<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">70,85d69
&lt; %% Concerning CRediT authorship contribution statement.
&lt; %% https://www.elsevier.com/researcher/author/policies-and-guidelines/credit-author-statement
&lt; 
&lt; %%\stmaucontribution[M. van Beuzekom]{Investigation, Software}
&lt; %%\stmaucontribution[Y. Bilevych]{Investigation, Resources}
&lt; %%\stmaucontribution[K. Desch]{Project administration, Funding acquisition}
&lt; %%\stmaucontribution[S. van Doesburg]{Investigation, Software, Validation}
&lt; %%\stmaucontribution[H. van der Graaf]{Investigation, Conceptualization}
&lt; %%\stmaucontribution[F. Hartjes]{Investigation, Resources, Methodology, Software, Validation}
&lt; %%\stmaucontribution[J. Kaminski]{Investigation, Resources, Methodology, Project administration, Writing - Review Editing}
&lt; %%\stmaucontribution[P.M. Kluit]{Investigation, Resources,  Conceptualization, Project administration, Software, Validation, Writing – original draft}
&lt; %%\stmaucontribution[N. van der Kolk]{Investigation, Software, Validation}
&lt; %%\stmaucontribution[C. Ligtenberg]{Investigation, Software, Validation}
&lt; %%\stmaucontribution[G. Raven]{Investigation, Project administration, Software, Validation}
&lt; %%\stmaucontribution[J. Timmermans]{Investigation, Conceptualization, Software, Validation, Writing - Review Editing}
&lt; 
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&lt; A Time Projection Chamber (TPC) module with 32 GridPixes was constructed and the performance was measured using data taken in a test beam at DESY in 2021. 
&lt; %  used a 95/3/2 gas mixture (by volume) of {Ar}/{CF$_4$}/{iC$_4$H$_{10}$ with a small amount of oxygen and water vapour. 
&lt;   The data analysed were taken at electron beam momenta of 5 and 6 GeV/c and at magnetic fields of 0 and 1 Tesla(T). 
---
&gt; A Time Projection Chamber (TPC) module with 32 GridPix chips was constructed and the performance was measured using data taken in a test beam at DESY in 2021 using a 93.6/5.0/1.4 gas mixture (by volume) of {Ar}/{iC$_4$H$_{10}$}/{CO$_2$} with a small amount of oxygen and water vapour.. 
&gt;   The analysed data were taken at electron beam momenta of 5 and 6 GeV/c and at magnetic fields of 0 and 1 Tesla(T). 
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&lt;   For hit rates up to 5.7 kHz per GridPix a reduction of at most 0.6\% in the relative efficiency was measured.
---
&gt;   For hit rates up 5.7 kHz per chip a reduction of at most 0.6\% in the relative efficiency was measured.
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&lt;   Large localized hit bursts from low energetic curling electrons were characterised.
---
&gt;   Hit bursts due to highly ionising particles were characterised.
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&lt;   The single-electron resolution in the $xy$ precision plane as a function of the local track angle $\phi$ was measured in the $B$ = 1 T data using reconstructed circular tracks. The resolution is - as expected - independent of the local track angle within an uncertainty of 16 $\rm \mu$m.
---
&gt;   The resolution in the precision plane as a function of the local track angle was measured in the $B$ = 1 T data using reconstructed circle tracks.
&gt;   The resolution in the precision plane is - as expected - independent of the local track angle $\phi$ within an uncertainty of 16 $\rm \mu$m.
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&lt;  As a step towards a Pixel Time Projection Chamber for a future collider experiment \cite{Lupberger:2017uiv}, \cite{Ligtenberg:2021}, a module consisting of 32 GridPixes based on the Timepix3 ASIC was constructed.
&lt;  The GridPixes have a very fine granularity of 256$\times$256 pixels of {55$\times$55}{ $\rm \mu m^2$} and a high efficiency of about 85\%  to detect single ionisation electrons.
---
&gt;  As a step towards a Pixel Time Projection Chamber for a future collider experiment \cite{Lupberger:2017uiv}, \cite{Ligtenberg:2021}, a module consisting of 32 GridPix chips based on the Timepix3 chip was constructed.
&gt;  The GridPix chips have a very fine granularity of 256$\times$256 pixels of {55$\times$55}{ $\rm \mu m^2$} and a high efficiency of about 85\%  to detect single ionisation electrons.
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&lt;  The 32-GridPix chip detector was put in a test beam at DESY and complemented with two sets of silicon detector planes.
&lt;  The data analysed were taken at electron beam momenta of 5 and 6 GeV/c and at magnetic fields of 0 and 1 T. The TPC was operated using a so-called T2K  gas mixture of 95/3/2 gas of {Ar}/{CF$_4$}/{iC$_4$H$_{10}$  (by volume) with a small amount of oxygen and water vapour.
