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SVT Alignment. Marcelo G. Munhoz Universidade de São Paulo. Introduction. We seek for 6 parameters that must be adjusted in order to have the SVT aligned to the TPC: x shift y shift z shift xy rotation xz rotation yz rotation. Basic question:. - PowerPoint PPT Presentation
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SVT Alignment
Marcelo G. Munhoz
Universidade de São Paulo
Introduction
We seek for 6 parameters that must be adjusted in order to have the SVT aligned to the TPC:– x shift– y shift– z shift– xy rotation– xz rotation– yz rotation
Basic question:
How to disentangle and extract them without ambiguity from the data?
Many approaches are possible. We are using two of them...
Approaches
First approach:– calculate the “residuals” between the projections of
TPC tracks and the closest SVT hit in a particular wafer;
– Advantage:• can be done immediately after some TPC calibration is ready,
even without B=0 data;
– Disadvantage:• highly dependent on TPC calibration; • the width of these “residuals” distributions and therefore the
precision of the procedure is determined by the projection resolution.
Approaches
Second approach:– use only SVT hits in order to perform a self-
alignment of the detector;– Advantage:
• a better precision can be achieved; • does not depend on TPC calibration;
– Disadvantage: • it is harder to disentangle the various degrees of freedom
of the detector (need to use primary vertex as an external reference);
• depends on B=0 data (can take longer to get started).
First approach: TPC tracks projection (B 0) Try to disentangle the 6 correction
parameters in 2 classes:– x shift, y shift and xy rotation;– z shift, xz rotation and yz rotation.
They are not completely disentangled, but it works as a first approximation...
First approach: TPC tracks projection (B 0) Make the alignment in steps:
1 - global alignment, i.e., one set of parameters for the whole detector;
2 - ladder by ladder alignment, i.e., a set of parameters for each ladder;
3 - wafer by wafer alignment, i.e., a set of parameters for each wafer.
Global parameters: x shift, y shift and xy rotation Look at “residuals” from the SVT drift
direction (global x-y plane); Study them as a function of x shift (x), y shift (y) and xy rotation
() should show up, approximately, as:
tan 1 y x
res x ydrift sin cos
Global parameters: x shift, y shift and xy rotation The equation
is just an approximation because:– tracks are not straight lines;– a xz rotation, for instance, can change the parameter
x as a function of z;
– miscalibration of the detector (t0 and drift velocity) also changes the “residuals” distribution.
But overall, the method is a very good starting point...
res x ydrift sin cos
First look, no correction:
res x ydrift sin cos
x = -1.9 mm
y = 0.36 mm
= -0.017 rad
Matches well the survey data
After first correction (only x):
res x ydrift sin cos
x = -0.72 mm
y = 0.25 mm
= -0.019 rad
After second correction: (y and included)
res x ydrift sin cos
x = -0.25 mm
y = 0.10 mm
= -0.0018 rad
Global parameters: z shift, xz rotation, yz rotation Look at “residuals” from the SVT anode
direction (global z direction); Choose tracks that have dip angle close to
zero ( tracks parallel to the xy plane); Study them as a function of z; The parameters should show up as
deviations from a flat distribution centered at zero.
First look, no correction: only ladders at xz plane
First look, no correction: only ladders at yz plane
Conclusion - I:
Global alignment for x and y shifts and xy rotation is done;
Z shift and xz and yz rotations can be worked out;
Moved to next step (ladder alignment) of x and y shifts since it involves some calibration issues as well.
First approach: TPC tracks projection (B 0) Make the alignment in steps:
1 - global alignment, i.e., one set of parameters for the whole detector;
2 - ladder by ladder alignment, i.e., a set of parameters for each ladder;
3 - wafer by wafer alignment, i.e., a set of parameters for each wafer.
Ladder parameters: x shift, y shift and xy rotation Look at “residuals” from the SVT drift
direction (global x-y plane); Study them as a function of drift
distance (xlocal) for each wafer; In this case, influence of miscalibration
(t0 and drift velocity) cannot be neglected.
Ladder parameters: x shift, y shift and xy rotation Once more, x shift (x), y shift (y) and
xy rotation () should show up, approximately, as:
res x x y xdrift local local sin cos
Ladder parameters: x shift, y shift and xy rotation
These two equations can be used to fit the “residuals” distribution fixing the same geometrical parameters for all wafers.
res xv
vx L v t t Ldrift local local
0 0
0, if t0 is Ok But, we must add the effect of an eventual
miscalibration,
where v` is the correct drift velocity and t0` is the correct time zero.
First look ladder by ladder after global corrections: x = -0.81 mm
y = 0.56 mm
After first correction (only x and y): x = -0.19 mm
y = 0.024 mm
Conclusion - II:
Need to go ladder by ladder (36 total) checking the correction numbers and the effect of them on the “residuals”;
Next step is to fit each wafer separately; Still need to consider the rotation
degree of freedom.
First approach: TPC tracks projection (B 0) Make the alignment in steps:
1 - global alignment, i.e., one set of parameters for the whole detector;
2 - ladder by ladder alignment, i.e., a set of parameters for each ladder;
3 - wafer by wafer alignment, i.e., a set of parameters for each wafer.
Wafer parameters: x shift, y shift
wafer x (m) y (m)1 -190 1512 -62 673 -34 834 -92 58
First approach: TPC tracks projection (B=0) The exactly same method can be
applied to the B=0 data; It should give better results with the
straight tracks; That can be done as soon as we have
the data processed.
Second approach: SVT hits only (B = 0) Associate two angles to each hit:
where x0 , y0 and z0 are the coordinates of the primary vertex
tan 1 0
0
y yx x
tan 1 0
0
2
0
2
z z
x x y y
Second approach: SVT hits only (B = 0) Using the TPC+SVT tracking, identify the 3
hits belonging to a track; In order to study x and y shifts and xy
rotations, calculate the distributions of:
12(1 , z) = 1 - 2 as a function of 1, for each z slice and 1 0;
13(1 , z) = 1 - 3 as a function of 1, for each z slice and 1 0;
Second approach: SVT hits only (B = 0) These distributions can be fit with similar
equations as the first approach in order to get the alignment parameters;
We will get corrections as a function o z, that can bring information about xz and yz rotations:
x(z) = z tan(xz )
y(z) = z tan(yz )
Second approach: SVT hits only (B = 0) In order to study z shift, xz and yz rotations,
calculate the distributions of:
12(1 , 1) = 1 - 2 as a function of 1 for each 1
13(1 , 1) = 1 - 3 as a function of 1 for each 1
These distributions can be treated as the “residuals” in the anode direction.
Near future perspectives Finalize first approach:
– calculate x, y, and ladder by ladder;– extend it to wafer by wafer making small
corrections if necessary;– calculate z shift, xz rotation and yz rotation
(global, ladder by ladder and wafer by wafer - they should be small);
– use B=0 data. Start second approach once B=0 data is
ready.
Near future perspectives
It is a lot of work, but it depends mostly on man power. Software is ready;
The whole procedure does not depend on many iterations of the reconstruction chain. Corrections can be applied and tested without reconstruction (although final tests need that).