From: Jan Michel Date: Mon, 28 Jan 2019 15:40:19 +0000 (+0100) Subject: add CBM Note on MVD rates X-Git-Url: https://jspc29.x-matter.uni-frankfurt.de/git/?a=commitdiff_plain;h=ddb3f62857434e46d969affa9750d18ecbd963e3;p=mvd_docu.git add CBM Note on MVD rates --- diff --git a/notes/2019-mvdrates-CBM-TN/cbm_note.tex b/notes/2019-mvdrates-CBM-TN/cbm_note.tex new file mode 100644 index 0000000..e199323 --- /dev/null +++ b/notes/2019-mvdrates-CBM-TN/cbm_note.tex @@ -0,0 +1,51 @@ +\documentclass[CBM,manyauthors]{cbm_notes} +\newcommand{\slfrac}[2]{\left.#1\right/#2} +\usepackage{rotating} +% +\usepackage[english]{babel} +\usepackage{amsmath} +\usepackage{multirow} +\usepackage{upgreek} +% \setlength{marginparwidth}{2cm} +% \usepackage[textsize=tiny]{todonotes} + +%%% Insert here the note number +\newcommand\NOTENUMBER{1900X} + +\begin{document}% + +%%%%%%%%%%%%%%% Title page %%%%%%%%%%%%%%%%%%%%%%%% +\begin{titlepage} +% +% +% Replace "TN" by "CN" or "PN" if appropriate. +\PHnumber{CBM-TN-\NOTENUMBER} +\PHdate{\today} +% +%%% Put your own title + short title here: +\title{MVD: Hit Rates, Link Bandwidth and Interaction Rates} +\ShortTitle{MVD: Hit Rates, Bandwidth and Interaction Rates} % appears on right page headers +% +\author{Qiyan Li$^{1}$, Jan Michel$^{1}$} +\author{ +1. Institute for Nuclear Physics, Goethe-University Frankfurt, Germany\\ +} +\author{Email: michel@physik.uni-frankfurt.de} +% +%% Appears on left page headers. Replace "Technical" by "Computing" or "Physics" if appropriate. +\ShortAuthor{CBM Technical Note \NOTENUMBER} +% +\begin{abstract} +This note was driven by the question on how many links, i.e. GBTx chips are required to run the MVD at different +setup scenarios. We present the related detector and station configurations and estimate the load based on MC +simulations for 2 benchmark physics cases Au+Au and p+Au at SIS-100 energies. In the end we comment on possible +modifications to improve the maximum possible interaction rate, or lower the dissipated heat in the system. + +\end{abstract} + +\end{titlepage} +% + +\input{mvdrates.tex} %%%%%%%%%%% put the body of the article here + +\end{document} diff --git a/notes/2019-mvdrates-CBM-TN/cbm_notes.cls b/notes/2019-mvdrates-CBM-TN/cbm_notes.cls new file mode 100644 index 0000000..eec4bcb --- /dev/null +++ b/notes/2019-mvdrates-CBM-TN/cbm_notes.cls @@ -0,0 +1,477 @@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Name: cbm_notes.cls % +% % +% Purpose: Set LaTeX parameters For preprint/Notes % +% % +% Rewrite of CERN preprint class For CBM/FAIR % +% % +% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\def\fileversion{1.06} +\def\filedate{8 July 2010} +\def\docdate{8 July 2010} +\typeout{Document Style 'cbm_notes'. 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The three major factors are the collision system, the beam +energy and the magnetic field applied. + +We did a study based on simulated events for 4 different cases: + + +\begin{table}[h] + \begin{center} +\begin{tabular}{c|c|c|c|c|c} + \textbf{Case} &\textbf{System} &\textbf{Energy} &\textbf{Magnetic Field} &\textbf{Interaction +Rate} &\textbf{Interaction Probability} \\ +\hline +1 & p + Au & 25 GeV & 100\% & 10 MHz & not important\\ +2a & Au + Au & 10 GeV/u & 100\% & 100 kHz & 1\%\\ +2b & Au + Au & 10 GeV/u & 50\% & 100 kHz & 1\%\\ +3 & Au + Au & 4 GeV/u & 50\% & 100 kHz & 1\% +\end{tabular} +\caption{The four experimental cases studied} +\end{center} +\end{table} +For experiments using a gold ion beam, the interaction probability has to be defined, as the main +data load on the most critical sensors is not set by the number of interactions but by the number +of delta-electrons generated by the beam ions traversing the target. +Experimental case 2b using a high energy beam and reduced magnetic field might not be used in reality, +but this