---
&gt;  The 32-GridPix chip detector was put in a test beam at DESY and complemented with two sets of Mimosa26 silicon detector planes.
&gt;  The analysed data were taken at electron beam momenta of 5 and 6 GeV/c and at magnetic fields of 0 and 1 T. The TPC was operated using used a 93.6/5.0/1.4 gas mixture (by volume) of {Ar}/{iC$_4$H$_{10}$}/{CO$_2$} with a small amount of oxygen and water vapour.
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&lt;  The construction of the GridPix TPC module, the test beam setup and data taking conditions have been described in part I of our paper \cite{Beuzekom:2024part1}, that also presents the track reconstruction procedure and the precise TPC tracking results.
---
&gt;  A description of the construction of the GridPix TPC module, the test beam setup and data taking conditions can be found in part I of our paper \cite{Beuzekom:2024part1}, which explains the track reconstruction procedure and the precise TPC tracking results that were obtained.
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&lt;   In the following sections, the test beam analysis results for several topics will be presented.
---
&gt;   In the following sections the analysis results for different topics will be presented.
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&lt; Thirdly, the characterisation of large localized hit bursts caused by from low energetic curling electrons will be presented.
&lt; Fourth, the single-electron resolution in the $xy$ precision plane as a function of the local track angle will be measured.
---
&gt; Thirdly, the characterisation of large hit bursts caused by highly ionising particles will be presented.
&gt; Fourth, the resolution in the precision plane as a function of the local track angle will be measured.
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&lt; %A selected TPC track in the {$B = 0 ~{\rm T}$} data has on average 1000 hits.
&lt; %The tracking precision in the middle of the TPC was derived on a track-by-track bais and found to be  on average {9}{ $\rm \mu$m} in the $xy$ precision plane and {13}{ $\rm \mu$m} in $z$. The angular resolution in $dx/dy$ was on average 0.19 mrad and for dz/dy 0.25 mrad. It is clear that the position resolution in the TPC in the precision and drift coordinates is impressive for a track length of (only) 158 mm. The values are smaller than the uncertainty on the track prediction from the silicon telescope of {26}{ $\rm \mu$m} on average that is dominated by multiple scattering.
---
&gt; %A selected TPC track in the {$B$ = 0 T} data has on average 1000 hits.
&gt; %The tracking precision in the middle of the TPC was derived on a track-by-track bais and found to be  on average {9}{ $\rm \mu$m} in the precision plane and {13}{ $\rm \mu$m} in z. The angular resolution in dx/dy was on average 0.19 mrad and for dz/dy 0.25 mrad. It is clear that the position resolution in the TPC in the precision and drift coordinates is impressive for a track length of (only) 158 mm. The values are smaller than the uncertainty on the track prediction from the silicon telescope of {26}{ $\rm \mu$m} on average that is dominated by multiple scattering.
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&lt;  Particles can be identified by their characteristic energy loss per unit of track length, $dE/dx$ and/or the number of primary clusters, $dN/dx$ produced along the track. In a GridPix detector one can measure both the number of hits produced along the track and their relative distance.
---
&gt;  Particles can be identified by their characteristic energy loss per unit of track length, $dE/dx$ loss and/or the number of primary clusters, $dN/dx$ produced along the track. In a GridPix detector one can measure both the number of hits produced along the track and their relative distance.
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&lt; The distribution of the number of TPC track hits per GridPix for the {$B = 0 ~{\rm T}$} and for the {$B = 1 ~{\rm T}$} data sets are a starting point for a measurement of the $dE/dx$ or $dN/dx$ performance.
&lt; As was discussed in part I of the paper \cite{Beuzekom:2024part1}, the mean number of hits per GridPix were measured to be 124 and 89 in the {$B$ = 0 T} and 1 T data sets respectively. The most probable values are respectively 87 and 64.    
---
&gt; The distribution of the number of TPC track hits per chip for the {$B$ = 0 T} and for the {$B$ = 1 T} data sets are a starting point for a measurement of the $dE/dx$ or $dN/dx$ performance.
&gt; As was discussed in part I of the paper \cite{Beuzekom:2024part1}, the mean number of hits per chip were measured to be 124 and 89 in the {$B$ = 0 T} and 1 T data sets respectively. The most probable values are respectively 87 and 64.    
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&lt; In order to measure the track performance of $dE/dx$ or $dN/dx$, a track selection was applied selecting tracks crossing the central chips - defined in \cite{Beuzekom:2024part1}. The number of hits of different GridPixes were weighted to give the same mean number of hits per GridPix. By combining the hits associated to the track from several events, a new 1 m long track was formed. The 1 m long track has a coverage of 60\% because inactive regions (chip edges and e.g. guard plate) were included.
