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Hi Glen and Dick

I've been trying to work out how to assign a systematic
uncertainty due to our knowledge of the angle RMS (this
excludes the contribution from the algorithm, which is
now tiny). Specifically, this is the problem that the
measured RMS won't be equal to true RMS because of plane
aging and the distance of the beam from the sense plane.

Let me present two different methods:

1. Using number of wires fired

A definition: n wires fired = mean of H61255 (x) or H61256 (y);
this is the number of hits used in the final fit, which is
equal to the number of wires fired.


The TEC-in dataset gave a nice linear relationship
between RMS and number of wires fired.
(attach p8 of ms_correct_v1.pdf)
For n in the range ~10 to ~14:

            relationship 
x-module:   26.6 - 0.90 n_x
y-module:   30.5 - 0.68 n_y
   

To first order, our 'deconvolution factors' (c_x,c_y)
are only correcting for multiple scattering.

For any given characterisation run, we have
n_x (n_y) and RMS-x (RMS-y), and we simulate
using [RMS-x/c_x] and [RMS-y/c_y].

As  n wires fired drops, either because of
aging or beam steering, the RMS.

We know from the simulation where the RMS
actually starts to change.

The gradient of this relationship


A reminder: we deliberately don't run....



number of wires fired = number used in fit?

I looked into estimating the systematic uncertainty
due to TEC aging.

The problem: the RMS of the angles is related to
the number of wires fired. It also depends on 
the beam tune (i.e. how close to the sense plane
the beam was), and the voltage (i.e. where we had
them set to deal with oscillations).





The c_x and c_y values were tuned using
a run that had


The 'deconvolution' factors were tuned using the
set 75 'end-of-set' profile.
In data, the TEC analysis of these characterisation
runs found:

module:           x       y
n wires fired:    15.0    15.9
RMS of angles:    14.1    21.3



RMS vs n and other plots.
Problem: you don't want to say 'oh, the RMS is bigger,
I should correct it

The best measure we have for RMS vs n comes from
controlled conditions i.e. the TEC-in.

Work out how much RMS needs correcting.


In the past I have plotted up RMS vs 


For each characterisation run I worked out
the total number of M-counts accumulated.
M counts and the TEC voltage.
For each characteristion run, I then
worked out the total number of M-counts
accumulated.
need a table of charac (can use run numbers from caldb) and #Ms


s68 should be corrected to use the G-plane pmu0.

set    run numbers gen  planes  Integral-M       nx      ny
                                (x 10^6)
s68    37717-37723 *    F       need voltages    13.2    14.7
       38691-38694      G       3                15.0    16.5
s70    39165-39169      G       13               14.9    16.0
       40025-40033 *    G       18               14.6    15.7
s71    40318-40320 *    G       34               
       41089-41093      G       43
s72    41335-41340 *    G       122
       42605-42609      G       1200 (!)
s74    43667-43673 *    H       5
s75    44374-44381      H       26
       45275-45280 *    H       31
s76    45310-45314 *    H       45
       46174-46178      H       51

s80    47239-47242   A       349  (1)  US-stops
s82    47884-47888   A       424  (!)  TEC-in spread beam
s83    49302-49306   A       1582 (!)  Fortunately production used end of set!
       50492-50507   B       6
s84    50706-50710   B       103
       51807-51811   B       116
s86    52318-52322   B       150
       53610-53616   B       172
s87    53860-53865   B       185
       54915-54919   B       196

s91    55544-55549   C       170
s92    56144-56149   C       182
       56357-56360   C       192
s93    56428-56432   C       183