FPD Level 1 Trigger

        The way the FPD L1 trigger works is shown in fig. 1.  The idea is that every equation take as a reference the pixel of the detector 1 (consisting of six planes of fibers, U1,V1,X1 and U1P, V1P,X2P)  where the particle get through, and then make a set of possible pixels where the same particles can strike in the detector 2. For example if one particle hits the pixel number 5 in detector 1 it can hit a variety of pixels in the detector 2 (one per each energy), for example pixels #3,6,9,10 ... and any other pixels physically allowed (in accordance with the possible beam trajectory ). So now we will have equations of the type:

        PIXEL 1 AND (SUM OF ALLOWED PIXELS IN DETECTOR 2 RELATED TO PIXEL 1 IN DETECTOR 1) OR
        PIXEL 2 AND (SUM OF ALLOWED PIXELS IN DETECTOR 2 RELATED TO PIXEL 2 IN DETECTOR 1) OR
        .
        .
        As many as pixels exist in detector 1
 

        Note that now we have to leave behind the idea that every equation represents a trajectory, what every equation is doing now is searching if there were a hit in that combination or the other combination of pixels with the final answer of yes or no (we leave it for the tracking at L3 because we are not concerning about the reconstruction now).

        In order to reduce the number of LUTs (Logical Unit Table) used by the Virtex chip, we will use only two planes of the six available in detector 2. In detector 1 we will use the full information, so the efficiency there will be the best possible.

                                       Multiple Interaction Rejection

        In case of multiple interactions we have the problem that the Virtex chip cannot distinguish between one pixel or another (in both detectors).

        For detector 1 we will have the problem only if both particles strikes in the same X and XPRIME fibers used as a confirmation in the same plane, ie both particles must strike X1 (or X1P) for the first plane and the same X2 (or X2P) in the second plane. These possibilities are very rare but we should be aware that can exists.

For detector 2 things are different because we don't use the X fibers needed for confirmation. This make the situation more complicated because
for example if we have two hits going through detector 1 and 2 hitting the following fibers:

        PIXEL 1 AND (U2(2) AND V2(4))
        PIXEL 1 AND (U2(1) AND V2(5))

when the signals arrive to the chip, this can make these coincidences plus the following ones:

        PIXEL 1 AND (U2(2) AND V2(4))
        PIXEL 1 AND (U2(1) AND V2(5))

so now we'll have two times the original ones.

One way to solve that would be to have all the planes enables in the second detector but in that case we fall in the problem of space available in the chip.

This is a issue that we have to think better, any ways the plan now is try to solve first the situation for  singles hits and then turn our attention to this problem.