---
&gt; In order to measure the track performance of $dE/dx$ or $dN/dx$, a track selection was applied selecting tracks crossing the central chips - defined in \cite{Beuzekom:2024part1}. The individual chips were calibrated to give the same mean number of hits per chip.  By combining the hits associated to the track from several events, a new 1 m long track was formed. The 1 m long track has a coverage of 60\% because inactive regions (chip edges and e.g. guard plate) were included.
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&lt; By applying two different analysis methods, the $dE/dx$ or $dN/dx$ resolution is measured from data.
---
&gt; By applying different analysis methods, the $dE/dx$ or $dN/dx$ resolution can be measured from data.
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&lt; Both methods project the hits along the track on the $y$ axis - along the beam direction - of the $xy$ pixel readout plane. This gives a distribution of hits as a function of the distance along the track in pixel units.
---
&gt; Both methods project the hits along the track in the $xy$ plane. This gives a distribution of hits as a function of the distance along the track in pixel units.
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&lt; The second method exploits the distribution of the minimum distance between consecutive hits in the pixel readout plane. If only single-electron clusters were produced in a gas, one would expect an exponentially falling distance distribution. Multi-electron clusters will give rise to a peak at low distances in the $dN/dx$ distribution that is smeared out by the transverse diffusion process. The slope of the exponential distribution is proportional to the $dN/dx$ i.e. the clusters produced by the traversing beam electron. The long Landau tail in the $dE/dx$ distribution is coming from the multi-electron clusters that will peak at low distances and are smeared out by the diffusion proces.
---
&gt; The second method exploits the distribution of the minimum distance between consecutive hits in the $xy$ precision plane. If only single-electron clusters were produced in a gas, one would expect an exponentially falling distance distribution. Multi-electron clusters will give rise to a peak at low distances in the $dN/dx$ distribution that is smeared out by the transverse diffusion process. The slope of the exponential distribution is proportional to the $dN/dx$ i.e. the clusters produced by the traversing beam electron. The long Landau tail in the $dE/dx$ distribution is coming from the multi-electron clusters that will peak at low distances.
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&lt; Using a large number of tracks, it is possible to measure from data the shape of the minimum distance distribution. At distances above approximately 10 pixels the distribution follows an exponential distribution. At lower distance, weights for the {$B$= 0 T} and  1 T data are determined and applied to ensure an exponential distribution over the whole range. The values of the weights at low distances depend on the transverse diffusion coefficient and the drift length.  
&lt; The distribution of hits as a function of the distance $d_y$ is shown with black points in \ref{fig:dist} for the {$B$= 1T} data. 
&lt; The weighted distribution is shown in blue and the exponential fit result - in the range of above 10 pixels -  with a red line.
&lt; %% FCN=34.2842 FROM MIGRAD    STATUS=CONVERGED      45 CALLS          46 TOTAL
&lt; %%                     EDM=7.86544e-08    STRATEGY= 1      ERROR MATRIX ACCURATE 
&lt; %%  EXT PARAMETER                                   STEP         FIRST   
&lt; %%  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
&lt; %%   1  p0           2.87324e+05   1.17683e+03   1.74783e+00   1.29171e-07
&lt; %%   2  p1           1.52216e-01   2.38121e-04   3.55641e-07   5.60373e-01
&lt; %%                               ERR DEF= 0.5
&lt; %% Info in &lt;TCanvas::Print&gt;: pdf file dedxPlots/DistanceFit_B=1T.pdf has been created
---
&gt; Using a large number of tracks, it is possible to measure from data the shape of the minimum distance distribution. At distances above approximately 10 pixels the distribution follows an exponential distribution - see Fig 5.19 in \cite{Ligtenberg:2021}. At lower distance, weights for the {$B$= 0 T} and  1 T data are determined and applied to ensure an exponential distribution over the whole range.
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&lt; \begin{figure}
&lt;     \centering
&lt;     \includegraphics[width=0.9\textwidth]{DistanceFit_B=1T.pdf}
&lt; 	\caption{Distribution of the number of selected hits as a function of the distance $d_y$ in pixel unitsi for the {$B$= 1T} data is show in black. The weighted distribution is shown with blue points and the exponential fit result with a red line.}
&lt;     \label{fig:dist}
&lt; \end{figure}
&lt; 
&lt;  
&lt; %%aWeights $B$ = 0 = { 35.0467 , 12.1497 , 4.52914 , 2.76311 , 1.99386 , 1.59795 , 1.3656 , 1.21409 , 1.11898 , 1.04385 };
---
&gt; %% Weights $B$ = 0 = { 35.0467 , 12.1497 , 4.52914 , 2.76311 , 1.99386 , 1.59795 , 1.3656 , 1.21409 , 1.11898 , 1.04385 };
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&lt; Finally, per event with 1 m of track length, a maximum likelihood fit to the distance distribution in data is performed with the following template function:
---
&gt; Finally, per 1 m of track length, a fit to the distance distribution in data is performed with the following template function:
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&lt; 	 N (d_{y}) = N_0 ~ \mathrm{weight}(d_{y}) ~ e^{ -{\alpha}~\cdot ~d_{y} },
---
&gt; 	 N (d_{xy}) = N_0 ~ \mathrm{weight}(d_{xy}) ~ e^{ -{\alpha}~\cdot ~d_{xy} },
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&lt;  where $d_{y}$ is the minimum distance of the hits in the $y$ direction of the precision plane in pixel units.
