Tilt method and optimization

In the pilot (e,e'K) hypernuclear experiment, E89-009, the electrons associated with bremsstrahlung dominated the background in the scattered electron spectrometer. The idea to suppress the bremsstrahlung background is to use the difference of the angular distributions between bremsstrahlung electrons and scattered electrons associated with the virtual photons which contributes to kaon production. The tilt of the Enge spectrometer off the bending plane of the Splitter magnet allows us to avoid the extremely high rate electrons originating from bremsstrahlung and M$\phi$ller scattering. However, increasing the tilt angle, the number of the accepted virtual photons will decrease. Therefore, we need to take following rates into account to optimize the tilt angle:

1. virtual photons associated with hypernuclear production,
2. electrons associated with bremsstrahlung, and
3. M$\phi$ller scattering electrons.

Originally we chose an Enge tilt angle of 4.5 degrees to optimize the best virtual photon flux and bremsstrahlung electron rate. After the first readiness review, we performed a more realistic optics study based on the 3D magnetic field distribution of the Splitter calculated with TOSCA and found the original Enge tilt angle (4.5 degrees) has still a significant acceptance to M$\phi$ller electrons.

Figure 14 shows the electron scattering angle distributions at the target for the 4.5 degree tilt and 4.5 cm offset in vertical direction of the spectrometer. The blue dots and black dots show the electron distributions associated with virtual photons and M$\phi$ller scattering, respectively. Since the beam energy is fixed, the scattering angle and momentum for M$\phi$ller scattering electrons have one to one correspondence, and thus a ring shaped distribution results from the M$\phi$ller scattering within momentum acceptance of the Enge spectrometer.

Using a RAYTRACE Monte Carlo simulation, the events which passed through the Enge spectrometer without hitting the pole or collimators were selected. The magenta points are the electrons associated with virtual photons which passed through the spectrometer and the red points are for M$\phi$ller electrons. Due to the effect of fringe fields, the 4.5 degree tilt of the Enge spectrometer selects the electrons with scattering angle of 2.8 degrees (50 mr).

Figure 15 summarizes the RAYTRACE study for electron rates associated with bremsstrahlung, M$\phi$ller scattering and virtual photons. The rates depend on the vertical offset of the Enge as well as its tilt angle. From the figure, one can see, 1) bremsstrahlung electrons are more forward peaked than M$\phi$ller and VP, 2) M$\phi$ller scattered electrons peak around ($\theta = 4-6$ degrees , off$=2-6$ cm), 3) it is possible to select the Enge tilt parameters around (7$\sim$9 deg, 5$\sim$6 cm) to reduce bremsstrahlung + M$\phi$ller rate to an acceptable level and to have as much as possible virtual photon yield.

Figure 16 shows the same plot as figure 14 for a tilt angle of 7.75 degrees. The simulation was performed for vertical offsets of 5.5 and 6.0 cm. One can see that the Enge acceptance is now out of M$\phi$ller ring. If the real fringe field shape should differ from this calculation, the Enge acceptance can be adjusted with hydraulic jacks.

Figure 17 shows the distribution at the sieve slit. Densities of points are arbitrarily changed to see the distribution clearly. Blue points are bremsstrahlung electrons, magenta the electrons associated with virtual photon, green M$\phi$ller scattered electrons, and red the electrons that passed through the Enge spectrometer and were associated with virtual photons. It can be seen that the tilt and shift of the Enge spectrometer shifts the acceptance just outside of M$\phi$ller electrons and ultra-high-rate bremsstrahlung electrons on the Splitter's bending plane.

The virtual photon yield is reduced by the larger tilt, but this factor could be still recoverable by increasing the beam current if the total rate at the Enge focal plane is less than the detectors' limit.

Figure 5 summarizes the Enge tilt angle dependences for the figure of merit of the virtual photon flux, background rates.