Optics study of the Enge spectrometer with the Splitter magnet

The Enge spectrometer used for E89-009 will be installed as an electron spectrometer to analyze scattered electron momentum. As already mentioned, it will be vertically pivoted by 7.75 degrees on the virtual target point (rotation radius 44.5 cm) in the E01-011 experiment. Figures 62 graphically demonstrates the kinematic parameters which describe an optical feature of the tilted Enge system obtained by the RAYTRACE simulation. The scattering angle distribution ($\theta _{e'}$ , top-left) shows that the tilted Enge system has an angular acceptance with a maximum around 5 degrees and clear cut off at 3.7 degrees (65 mr). The electron rate, which limited the beam intensity and target thickness in the E89-009 experiment, can be reduced to a few MHz, keeping the scattering angle as small as possible to maximize the virtual photon yield. This feature enables us to optimize the signal to bremsstrahlung background ratio for electrons.

The parameters for the Enge spectrometer were optimized with the RAYTRACE simulation based on the calculated angular and momentum distributions of electrons from the virtual photon process. The simulation result and matching with the kaon spectrometer parameters set the electron central momentum as 316 MeV/$c$. Figure 63 shows correlations between electron momentum and position or angle on the focal plane; the original symmetries of the optics were lost due to the tilt of the Enge spectrometer. Therefore, position measurement is not sufficient for the present configuration and it is essential to track the electrons to achieve the required momentum resolution of $4 \times 10^{-4}$. The expected total rate on the focal plane is a few MHz which is two orders of magnitude smaller than that of E89-009. Therefore, simultaneous measurements of position and angle are possible with a conventional tracking technique.

All focal plane parameters, x, x', y and y' (x' and y' are respectively in- and out- plane angles) will be measured to reconstruct momentum and scattering angle of electrons. Figure 64 provides the beam image on the focal plane and the detector size was determined to cover it. The momentum resolution was studied with a RAYTRACE simulation as functions of possible position and angular errors in the focal plane parameters. The results are shown in figure 65; the momentum resolution can be better than $4 \times 10^{-4}$ (FWHM) if the horizontal angular resolution is better than 2 mr (rms) (more moderate vertical angular resolution is acceptable) with a position resolution of $<$100 $\mu$m (rms). Since, the multiple scattering through detector materials as well as the position resolution will contribute to the total angular resolution, it is a key issue to control the multiple scattering in the detector though above requirements can be achieved with a conventional technique. The electron arm contribution to the hypernuclear mass resolution is about 120 keV (FWHM) assuming the electron momentum of 300 MeV/$c$. This is small enough compared with the other contributions.