<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">42d41
&lt; \usepackage[obeyspaces]{url}
120,121c119,120
&lt; 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.. 
&lt;   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). 
---
&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 Tesla(T).
154c153
&lt;  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.
---
&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.
204c203
&lt; 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.
---
&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 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.
212c211
&lt; 	 N (d_{xy}) = N_0 ~ \mathrm{weight}(d_{xy}) ~ e^{ -{\alpha}~\cdot ~d_{xy} },
---
&gt; 	 N (d_{xy}) = N_0 ~ \mathrm{weight}(d_{xy}) ~ e^{ -{\alpha} ~. ~d_{xy} },
215c214
&lt;  where $d_{xy}$ is the minimum distance of the hits in the precision plane ($xy$) in pixel units.
---
&gt;  where $d_{xy}$ is the minimum distance of the hits in the precision plane ($xy$).
221c220
&lt;  The relative resolution is defined as the r.m.s. of the distribution, divided by the mean and the results are shown in Table~\ref{tab:dEdxresolution}. 
---
&gt;  The relative resolution is defined as the r.m.s. of the distribution divided by the mean and the results are shown in Table~\ref{tab:dEdxresolution}. 
245c244
&lt;  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.   
---
&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 method 1 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.   
321c320
&lt; 	 \delta \epsilon / \epsilon  = d ~ \delta \rm {ToT/ ToT}.
---
&gt; 	 \delta \rm {ToT/ ToT}  = d ~ \delta \epsilon / \epsilon.
324c323
&lt;   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}.
---
&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 inFig. 4.7 of \cite{Ligtenberg:2021}.
332c331
&lt;   In event displays hit bursts caused by highly ionising particles (e.g. alpha particles or delta electrons)
---
&gt;   In event displays hit burst caused by highly ionising particles (e.g. alpha particles or delta electrons)
343c342
&lt;     \caption{An event display for run 6969 event 2 taken at a 6 GeV/c beam momentum in a $B$ = 1 T field. The hits are shown in the $xy$ plane, in colour the time of arrival is shown.}
---
&gt;     \caption{An event display for run 6969 event 2 taken at a 5 GeV/c beam momentum in a $B$ = 1 T field. The hits are shown in the $xy$ plane, in colour the time of arrival is shown.}
348c347
&lt;   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. 
---
&gt;   To study the hit bursts, the data of run 6969 - taken at a 5 GeV/c beam momentum in a $B$ = 1 T field -  were analysed. %No acceptance or track selection cuts were applied. 
382,385c381
&lt; %% Calculate phi around the circle (phi = 0 is pointing opposite the local y axis = right to left in the event display).
&lt; 
&lt; 
&lt; 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; The resolution in the precision plane as a function of the local track angle will be measured in the $B$ = 1 T data set. For a pad based readout system the resolution has a strong dependence on the local track 
391c387
&lt; 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.
---
&gt; Using the residuals in the $xy$ plane, it is possible to measure the resolution of the hits as a function of the local track angle.
404c400
&lt; 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.
---
&gt; Because the resolution depends on the radius (i.e. the momentum) and small radii span a large $\phi$ range, the data were re-weighted as a function of the circle radius.
410c406
&lt;   \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}.}
---
&gt;   \caption{The fitted resolution in $xy$ as a function of the local track angle $\phi$ for the hits on the circle. The fitted curved in red is given in Eq.~\ref{eq:res}.}
436c432
&lt; \section{Projected particle identification performance for a Pixel TPC in the proposed experiment ILD at a future ILC} 
---
&gt; \subsection{Projected particle identification performance for a Pixel TPC in the proposed experiment ILD at a future ILC} 
440c436
&lt;  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;  The expected 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. 
444c440
&lt; 	 \sigma_{i} =  \sigma_{e} \sqrt{{\rm tlength}_0 ~\cdot ~E_{e}}/\sqrt{{\rm tlength} ~ E_{i}},
---
&gt; 	 \sigma_{i} =  \sigma_{e} \sqrt{{\rm tlength}_0 ~. ~E_{e}}/\sqrt{{\rm tlength} ~ E_{i}},
545,548c541,542
&lt;   Collider}}, Ph.D. thesis, {Free University of Amsterdam} (2021).  \urlprefix
&lt; %\newline\urlprefix\url{https://www.nikhef.nl/pub/services/biblio/theses_pdf/thesis\_C\_Ligtenberg.pdf}
&lt; \newline  
&lt; \mbox{\small\url{www.nikhef.nl/pub/services/biblio/theses_pdf/thesis_C_Ligtenberg.pdf}}
---
&gt;   Collider}}, Ph.D. thesis, {Free University of Amsterdam} (2021).
&gt; \newline\urlprefix\url{https://www.nikhef.nl/pub/services/biblio/theses\_pdf/thesis\_C\_Ligtenberg.pdf}
570c564
&lt; iLCSoft, Linear Collider Software, \newline\urlprefix\small\url{https://github.com/iLCSoft/MarlinReco/blob/master/Analysis/PIDTools/}, based on version v02-02-01. 
---
&gt; iLCSoft, Linear Collider Software, \newline\urlprefix\url{https://github.com/iLCSoft/MarlinReco/blob/master/Analysis/PIDTools/}, based on version v02-02-01. 
</pre></body></html>