Proposed WFD Fan-In Scheme
==========================
This document contains notes regarding a proposed scheme for fanning
in the PMT signals to the WFD system.
Constraints:
- 4 inputs per WFD channel
- 4 channels per WFD card
- 18 WFD slots per VME crate
- 16 x 2 signals for Bottom layer
- 16 x 2 signals for Center layer
- 18 x 2 signals for Top layer
- 14 x 2 signals for East layer
- 14 x 2 signals for West layer
- 8 x 2 signals for North (or South) layer
- goal of 2:1 fan-in for horizontal tanks
Strictly obeying 2:1 fan-in for all signals would require 86 WFD
channels, equivalently 21.5 WFD cards. Unfortunately, there are only 18
slots per crate available for WFD cards. This number is so close to the
total needed that it is worth considering how we squeeze them in.
One mitigating factor is that a vertical tank contains 71% of the
scintillator volume of a horizontal tank. For random backgrounds, this
implies that 3:1 fan-in for vertical tanks is equivalent to 2:1 fan-in
for horizontal tanks. Furthermore, the singles rates in vertical tanks
are more like half that of horizontal tanks. Unfortunately, a 3:1
fan-in for verticals still does not free enough channels. However, by
selecting *some* vertical tanks for 4:1 fan-in, we can fit all 172
signals into 1 crate of WFDs. Note that I am calculating the case for
SM-1 and SM-6 where we have North and South faces; for SM-2 through SM-5
those channels would be unused. Note also that I am assuming that power
distribution and cooling problems are tractable.
As was discussed in the WFD meeting of 6-May, we may arrange the
multiplexing so that adjacent tank signals are not fanned into the same
WFD channel. This will help the granularity of information for particles
which span inter-tank boundaries.
Below is the table that assigns tank signals to WFD channels for SM-1.
One line is one WFD card; unused inputs are indicated by "---". To save
space and make this readable, I omitted the indication for tank-end
(0,1). However, you will notice that each entry occurs twice, once for
end-0 and once for end-1.
wfd_channel_0 wfd_channel_1 wfd_channel_2 wfd_channel_3
1) N01 N03 N05 N07 N01 N03 N05 N07 N02 N04 N06 N08 N02 N04 N06 N08
2) B01 B03 --- --- B01 B03 --- --- B02 B04 --- --- B02 B04 --- ---
3) B05 B07 --- --- B05 B07 --- --- B06 B08 --- --- B06 B08 --- ---
4) B09 B11 --- --- B09 B11 --- --- B10 B12 --- --- B10 B12 --- ---
5) B13 B15 --- --- B13 B15 --- --- B14 B16 --- --- B14 B16 --- ---
6) C01 C03 --- --- C01 C03 --- --- C02 C04 --- --- C02 C04 --- ---
7) C05 C07 --- --- C05 C07 --- --- C06 C08 --- --- C06 C08 --- ---
8) C09 C11 --- --- C09 C11 --- --- C10 C12 --- --- C10 C12 --- ---
9) C13 C15 --- --- C13 C15 --- --- C14 C16 --- --- C14 C16 --- ---
10) T01 T03 --- --- T01 T03 --- --- T02 T04 --- --- T02 T04 --- ---
11) T05 T07 --- --- T05 T07 --- --- T06 T08 --- --- T06 T08 --- ---
12) T09 T11 --- --- T09 T11 --- --- T10 T12 --- --- T10 T12 --- ---
13) T13 T15 --- --- T13 T15 --- --- T14 T16 --- --- T14 T16 --- ---
14) T17 --- --- --- T17 --- --- --- T18 --- --- --- T18 --- --- ---
15) E01 E03 E05 E07 E01 E03 E05 E07 E02 E04 E06 --- E02 E04 E06 ---
16) E08 E10 E12 E14 E08 E10 E12 E14 E09 E11 E13 --- E09 E11 E13 ---
17) W01 W03 W05 W07 W01 W03 W05 W07 W02 W04 W06 --- W02 W04 W06 ---
18) W08 W10 W12 W14 W08 W10 W12 W14 W09 W11 W13 --- W09 W11 W13 ---
Please comment on whether this proposed scheme is satisfactory for our
physics goals.