs. momentum, initial incident angles from the target can be found for each event. Figure 66 shows incident angle (in-plane, $xpi$ and off-plane, $ypi$) correlations with momentum ($dp$ = 100 $\times (p - p_0)/p_0$) obtained by a RAYTRACE simulation for electrons that passed through the Enge sieve slit. Each correlation band represents events from a single row (in-plane) or a column (off-plane) of holes and they follow the same function. Thus, only one function is needed per row and per column. The broadening or width of the band is due to the hole size. The accuracy of the needed functions relies on the central fitting only.

At this stage, the sieve-slit data is recovered to contain all angular information and known initial momentum. Therefore, the normal sieve-slit optimization process can be applied.

• Enge sieve slit and collimator
  A sieve slit and collimator plate made of HEAVIMET (1" thick tungsten alloy) will be installed at the entrance of the Enge spectrometer for the calibration of the optics. Figure 17 shows that the bremsstrahlung electrons are concentrated in the Splitter mid-plane which is about 8 cm below the Enge spectrometer collimator opening. The opening of the collimator should be designed to block the bremsstrahlung (blue) and M$\phi$ller (green) electrons and additional local lead shielding will be installed outside the vacuum connection. The scattered electrons associated with the virtual photons (magenta) are also peaked on the Splitter bending plane but they fall off slower than bremsstrahlung does. The electrons associated with virtual photons accepted by the Enge spectrometer at the focal plane are plotted with the red points in figure 17 to determine the collimator and sieve slit size.

  Figure 67 shows correlations between focal plane parameters for sieve slit image (the sieve slit plate has 35 holes, 5 rows and 7 columns). The first plot shows the accepted events reconstructed to the sieve slit plate calculated with the RAYTRACE simulation. A clear hole pattern was observed. Cuts could be applied to separate events for a specific hole to calculate the incident angles at the target.

• HKS sieve slit and collimator
  

  Similar to the Enge sieve slit, a sieve slit and collimator plate made of HEAVIMET (2'' thick) will be installed between the Splitter and Q1 magnets. A hole pattern is given in figure 68. The holes are drilled to aim at the virtual target position rather than to be straight.

  Figure 69 shows the correlation between focal plane parameters calculated with the GEANT simulation. The hole diameter was determined to be 0.25'' by optimization of S/N ratio and hole pattern yield (Only the center hole has a smaller diameter for the resolution study). By combination of the focal plane parameters, we can select the events which passed through a specific hole.