Difference: MuSunPKKinetics (1 vs. 12)

Revision 122011-04-22 - PeterWinter

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META TOPICPARENT name="PeterKMuSun"
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* SET ALLOWTOPICCHANGE = MuSunGroup

-- PeterKammel - 07 Dec 2007

Kinetics study

My kinetics study is documented in a math notebook kine.nb and the corresponding pdf file kine.pdf (The nb file has been revised and uploaded 12/13/07. Mistakes in the 2 node solutions were corrected and neutron time distribution have been included). Steve prepared a notebook to analyze the sensitivities with his method steve_kinetics.nb.

Peter's notbook consists of

Analysis of the two node mu-d hfs system

This allows analytical solutions using the 1st moment definition of the lifetime.

Analysis of full kinetics

The full kinetics was solved numerically. The detailed results are given in the notebook and latest revisions are included in the proposal.

Remaining work

  • The moment method used is an approximation for reduced fit regions, we should compare with Steve's method.
  • All the formalism and numbers used are presented in the math notebook. They should be checked by an independent colleague.

Some words about neutrons

  • neutron.pdf
  • I prepared the musunf.cpp on home/kammel/MuSun/studies/kinetics/root to fit for Rq. The fit function is based on Sara's routine. I estimate to get 2.7% fit uncertainty in Rq for 1e11 muons and n-detector efficiency of 0.1.

MSR

  • Peter et al. old, unpublished polarization study (still worth finishing). But it is old, don't trust it. E.g. eq. 42 ff is wrong.
>
>
Please go to https://muon.npl.washington.edu/twiki/bin/view/Main/MuSunPKKinetics
 
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Revision 112008-02-26 - PeterKammel

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META TOPICPARENT name="PeterKMuSun"
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Analysis of the two node mu-d hfs system

This allows analytical solutions using the 1st moment definition of the lifetime.
Deleted:
<
<
2node.png

The time distributions are clear. The delta_lambda are calculated for a 10% uncertainty in rqd (blue) and rq (green), respectively. The gray shade area indicated the delta_lambda resulting from a 1% change in Rd (doublet capture rate).

 

Analysis of full kinetics

Changed:
<
<
The full kinetics was solved numerically.

  • gr30.png:
    gr30.png

  • gr300.png:
    gr300.png

Population n(t): quartet (black), doublet (red), quartet+doublet (blue), 3-He (green)

lp30.png lp30a.png

lp300.png lp300a.png
>
>
The full kinetics was solved numerically. The detailed results are given in the notebook and latest revisions are included in the proposal.
 
Deleted:
<
<
The figure above shows the complete error budget from the kinetic fit, again assuming 10% for all kinetic input parameters (pessimistic at 30 K) and the desired 1% precision range for Rd. The left column is for the fit over the full time range (1st moment appoximation), the right column for a fit from 1 us to 20 us.
 

Remaining work

  • The moment method used is an approximation for reduced fit regions, we should compare with Steve's method.
Deleted:
<
<
  • For the baseline case, real ROOT fits on simulated data + accidental should be performed.
 
  • All the formalism and numbers used are presented in the math notebook. They should be checked by an independent colleague.

Some words about neutrons

Revision 102008-02-04 - PeterKammel

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META TOPICPARENT name="PeterKMuSun"
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Some words about neutrons

Deleted:
<
<
 
Added:
>
>
  • I prepared the musunf.cpp on home/kammel/MuSun/studies/kinetics/root to fit for Rq. The fit function is based on Sara's routine. I estimate to get 2.7% fit uncertainty in Rq for 1e11 muons and n-detector efficiency of 0.1.
 

MSR

Revision 92008-01-17 - PeterKammel

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META TOPICPARENT name="PeterKMuSun"
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MSR

Changed:
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<
  • Peter et al. old, unpublished polarization study (still worth finishing)
>
>
  • Peter et al. old, unpublished polarization study (still worth finishing). But it is old, don't trust it. E.g. eq. 42 ff is wrong.
 