---
&gt;  where $d_{xy}$ is the minimum distance of the hits in the precision plane ($xy$) in pixel units.
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&lt;  
&lt; %% dEdxPerformance fit_distance = true 
&lt; %% h_ddist_track_all  and plot  DistanceFit*.pdf 
&lt;  
&lt;  The test beam data provide a $dE/dx$ or $dN/dx$ measurement for electrons with a beam momentum of 5 or 6 GeV.c. 
&lt;  The data were also used to perform a measurement of the response of a minimum ionising particle (MIP) - here defined as a particle that produced 70\% of the electron $dE/dx$.
&lt;  By dropping 30\% of the hits associated to the track, the response of a MIP defined in terms of the number of hits (truncation method) and the fitted slope (template) was measured.
&lt; % and the linearity of the methods tested. 
---
&gt;   
&gt;  The test beam data provide a $dE/dx$ or $dN/dx$ measurement for electrons. The data were also used to perform a measurement of the response of a minimum ionising particle (MIP) - here defined as a particle that produced 70\% of the electron $dE/dx$.
&gt; By dropping 30\% of the hits associated to the track and applying the two methods, the response of a MIP was measured and the linearity of the methods tested. 
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&lt;  The resolution of the $B$ = 1 T data is about 40\% better than the $B$ = 0 T data. This is consistent with the smaller fluctuations that are present in the distributions of the number of hits per GridPix in the $B$ = 1 T data \cite{Beuzekom:2024part1}.
---
&gt;  The resolution of the $B$ = 1 T data is about 40\% better than the $B$ = 0 T data. This is consistent with the smaller fluctuations that are present in the distributions of the number of hits per chip in the $B$ = 1 T data \cite{Beuzekom:2024part1}.
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&lt;  The results for the 1 T data are shown in Fig.~\ref{fig:dEdx}, for electrons and MIPs and for the $dE/dx$ truncation and template fit methods. The relative error on the measured resolutions are smaller than 2.6 \% and therefore neglected.   
---
&gt;  The results for the 1 T data are shown in Fig.~\ref{fig:dEdx}, for electrons and MIPs and for the $dE/dx$ truncation and template fit methods.  
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&gt;  The linearity - defined as the mean MIP response divided by the mean electron response divided by 0.7 -  was measured to be 1.03 for the truncation method and 1.07 for the template fit method. This value is slightly different from 1, and can be corrected by scaling the expected values for different particles as a function of the measured momentum.   
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&lt;  In order to estimate the performance for different particles it is important to quantify the linearity of the methods.  
&lt;  The linearity is defined as the mean MIP response, divided by the mean electron response divided by 0.7.
&lt;  Clearly, one wants to use an algorithm for which the linearity is close to 1. E.g. a value of 1.2 would imply that the MIP-electron separation is 20% smaller.  
&lt;  In our case the linearity was measured to be 1.03 for the truncation method and 1.07 for the template fit method. The statistical error on this measurement is less than 0.1 \% and therefore neglected.
&lt;  This value is slightly different from 1. The PID performance can be corrected for by scaling the expectation values for different particles as a function of the measured momentum.   
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&lt; %% 
&lt; 
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&lt; The single-electron efficiency of the GridPix detector can be reduced in a high background environment due to the charge up of the resistive layers and the effective reduction of the amplification field. It is therefore important to measure the single-electron efficiency in different background conditions.
&lt; The ToT is related to the deposited charge on the pixel and the single-electron efficiency of the detector.
&lt; The relative change in the single-electron efficiency  $\delta \epsilon / \epsilon$  
&lt;   can be related to the relative change in the mean ToT by
&lt;  \begin{equation}
&lt; 	 \delta \epsilon / \epsilon  = d ~ \delta \rm {ToT/ ToT}.
&lt;     \label{eq:tot}
&lt;  \end{equation}
&lt;   The derivative $d$ is about 0.5 at the mean working point of ToT=0.65 $\rm \mu s$ and is determined from the measured efficiency-ToT curve in Fig. 4.7 of \cite{Ligtenberg:2021}.
