1) General description of the beam Monte Carlo.
 (draft) This mini-document is not really a figure to present.
It is a short description of the contents of the beam MC.
The first page is about proton-aluminnum interactions,
and the second is about other aspects of the code.
A third page is added for some references on pion production.

2) General figure of the beamline geometry.

3) Expected spectrum on and off axis.
   This has two versions available. It is meant to address the
 question "What if your whole front site is mis-aimed compared to 
 the far site?" Note that this is very different from the information 
 on aiming from neutrino detectors or beam monitors.
 This is .NOT. an explicit error term in any calculation and the
 levels of mis-aiming on the plots are .NOT. given as representing
 'reasonable cases.' In particular, the extra parts of the second 
 version are huge compared to any reasonable estimate of possible 
 mistakes.

4) Distribution of production points of parents of neutrinos.
 This is meant to address the question "What if the beamline components
 downstream of the target are not modeled properly?" Again, it is
 .NOT. put into any explicit error term. The point is that so much
 of the production is in the target that getting anything else wrong
 makes very little difference to the end result.
 The neutrinos here are those nu_mu with >0.5GeV which pass within
 400m of SK.

5) Distribution of production points of neutrinos.
 The neutrinos here are those nu_mu with >0.5GeV which pass within
 400m of SK.
 The point at which the plot starts to rise again is where the
 decay tunnel widens. The dotted line is for the subset of these
 neutrinos that are produced within 1m of the beam axis. This has
 the expected nearly exponential shape after the horns.

6) Systematic error as a function of neutrino momentum for
 (purely) Monte Carlo based extrapolation. This is the combination 
 of several studies of beam MC with varied inputs. 
 The errors are slightly larger than those for analysis using monitor 
 data directly. For analysis with FD data below the pion monitor
 threshold, the low energy bins of this are necessary to supplement
 the monitor data.
  Sources of error considered are: 
   - Nuclear model dependence of pi+ production. 
     This uses the 64 nuclear model study and the fitted pion monitor data. 
   - Nuclear extrapolation from Be to Al. 
     This (a much smaller effect than the previous) is a study changing 
     the nuclear corrrection factor in the MC. 
   - Normalization of Kaon production. This uses the difference 
     between pion cross section measurements from the Derrick 
     experiment (our main source for pion production) and the 
     Yamamoto paper (from which we get kaon production). 
     This term is still being checked, but it is only large in the 
     highest energy bin. 
   - Magnetic field perturbations in the horn. 
   - Proton profile and centering. 
   - Mechanical sagging of the target. (This is probably over-estimated.)