LHCb B Field Map

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LHCb B Field MapLHCb B Field Map

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IT SurveyIT Survey

EPFL, the 21th of May 2007

Monday Seminar

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Parameterized Parameterized LHCb B Field LHCb B Field

MapMap

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Outline …

Analytical Field Service

Reminder of the Goal

May 21, 2007 Monday Seminar, EPFL

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MC Parameterization

Iterative Polynomial Fitting Method

One-go 3D Fitting Method

Choice of Regions

Results in the Acceptance Region

Residual Parameterization

Measurement Matching MethodPreliminary Results

Analytic Parameterization

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B measurement Campaign (Dec. 2005)

B Measurements done…

by 3D Hall probes arranged in a fixed configuration on a movable support

obtained for the two polarities

cover most of LHCb acceptance: Upstream : x = [-1.0, 1.0] m y = [-0.4, 0.4] m

Magnet : x = [-2.7, 2.4] m y = [-1.0, 1.0] m

Downstream : x = [-2.5, 2.5] m y = [-1.7, 1.7] m

(with demagnetization cycle)

(fine grid of 8x8x10 cm)


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Reminder of the Goal

1) TOSCA simulated B field map (grid of 10x10x10 cm)

2) Measurements (They don’t cover all the acceptance)

Why is a parameterized B field map needed ?

1) The real measurements can be compared with MC data to model the residuals : Residual parameterization.

Provide an accurate determination of the B field map as close as possible to the measurements

What is available to perform the parameterizations?

Goal

2) The extrapolation of the Residual parameterization can be realized for the regions where no measurement is available.


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B-Field Map based B-Field Map based on MC dataon MC data

(MC Parameterization)

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Principle of the Method (eg. By component) :

Iterative Multipolynomial Fitting Method (1)

Fit By as a function of y with x,z fixed. By(y) for x=10cm and z=830cm

Fit Ai as a function of z with x fixed.

Fit Bj as a function of x.

At the end: N·M·P coefficients to cover the map.


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N coefficients Ai for each slice.

M coefficients Bj

for each slice.P coefficients Ck.

Pol(4)A0

A1

A2

A3

A4

B0

B1

B2

B3

B4z

z

z

z

z x

x

x

x

x

Ai(z) for x=210cm : Bj(x) for A0 :

Pol(4)

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Iterative Multipolynomial Fitting Method (2)


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The method works well, but not easy to achieve the final precision because of the difficulty of optimizing iteratively.

Downstream region is… Magnet region… Residuals ∆(BMC - Banalytic) at z=830cm Bx(y) for x=90cm and z=[350,680] cm

…reasonably described.

…needs Fourier parameterization due to oscillatory pattern.

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One-go 3D Fitting Method (1)

Least square procedure : Determine the cn coefficients and the Fn functions, such that :

Modified Gram-Schmidt orthogonalisation algorithm to keep the functions Fn that significantly reduce S :

Basis change to have Wn functions which are orthogonal between them.

Wn

Fn

WnFn

To decide if the Nth function is to be kept, the projection of Fn

on Wn is measured and should be greater than a given value to contribute significantly to the reduction of S (the angle should be greater than a given value) . See H. Wind, Yellow report, vol.72-21,CERN,1972 ; H. Wind, Yellow report EP/81-12,CERN,1981


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is minimal, with

Fn are not orthogonal between them.

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Implementation of the method (2)

An implementation of the method is available in ROOT (TMultiDimFit Class). Some technical problems have been encountered, but solved thanks to René Brun.

Configuration of the optimization :

A) Type of Polynomials : Monomials, Legendre, Chebyshev

C) Main limits to the number of terms in the parameterization :

1) Max. of terms in the final parameterization

2) Max. of powers for each variable x,y,z to be considered

3) Min. angle

B) Relative error accepted :


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Compromise between relative precision, small number of regions, small number of terms in the parameterization.

Regions Definition for the B field Maps (1)

Regions definitions as simple as possible.


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acceptance angles z coordinate x and y coordinates

Lots of different cuttings tested :

Cuttings with respect to B field gradient have been tested too, but the geometry of the cuttings was too complicate.