&lt; %Using the test beam data, it is possible to measure the relative efficiency change comparing a high and a low background hit rate samples. 
&lt; By measuring the mean ToT in a high (low) rate environment runs at $B$ fields of 0 and 1 T, the relative change in single-electron efficiency is extracted. 
&lt;       
&lt; % The efficiency of the GridPix device to detect a hit in a high (low) rate environment is measured comparing the mean time over threshold (ToT) for low and high rate runs at B fields of 0 and 1 T. The mean ToT is sensitive to the single-electron efficiency of the detector.
&lt;  In order to obtain a precise result for the mean ToT, hits associated to TPC tracks were used. The track selection is the same as in section 2.
&lt;  The analysed runs runs 6934 and 6935 and 6983 have a high hit rate and were taken at a beam momentum of 5 GeV/c. 
&lt;  Runs 6916 and 6969 were taken at a beam momentum of 6 GeV/c and have a low hit rate. 
---
&gt; The efficiency of the GridPix device to detect a hit in a high (low) rate environment is measured comparing the mean time over threshold (ToT) for low and high rate runs at B fields of 0 and 1 T. The mean ToT is sensitive to the single-electron efficiency of the detector.
&gt;  In order to extract a precise result, hits associated to TPC tracks were used. The track selection is the same as in section 2.
&gt;  The analysed runs for the $B$ = 0 T data set were runs 6916, 6934 and 6935 and for the $B$ = 1 T data set runs 6969 and 6983. 
&gt;   
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&lt;  The results for the measured mean ToT for different runs and hit rates are summarised in Table~\ref{tab:hitrates}.
---
&gt;  The results for the measured average ToT for different runs and hit rates are summarised in Table~\ref{tab:hitrates}.
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&lt;  The instantaneous rate in the high rate runs 6934, 6935 and 6983 is about a factor 3 higher (due to the duty cycle of the machine).
&lt;   
---
&gt;  The instantaneous rate in runs 6934, 6935 and 6983 taken at 5 GeV/c is about a factor 3 higher (due to the duty cycle of the machine).
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&lt;  In this case the rate goes up to 34 kHz for 6 chips or 5.7 kHz per GridPix.
---
&gt;  In this case the rate goes up to 34 kHz for 6 chips or 5.7 kHz per chip.
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&lt;   The rate goes up to 20 kHz for 6 chips or 3.3 kHz per GridPix.
---
&gt;   The rate goes up to 20 kHz for 6 chips or 3.3 kHz per chip.
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&gt;   The relative change in the mean ToT can be related to the relative change in the single-electron efficiency  $\delta \epsilon / \epsilon$ by: 
&gt;  \begin{equation}
&gt; 	 \delta \epsilon / \epsilon  = d ~ \delta \rm {ToT/ ToT}.
&gt;     \label{eq:tot}
&gt;  \end{equation}
&gt;   The derivative $\rm d$ is about 0.5 at the mean working point of ToT=0.65 $\rm \mu s$ and is determined from the measured efficiency-ToT curve in Fig. 4.7 of \cite{Ligtenberg:2021}.
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&lt; Using Eq.~\ref{eq:tot}, this means that the relative change in the single-electron efficiency  $\delta \epsilon / \epsilon$ is stable at the level of +0.9\% ($B$ = 1 T) and -0.6\% ($B$ = 0 T) for hit  rates up to 3.3 (5.7) kHz per GridPix.
&lt; To conclude, running at hit rates up 5.7 kHz per GridPix gives a reduction of at most 0.6\% in the relative efficiency. 
---
&gt; This means that the relative efficiency is stable at the level of +0.9\% ($B$ = 1 T) and -0.6\% ($B$ = 0 T) for hit  rates up to 3.3 (5.7) kHz per chip.
&gt; To conclude, running at hit rates up 5.7 kHz per chip gives a reduction of at most 0.6\% in the relative efficiency. 
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&lt; \section{Characterisation of large localized hit bursts}
&lt;   In event displays large localized hit bursts from low energetic curling electrons 
---
&gt; \section{Characterisation of hit bursts}
&gt; %Here the characterisation of large hit bursts caused by highly ionising particles will be presented.
&gt;   In event displays hit bursts caused by highly ionising particles (e.g. alpha particles or delta electrons)
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&lt;   A large variety of hit patterns can be observed: large radii (open) circular tracks, smaller size radius circular tracks from low momentum particles, curlers and more confined bursts. A track with a momentum of $\rm{1 ~MeV/c}$ will have a typical radius of 60 pixels. 
---
&gt;   A large variety of hit patterns can be observed: large radii (open) circles, smaller size radius circles from low momentum particles, curlers and more confined bursts. A track with a momentum of 1 MeV/c will have a typical radius of 60 pixels. 