case can be understood as a worst case scenario as is shown below. + +For this study we can rely on the average number of minimum bias interactions, not taking into +account fluctuations in beam intensity, centrality of collisions and statistical fluctuations for both +interactions per time interval and hit rate per area. These are accounted for in the sensor design +by both a fast internal data bus and a on-chip buffer memory to smooth out any fluctuations over +several hundred microseconds. + +\section{MVD Set-ups} +The typical set-up of the MVD consists of four stations located between 5 and 20 cm downstream the target. +Each station consists of two half-stations that can be moved sideways to a safe position during beam tuning. +Each half-station consists of two quadrants and is equipped with sensors from both sides (front and back). + +The increasing distance from the target of the stations asks for different size of the +stations. The original design contains four different station sizes (``Types'') as shown in figure \ref{fig:stations}. +Their respective number of sensors is listed in table \ref{tab:sensorcount}. + +\begin{table}[h] + \begin{center} +\begin{tabular}{c|c|c|c} + & \multicolumn{2}{c|}{\textbf{Sensors/Quadrant}} &\textbf{Sensors}\\ + \textbf{Type} & $\quad$\textbf{front}$\quad$ & $\quad$\textbf{back}$\quad$ & \textbf{total}\\ + \hline + 0 & 1 & 1 & 8 \\ + 1 & 4 & 4 & 32\\ + 2 & 9 & 6 & 60\\ + 3 & 16 & 12 & 112\\ +\end{tabular} +\caption{The four types of detector stations and their respective count of sensors.} +\label{tab:sensorcount} +\end{center} +\end{table} + +Meanwhile, there are two planned set-ups of the MVD defined, driven by physics cases: +One dedicated for best vertex resolution (``Vertexing +Geometry'') and one for improved tracking performance with larger acceptance (``Tracking +Geometry''). + +The Vertexing geometry consists of one station of each type located at 5, 10, 15 and 20 cm +downstream from the target. To ease construction, the type 2 station is replaced by +a type 3 station if constraints on hit rate and number of data links permit to do so. + +The Tracking geometry consists of two stations of type 1 and two stations of type 3 located at 8, +12, 16 and 20 cm downstream. + +\begin{table}[h] + \begin{center} +\begin{tabular}{c|cc|cc} + & \multicolumn{2}{c|}{\textbf{Vertexing}} & \multicolumn{2}{c}{\textbf{Tracking}}\\ + \textbf{Station} & \textbf{Type} & \textbf{Position} [cm] & \textbf{Type} & \textbf{Position} [cm]\\ + \hline + 0 & 0 & 5 & 1 & 8\\ + 1 & 1 & 10 & 1 & 12\\ + 2 & 3 & 15 & 3 & 16\\ + 3 & 3 & 20 & 3 & 20\\ +\end{tabular} +\caption{The two detector geometries and their respective setup consisting of four stations made up by three station types and positions.} +\end{center} +\end{table} + +\begin{figure}[t] + \begin{center} + \includegraphics[width=\textwidth]{figures/MVD_separated_full_station_acceptance_2.jpg} +\end{center} +\caption{The four different station types that cover the full acceptance at different distances to the target.} +\label{fig:stations} +\end{figure} + + +\section{Sensor Data Output} + +As we are not running a full simulation of sensor response and data conversion, we have to estimate +the number of data words generated. Each MIMOSIS sensor with an size of approximately 1 by 3 $\rm{cm}^2$ has 520,129 pixels, organized in a 508 x 1024 +matrix. It is divided into 64 regions (508 x 16 pixel) that are further divided into 8 +double-columns with 508 x 2 pixels each. The whole matrix is read out at a 200 kHz frame rate. + +All data is encoded in 16 Bit wide words according to the following rules: + +\begin{itemize} + \item Each frame is started with a 8 word header and ended with a 2 word trailer. These contain frame numbers, + link word alignment markers, error flags and a checksum. + \item Each region