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Cutting depends mainly on only one variable (z)

Downstream Magnet

8m

Upstream

3m 10m- 0.5m

4m

1 1.5 2 2.4 4.1 4.7 5.1 6.1 6.7 7.3 8.5 9 z(m)

y(m)


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The same cutting is chosen for Bx,By and Bz components.

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However, in the magnet region, [ymax-30cm,ymax] values have been fitted separately, but with the same z cuts to improve the fits.

Bx for x=1.3m and z=4.8m By for x=1.3m and z=4.8m

MC Parameterizations involve 50 to 150 terms, depending on the B field fluctuations.


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By map Result (x=0m, y=0m) (1)


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MC parameterized By

TOSCA simulated By

Very good matching !

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By map Result : Relative Precision (2)

Upstream Magnet Downstream

Relative precision on By < 0.001 inside the three regions

Relative precision :


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Bx map Result (x=0.4m, y=0.4m)


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MC parameterized By

TOSCA simulated By

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Bz map Result (x=0.4m, y=0.4m)


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MC parameterized By

TOSCA simulated By

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Continuity at the region boundaries

The relative discrepancy between MC parameterizations at the boundary of two regions is in the same order of the fit precision (~10-3).

Discrepancy between By parameterizations at the 14 boundaries Discrepancy between the two By parameterizations at the z=610cm boundary

Relative Discrepancy :


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By boundary at z=610cm

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Out of acceptance regions

The Downstream region has been already parameterized.

Problems (peaks) are encountered for the Upstream and Magnet regions to find a good parameterization, because we are inside material.


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Upstream Magnet Downstream

Parameterization needed, but with a less acurate precision.

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Matching with the Matching with the measurementsmeasurements

(Residual Parameterization)

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Clean-up of the measurements

Clean-up of the measurements done in the three regions (started by Adlene Hicheur).

Clean-up

Some non-physical behaviours observed in the measurements, which can perturb the parameterizations.


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Matching Method

Parameterize the residuals (Bmeasurements - Banalytic values) : Analytic Parameterization = MC Parameterization + Residual Parameterization

Extrapolate the Residual Parameterization to regions where no measurement is available.

Calculate the B values with the MC Parameterizations at the same measurement coordinates (x,y,z).

Measurements Analytic values Residuals


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By Residual Results (1)


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x=4cm, y=4cm, Magnetx=4cm, y=4cm, Upstream

InterpolationMC Parameterization

Analytic ParameterizationMeasurements

(MC + Residual Parameterization)

Non negligible corrections for the most important B component (By) near the centre (x~0cm and y~cm) !

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By Residual Results (2)


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x=100cm, y=4cm, Magnet x=204cm, y=164cm

x=140cm, y=140cm


Analytic ParameterizationMeasurements


The most important discrepancies between MC data and measurements are found for big x and/or y values

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Reverse Polarisation By Residuals (3)


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x=100cm, y=4cm, Magnet


Analytic Parameterization-(Reverse Polarisation Measurements)


The values obtained with the Analytic Parameterization (found for positive polarisation measurements) seems to match well with the reverse polarisation measurements. More comparisons still have to be done…

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Analytic Field Analytic Field ServiceService

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Analytic Field Service

Speed tests forseen with tracks Several scenarios :


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It has been implemented in Det/Magnet, but is not available in CVS yet.

However, according to preliminary tests, the speed of the B value access seems to be an issue…

1) Analytic Parameterization is faster or of the order of time of the interpolation method :

Best scenario : faster access and more accurate B values .

2) Analytic Parameterization is slower than the interpolation :

Only the Residual Parameterization could be used with the interpolation method to give more accurate B values .

A new file with B values used by the interpolation could begenerated with the help of the Analytic Parameterization .

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Conclusions and Perspectives

Residual parameterizations for Bx and Bz.

Extrapolate the Residual parameterizations to regions where no measurements are available.

Parameterization based on MC simulation data has been succesfully performed in the acceptance region by the One-go 3D Fitting Method and reaches a rel. Prec. < 10-3 for the By component in all the 3 regions.

MC parameterization of the « Out of acceptance » Magnet and Upstream regions.

On-going / to do :


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Speed tests of the Analytic Service with tracks.

Parameterization of the By residuals gives the expected more accurate B values with respect to the measurements.

Documents

LHCb B Field Map