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&lt;   To study the large localized hit bursts, the data of run 6969 - taken at a 6 GeV/c beam momentum in a $B$ = 1 T field -  were analysed. %No acceptance or track selection cuts were applied. 
---
&gt;   To study the hit bursts, the data of run 6969 - taken at a 6 GeV/c beam momentum in a $B$ = 1 T field -  were analysed. %No acceptance or track selection cuts were applied. 
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&lt;   The large localized hit bursts were characterised by the number of associated hits, the radius in which 90\% of the hits are found (radius90) and the time in which 90\% of the hits are detected (time90).
---
&gt;   The bursts were characterised by the number of associated hits, the radius in which 90\% of the hits are found (radius90) and the time in which 90\% of the hits are detected (time90).
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&lt; 	  \caption{The stacked distributions for radius90 and time90, for large localized hit bursts with more than 100 (blue), 200 (green) and 400 (red) hits, in run 6969.}
---
&gt; 	  \caption{The stacked distributions for radius90 and time90, for bursts with more than 100 (blue), 200 (green) and 400 (red) hits, in run 6969.}
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&lt;  Note that hits that end up on the same pixel within the Timepix3 pixel dead time of minimally 475 ns \cite{Poikela:2014joi}  will not be recorded, so part of the core of the burst may remain undetected.  
&lt; %% Still, the detector is able to record hit bursts of at most 7854 hits in a 50 pixel radius. 
&lt; The largest hit burst in the analysed run 6969 had 3180 hits.   
---
&gt;  Note that hits that end up on the same pixel within the Timepix3 pixel dead time of 475 ns will not be recorded, so part of the core of the burst may remain undetected.  
&gt;  Still, the detector is able to record hit bursts of at most 7854 hits in a 50 pixel radius. The largest hit burst in the run used in Fig.~\ref{fig:bursts} had 3180 hits.   
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&lt; For high momentum tracking it is important to cut tightly on the track residuals in $xy$ and $z$. In particular the cut in $z$ reduces the impact of hit bursts in the $B$ = 1 T data. Therefore in future pattern recognition software one could run a hit burst finding algorithm and down weight in the track fit the hits associated to bursts.      
---
&gt; For high momentum tracking it is important to cut tightly on the track residuals in $xy$ and $z$. In particular the cut in $z$ reduces the impact of bursts in the $B$ = 1 T data. Therefore in future pattern recognition software one could run a burst finding algorithm and down weight in the track fit the hits associated to bursts.      
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&lt; \section{Single-electron resolution as function of the local track angle}
---
&gt; \section{Track resolution as function of the local track angle}
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&lt; The single-electron resolution in the $xy$ precision plane as a function of the local track angle $\phi$ has been measured in run 6969 of the {$B$ = 1 T} data set taken at a beam momentum of 6 GeV/c. For a pad based readout system the resolution has a strong dependence on the local track 
&lt; angle see e.g. \cite{LCTPC:2016}. The resolution is the smallest if the local track angle is parallel to the strip direction. 
---
&gt; The resolution in the precision plane as a function of the local track angle will be measured in run 6969 of the $B$ = 1 T data set taken at a beam momentum of 6 GeV/c. For a pad based readout system the resolution has a strong dependence on the local track 
&gt; angle see e.g. \cite{LCTPC:2016}. The resolution is best if the local track angle is parallel to the strip direction. 
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&lt; In order to test experimentally this hypothesis, reconstructed circular tracks were selected. Examples of circular tracks can be observed in the event display shown in Fig.~\ref{fig:eventDisplay}. For circular tracks, the local track angle $\phi$ depends on the position of the individual hits on the circle
---
&gt; In order to test experimentally this hypothesis, reconstructed circle tracks were selected. Examples of circle tracks can be observed in the event display shown in Fig.~\ref{fig:eventDisplay}. For circles, the local track angle $\phi$ depends on the position of the individual hits on the circle
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&lt; Using the track residuals in the $xy$ plane, it is possible to measure the single-electron resolution of the hits as a function of the local track angle.
---
&gt; Using the track residuals in the $xy$ plane, it is possible to measure the resolution of the hits as a function of the local track angle.
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&lt; A dedicated pattern recognition program was written to find and fit multiple circular tracks in an event.
&lt; To find candidate circular tracks, a Hough transform was used to find the centre of the circle in the $xy$ plane.
---
&gt; A dedicated pattern recognition program was written to find and fit multiple circles in an event.
&gt; To find candidate circles, a Hough transform was used to find the centre of the circle in the $xy$ plane.
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&lt; In the circle fit, the coarse uncertainty in $xy$ was estimated to be about 4 pixels and in $z$  1 mm.
&lt; Outlier hits at more than 2.5 standard deviations were iteratively rejected.
