1. Using MICE to verify simulation codes?
Andreas Jansson

2. Intro
Recently, there has been a lot of discussion about what the follow-up cooling channel experiment should be.
I have come to the conclusion that to answer this question, we need to do some studies that could also benefit MICE.
In particular, I am interested in the question whether MICE (or any other cooling channel experiment) can actually test simulation codes.
If MICE can’t do it, not clear that it will be easier in the follow-up.
2/10/2009
MICE analysis meet

3. Possible follow-up experiments
MICE rebuilt as FOFO snake (Alexahin)
MANX w LHe, no RF (Muons Inc)
Mag. ins. Guggenheim section (Palmer)
HCC w. HP H2 RF (Palmer)
LiH wedge as MICE phase III (Rogers)
MICE analysis meet
2/10/2009

4. R&D goals Three types of goals for a cooling channel experiment
Demonstrate that the simulated cooling channel conditions can be created in reality.
Demonstrate cooling (emittance out < emittance in)
Experimentally validate simulation codes and models.
Note that
If A and C are achieved, in principle this implies B.
Achieving B does not imply C (or A).
MICE will do A and B, can it do C?
In fact, can C be done in any cooling channel experiment?
MICE analysis meet
2/10/2009

5. How to “Demonstrate cooling”?
MICE method:
Measure single tracks and form a beam off-line. Calculate emittance in and out of this beam.
A particular challenge is to make sure the off-line generated beam is properly matched
Bad matching can easily mask the small cooling effect.
Need a method to assign weights to the tracks, and make sure there are no voids in the initial distribution.
Significant progress on this recently, although perhaps not yet a done deal.
The method developed for MICE can probably be adapted for used in any future 6D cooling channel experiment.
2/10/2009
MICE analysis meet

6. How to “Verify simulations”
Stochastic process -> simple track-by-track comparison not possible.
Look at distributions of ensembles of tracks with similar (identical) initial values, and compare to these to MC of representative ensembles
Information about alignment errors, field errors, average energy loss in absorbers will appear as deviations in the mean values.
Information about energy straggling, tails of scattering distribution will appear as deviations in the distributions (sigmas or even shape)
How to select the ensembles?
Implies binning tracks with similar initial 6D phase space coordinates
For good resolution, bin size should be small compared to the effect to be measured (distribution of the ensembles at exit).
6D means a very large number of bins.
For decent statistics (say ~500 tracks per bin), need a huge number of measured tracks.
Many orders of magnitude more than to accurately measure cooling.
Even with large data set, sensitivity might not be high enough to resolve effect.
2/10/2009
MICE analysis meet

7. A comparison recipe
First, need a good recipe for how to compare to simulations (the following comes from a discussion with Chris Rogers)
For each measured track, run a MC of ~1000 particles with identical initial conditions (measured initial 6D phase space coordinates).
Calculate the difference between the measured exit coordinates and the mean of the MC distribution.
Normalize the deviation using the 6D covariance matrix of the MC tracks.
Calculate the average deviation and the distribution of normalized deviations in each 6D bin.
Distribution should have r.m.s=1, no correlations, and predictable tails.
The idea of this recipe is to minimize the effect of the bin size
Each track is compared to its own MC, rather than a representative MC or the bin (e.g. evenly distributed tracks or tracks starting in the bin center)
2/10/2009
MICE analysis meet

8. MANX example: ensemble transmission
Transmission for different input phase space coordinates
2/10/2009
MICE analysis meet

9. MANX example: ensemble exit mean values
Exit mean values for particles starting on the xy plane
2/10/2009
MICE analysis meet

10. MANX example: ensemble exit emittance
Exit emittance for different initial phase space coordinates
2/10/2009
MICE analysis meet

11. The next step/Conclusions
Would like input from you.
Is there a better way to do this type of analysis?
Would you be interested in working on it (perhaps someone already is)?
Would like to implement this recipe for MICE and run a MC study of the sensitivity using “planted errors”.
This should tell us something about whether it is realistic to achieve such a test in a follow-up experiment.
Even if the sensitivity is not good enough to measure e.g. dE/dx, this type of analysis might help to understand (and fix) alignment and field errors.
2/10/2009
MICE analysis meet