E-field and pitch corrections

E-field correction 
First order estimate depends on:
Momentum (radial) distribution
Quad voltage
      Momentum distribution is extracted from FR analysis (FFT and CERN)
Consistency of FFT and CERN methods ?
Bad resistors?

Do the FR analyses give the right answer? 

FR analysis is dominated by early time data – (before debunching)
First order correction in FFT method increases with delay of start time
The early time distribution may be biased 
     – what is the effect of scraping and the shifting of the closed orbit?
Is the momentum distribution correlated with time into the fill?
Are we looking at the right muons?


E-field correction 

Are there higher order contributions that would lead to modifications to the base correction? Due to 
Quad multipoles
Quad misalignment/field errors
Betatron amplitude
Non uniformity of the dispersion function
 
Detector effects
What is the effect of pile-up (especially at early time)
Does calorimeter gain bias the FR measurement  

How to test the FR analysis ?

Explore analytically dependence on betatron amplitude, quad offsets

Simulation

Generate a fast rotation signal in simulation with known momentum (radial) distribution and check that the FR analyses give the right answer
Generate distributions with/without scraping and determine if the momentum distribution is different and/or the FR analysis is consistent?
Explore dependence on quad misalignment, betatron amplitude
Our correction assumes that                      is a reliable proxy for E-field shift
Compare with simulation with spin-tracking
Muon losses – gm2ringsim – distribution of evolution of distribution including muon losses

Trackers
Measure radial distribution early to late to establish its stability.

Pile up ? Gain?



Pitch correction 
Lowest order estimate depends on:
Measure of vertical distribution
Quad voltage
      Vertical distribution is extracted from tracker and calo data
Consistency of tracker angular distribution with offset distribution (vertical)?
Tracker/calo consistency?
Consistency with simulation?

Higher order contributions from?
Radial B-field
Quad misalignment/field errors
Path length
Is the vertical distribution the whole story?

  Quantify these dependencies (analytically and with simulation) 

We determine pitch correction by estimating                        along the muon’s trajectory 
We can compute the pitch correction directly by spin-tracking.
    Are the results consistent?  (Check with simulation)

Simulate conditions of the different runs in as much detail as possible
Generate and track distribution and compute E-field and pitch corrections for that distribution

Not a substitute for measurement but a valuable cross check
 