&lt; For the selection of circular tracks it was required that the fit $\chi^2_{xy}/d.o.f.$ and $\chi^2_{z}/d.o.f.$ were less than 5.
&lt; Finally, the radius of the circle had to be larger than 50 pixels (corresponding to a momentum cut of 0.8 MeV/c) and at least 20 hits should lie on the circle. The total $\phi$ span of the selected hits on the circle should be at least 1 rad. The hits with local $\phi$ values below $\pi/8$ and above $15\pi/8$ were removed due to low statistics.
---
&gt; In the circle fit, the resolution in $xy$ was estimated to be about 4 pixels and in $z$ it was 1 mm.
&gt; Outlier hits at more than 2.5 standard deviation were iteratively rejected.
&gt; For the selection of circles it was required that the fit $\chi^2_{xy}/d.o.f.$ and $\chi^2_{z}/d.o.f.$ were less than 5.
&gt; Finally, the radius of the circle had to be larger than 50 pixels (corresponding to a momentum cut of 0.8 MeV/c) and at least 20 hits should lie on the circle. The total $\phi$ span of the selected hits on the circle should be at least 1 rad. The hits with local $\phi$ values below $\pi/8$ and above $15\pi/8$ were removed.
455,456c403,404
&lt; The selected data set has 973 circular tracks, with a mean radius of 155 pixels and a mean number of hits of 194.
&lt; Because the resolution depends on the radius (due to the multiple scattering that increases at low momentum) and small radii span a large $\phi$ range, the data were re-weighted as a function of the circle radius. The weights made the momentum distribution flat as a function of the local track angle $\phi$.
---
&gt; The selected data set has 973 circles, with a mean radius of 155 pixels and a mean number of hits of 194.
&gt; Because the resolution depends on the radius (due to the mutliple scattering that increases at low momentum) and small radii span a large $\phi$ range, the data were re-weighted as a function of the circle radius.
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&lt; The fitted  resolution in $xy$ as a function of the local track angle $\phi$ for the hits on the circle is shown in Fig.~\ref{fig:resolution}.
---
&gt; The fitted  resolution in $xy$  as a function of the local track angle $\phi$ for the hits on the circle is shown in Fig.~\ref{fig:resolution}.
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&lt;   \caption{The fitted single-electron resolution in $xy$ as a function of the local track angle $\phi$ for the hits on the circle. The fitted curve in red is given in Eq.~\ref{eq:res}.}
---
&gt;   \caption{The fitted resolution in $xy$ as a function of the local track angle $\phi$ for the hits on the circle. The fitted curve in red is given in Eq.~\ref{eq:res}.}
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&lt; It can therefore be concluded that the single-electron resolution in the $xy$ precision plane is independent of the local track angle $\phi$ within an uncertainty of 16 $\rm \mu$m.
---
&gt; It can therefore be concluded that the resolution in the precision plane is independent of the local track angle $\phi$ within an uncertainty of 16 $\rm \mu$m.
478c426
&lt; % Reject circular tracks with a better SL line fit by applying cuts on the c2  and number of hits for the circle and line hypothesis.
---
&gt; % Reject circles with a better SL line fit by applying cuts on the c2  and number of hits for the circle and line hypothesis.
492,493c440,441
&lt;  The electron PID resolution in the ILD TPC is expected to be 2.4\% (template fit) and 3\% (truncation method) at polar angles of $\theta =\pi/2$ ($\cos\theta=0$) and a track length ($\rm tlength_0$) of 1441 mm. 
&lt; %Depending on the B field value (3.5 T - foreseen at ILC - or e.g. 2 T), the PID resolution in the transverse plane after drifting to the endplate will be similar or worse than the test beam situation. The PID resolution for a GridPix TPC in ILD will therefore lie between 2.4 and 3\% at $\cos\theta=0$. The two points correspond respectively to the maximum and minimum resolution at $\cos\theta=0$. 
---
&gt;  The electron PID resolution in the ILD TPC is then expected to be 2.4\% (template fit) and 3\% (truncation method) at polar angles of $\theta =\pi/2$ ($\cos\theta=0$) and a track length ($\rm tlength_0$) of 1441 mm. 
&gt; %Depending on the B field value (3.5 T - foreseen at ILC - or e.g. 2 T), the PID resolution in the transverse plane after drifting to the endplate will be similar or worse than the test beam situation. The PID resolution for a GridPix TPC in ILD will therefore lie between 2.4 and 3\% at $\cos\theta=0$. 