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Added:
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META FILEATTACHMENT attr="" autoattached="1" comment="" date="1200257353" name="polarization.pdf" path="polarization.pdf" size="1364484" user="Main.PeterKammel" version="1"
 
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Revision 82008-01-13 - PeterKammel

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* SET ALLOWTOPICCHANGE = MuSunGroup
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Added:
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MSR

 
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Added:
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Revision 72007-12-17 - PeterKammel

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META TOPICPARENT name="PeterKMuSun"
* SET ALLOWTOPICCHANGE = MuSunGroup
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 -- PeterKammel - 07 Dec 2007

Kinetics study

Added:
>
>
  My kinetics study is documented in a math notebook kine.nb and the corresponding pdf file kine.pdf (The nb file has been revised and uploaded 12/13/07. Mistakes in the 2 node
Changed:
<
<
solutions were corrected and neutron time distribution have been included). It consists of
>
>
solutions were corrected and neutron time distribution have been included). Steve prepared a notebook to analyze the sensitivities with his method steve_kinetics.nb.

Peter's notbook consists of

 

Analysis of the two node mu-d hfs system

This allows analytical solutions using the 1st moment definition of the lifetime.
Line: 52 to 57
 
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>
>
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Revision 62007-12-14 - PeterKammel

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* SET ALLOWTOPICCHANGE = MuSunGroup
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Revision 52007-12-14 - PeterKammel

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META TOPICPARENT name="PeterKMuSun"
* SET ALLOWTOPICCHANGE = MuSunGroup
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  • For the baseline case, real ROOT fits on simulated data + accidental should be performed.
  • All the formalism and numbers used are presented in the math notebook. They should be checked by an independent colleague.
Added:
>
>

Some words about neutrons

 
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Revision 42007-12-13 - PeterKammel

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META TOPICPARENT name="PeterKMuSun"
* SET ALLOWTOPICCHANGE = MuSunGroup
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Kinetics study

My kinetics study is documented in a math notebook kine.nb and the corresponding
Changed:
<
<
pdf file kine.pdf. It consists of
>
>
pdf file kine.pdf (The nb file has been revised and uploaded 12/13/07. Mistakes in the 2 node solutions were corrected and neutron time distribution have been included). It consists of
 

Analysis of the two node mu-d hfs system

This allows analytical solutions using the 1st moment definition of the lifetime.
Line: 43 to 44
 
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Revision 32007-12-08 - PeterKammel

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* SET ALLOWTOPICCHANGE = MuSunGroup
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Revision 22007-12-07 - PeterKammel

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META TOPICPARENT name="PeterKMuSun"
* SET ALLOWTOPICCHANGE = MuSunGroup
Line: 41 to 41
 
  • For the baseline case, real ROOT fits on simulated data + accidental should be performed.
  • All the formalism and numbers used are presented in the math notebook. They should be checked by an independent colleague.
Changed:
<
<
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Revision 12007-12-07 - PeterKammel

Line: 1 to 1
Added:
>
>
META TOPICPARENT name="PeterKMuSun"
* SET ALLOWTOPICCHANGE = MuSunGroup

-- PeterKammel - 07 Dec 2007

Kinetics study

My kinetics study is documented in a math notebook kine.nb and the corresponding pdf file kine.pdf. It consists of

Analysis of the two node mu-d hfs system

This allows analytical solutions using the 1st moment definition of the lifetime.

2node.png

The time distributions are clear. The delta_lambda are calculated for a 10% uncertainty in rqd (blue) and rq (green), respectively. The gray shade area indicated the delta_lambda resulting from a 1% change in Rd (doublet capture rate).

Analysis of full kinetics

The full kinetics was solved numerically.

  • gr30.png:
    gr30.png

  • gr300.png:
    gr300.png

Population n(t): quartet (black), doublet (red), quartet+doublet (blue), 3-He (green)

lp30.png lp30a.png

lp300.png lp300a.png

The figure above shows the complete error budget from the kinetic fit, again assuming 10% for all kinetic input parameters (pessimistic at 30 K) and the desired 1% precision range for Rd. The left column is for the fit over the full time range (1st moment appoximation), the right column for a fit from 1 us to 20 us.

Remaining work

  • The moment method used is an approximation for reduced fit regions, we should compare with Steve's method.
  • For the baseline case, real ROOT fits on simulated data + accidental should be performed.
  • All the formalism and numbers used are presented in the math notebook. They should be checked by an independent colleague.

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