Optimization of the mirror positions

In order to optimize the mirror positions a number of constraints had to be considered :

• The detection efficiency should be optimized for high momentum electrons

• In order to increase the electron efficiency for low momentum electrons ( ) part of elliptical mirrors near the middle plane were made flat. This resulted in a diminished near-middle-plane efficiency for high energy electrons. We had to address the question how to keep the efficiency sufficiently high.

• Neighbouring mirrors overlap - they are wider than the distance between their centers. This was done to make sure that there will be no gaps between them. The goal was to minimize the interference of neighbouring mirrors.

The sensitivity of the Cerenkov detector optics to the exact mirror orientation can be seen in Fig. 9, which displays as a function of the azimuthal angle Phi for fixed polar angle Theta. Different symbols represent different rotation angles for the elliptical mirrors. The elliptical mirrors are rotated around the center of the bracket, positive direction is when the away side of the mirror is closer to the target.

Fig. 9a and 9b represents the case with additional cylindrical mirrors, Fig 9c and 9d - without it.

One can see, that

1. deviation in the elliptical mirror angle results in the loss of 2 - 3 photo-electrons. Such a loss would be unacceptable (see chapter 3.2). Therefore, the angle deviation should be smaller then .
2. The behavior at small Phi angles is different from the behavior at large Phi. Optimization requires finding a compromise position between highest and high efficiency near the middle plane.
3. Comparing figures with shows that the optimal position depends on whether the additional mirrors are implemented or not.
4. The additional cylindrical mirrors not only increase but also reduce the sensitivity to the deviation from the ideal mirror position. [Compare Fig. 9a) and Fig. 9c) ]