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Using MICE to verify simulation codes?. Andreas Jansson. 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.

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  • 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.

MICE analysis meet

Possible follow up experiments
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

R d goals
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

How to demonstrate cooling
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.

MICE analysis meet

How to verify simulations
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.

MICE analysis meet

A comparison recipe
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)

MICE analysis meet

Manx example ensemble transmission
MANX example: ensemble transmission

Transmission for different input phase space coordinates

MICE analysis meet

Manx example ensemble exit mean values
MANX example: ensemble exit mean values

Exit mean values for particles starting on the xy plane

MICE analysis meet

Manx example ensemble exit emittance
MANX example: ensemble exit emittance

Exit emittance for different initial phase space coordinates

MICE analysis meet

The next step conclusions
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.

MICE analysis meet