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&lt; 	 \sigma_{i} =  \sigma_{e} \sqrt{{\rm tlength}_0 ~\cdot ~E_{e}}/\sqrt{{\rm tlength} ~\cdot ~E_{i}},
---
&gt; 	 \sigma_{i} =  \sigma_{e} \sqrt{{\rm tlength}_0 ~\cdot ~E_{e}}/\sqrt{{\rm tlength} ~ E_{i}},
500,502c448,450
&lt; \footnote[1]{Clearly, the best PID resolution will be reached for the largest track length, which corresponds to $|\cos \theta|$ = 0.85 in ILD.}
&lt; 
&lt;  The ILD parametrisations of $dE/dx$ for different particles as a function of the momentum were used as given in \cite{ILCsoft}. They are based on full simulations of the ILD TPC operated with a T2K gas and running at atmospheric pressure.
---
&gt; Clearly, the best PID resolution will be reached for the largest track length, which corresponds to $\cos \theta$ = 0.85 in ILD.  
&gt;  
&gt;  The ILD parametrisations of the energy loss for different particles as a function of the momentum were used as given in \cite{ILCsoft}. They are based on full simulations of the ILD TPC operated with a T2K gas and running at atmospheric pressure.
525,526c473,475
&lt; A Time Projection Chamber (TPC) module with 32 GridPixes was constructed and the performance was measured using data taken in a test beam at DESY in 2021.  
&lt;   The data analysed were taken at electron beam momenta of 5 and 6 GeV/c and at magnetic fields of 0 and 1 T.
---
&gt; A Time Projection Chamber (TPC) module with 32 GridPix chips was constructed and the performance was measured using data taken in a test beam at DESY in 2021.  
&gt;   The analysed data were taken at electron beam momenta of 5 and 6 GeV/c and at magnetic fields of 0 and 1 T.
&gt; 
529c478
&lt;   The $dE/dx$ or $dN/dx$ resolution for electrons with a momentum of 6 GeV/c in the 1 T data for a 1 m long track with 60\% coverage was measured to be 3.6\% for the $dE/dx$ truncation method and 2.9\% for the template fit method.   
---
&gt;   The $dE/dx$ or $dN/dx$ resolution for electrons of momenta 5 and 6 GeV/c in the 1 T data for a 1 m long track with 60\% coverage was measured to be 3.6\% for the $dE/dx$ truncation method and 2.9\% for the template fit method.   
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&lt;   For hit rates up 5.7 kHz per GridPix a reduction of at most 0.6\% in the relative efficiency was measured. 
---
&gt;   For hit rates up 5.7 kHz per chip a reduction of at most 0.6\% in the relative efficiency was measured. 
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&lt;   Large localized hit bursts from low energetic curling electrons were characterised showing the pattern recognition capabilities of a GridPix Pixel TPC.
---
&gt;   Hit bursts due to highly ionising particles were characterised showing the pattern recognition capabilities of a GridPix Pixel TPC.
537c486
&lt;   The single-electron resolution in the $xy$ precision plane as a function of the local track angle was measured in the $B$ = 1 T data using reconstructed circular tracks. 
---
&gt;   The resolution in the precision plane as a function of the local track angle was measured in the $B$ = 1 T data using reconstructed circle tracks. 
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&lt;   At the CEPC a Pixel TPC is proposed, because of the precise tracking and particle identification capabilities.
---
&gt;   At the CEPC collider a Pixel TPC is proposed, because of the precise tracking and particle identification capabilities.
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&lt;  M.~van~Beuzekom et al., {Towards a Pixel TPC part I: construction and test of a 32-chip GridPix detector}, 
&lt; Nucl. Instrum. Meth. A 1075 (2025) 17039.
&lt; %\newblock \href {http://arxiv.org/abs/1808.04565} {\path{arXiv:1808.04565}},
&lt; \newblock \href {https://doi.org/10.1016/j.nima.2025.170397}
&lt;   {\path{doi:10.1016/j.nima.2025.170397}}. 
---
&gt;         M.~van~Beuzekom, et al., {Towards a Pixel TPC part I: construction and test of a 32-chip GridPix detector}, submitted to Nucl. Instrum. Meth. A.
624,633d568
&lt; \bibitem{Poikela:2014joi}
&lt; T.~Poikela, J.~Plosila, T.~Westerlund, M.~Campbell, M.~De~Gaspari, X.~Llopart,
&lt;   V.~Gromov, R.~Kluit, M.~van Beuzekom, F.~Zappon, V.~Zivkovic, C.~Brezina,
&lt;   K.~Desch, Y.~Fu, A.~Kruth,
&lt;   \href{http://stacks.iop.org/1748-0221/9/i=05/a=C05013}{{Timepix3: a 65K
&lt;   channel hybrid pixel read out chip with simultaneous ToA/ToT and sparse
&lt;   read out}}, JINST 9~(05) (2014) C05013.
&lt; \newline\urlprefix\url{http://stacks.iop.org/1748-0221/9/i=05/a=C05013}
&lt; 
&lt; 
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