has its own 1 word header containing the number of the region. It is skipped if the region contains no hits. + \item Each hit word contains a pixel address and the status of 4 adjacent pixels, but only within one double-column. + \item Due to the internal bus structure, data from each region must be aligned to 32 Bit boundaries, + hence an occasional blank word has to be accounted for if a region has an odd number of header and data words. +\end{itemize} + +To calculate the total amount of data, we have to estimate the number of data words generated by +one hit: + +\begin{itemize} + \item We assume that every hit fires pixels in a 2x2 pixel area (For delta-electrons this region is +likely smaller, for heavier fragments much larger. +\footnote{Clusters with up to 200 pixels have been observed in Mimosa-26 when hit by a heavy ion}) + + \item If the whole area falls into one double-column, it is encoded in one data word. If it +crosses a boundary, two words are generated. Both cases are assumed to be equally likely, which ignores the +probability of smaller clusters that always require only one word.\\ + $\rightarrow\quad$On average, 1.5 data words are generated for each hit, not accounting for headers. + + \item We assume an even distribution of hits across the sensor which is true in areas with low hit +rate. In regions with high hit density this is not necessarily true (compare plots of delta-electron distribution), +but here this assumption has no impact in high rate areas.\\ + $\rightarrow\quad$When a sensor has few hits, each of them is in a separate region with its own header. + This is the worst case in terms of data rate at low occupancy. + + \item Further, we assume a fake hit rate in the order of $10^{-5}$, i.e. 5 to 10 pixel per frame from each sensor. + +\end{itemize} + +In summary, this gives us the following amounts of words: +\begin{itemize} + \item Each frame starts with a 10 word overhead for header and trailer.\\$\rightarrow\quad$ 10 words/frame + \item There are 10 fake hits, each encoded in one data word and a region header.\\ + $\rightarrow\quad$ 20 words/frame + \item The first 54 real hits (64 regions minus those with a fake hit) need to have a region header +plus 1.5 data words plus 0.5 blank words. \footnote{In rare cases (6\%), a hit will fire pixels across a region boundary and requires +two region headers. This minor effect on the data rate will be ignored.}\\ +$\rightarrow\quad$ 3 words/hit + \item All subsequent hits generate 1.5 data words because headers have already been added for the first hit in each region. Blank words + can be ignored as it is equally likely to add or remove one. + \\$\rightarrow\quad$ 1.5 words/hit +\end{itemize} +Or in mathematical terms: +$$N = \begin{cases} 30~\rm{words} + 3\frac{\rm{words}}{\rm{hit}} \cdot \rm{hits} & \rm{for~hits} <= 54 \\ +111~\rm{words} + 1.5\frac{\rm{words}}{\rm{hit}} \cdot \rm{hits}& \rm{for~hits} > 54 \end{cases}$$ + +The sensors can operate with 2, 4 or 8 active links. Each runs at 320 MBit/s and can transport 100 +words for one frame of 5~$\upmu$s. This gives us the following hit rate limits: +\begin{description} + \item [2 links:] 55 hits/frame + \item [4 links:] 190 hits/frame + \item [8 links:] 460 hits/frame +\end{description} + + +\section{Simulation Results} +\begin{table} +\setlength{\tabcolsep}{-0.25pt} + \begin{center} +\begin{tabularx}{\textwidth}{lXX} + \textbf{\#} & \multicolumn{1}{c}{\textbf{Vertexing}} & \multicolumn{1}{c}{\textbf{Tracking}} \\ + \textbf{1} & \includegraphics[width=0.49\textwidth]{figures/pAu25Vx100new.png} + & \includegraphics[width=0.49\textwidth]{figures/pAu25Tr100new.png} + \\ + \textbf{2a} & \includegraphics[width=0.49\textwidth]{figures/AuAu10Vx100new.png} + & \includegraphics[width=0.49\textwidth]{figures/AuAu10Tr100new.png} + \\ + \textbf{2b} & \includegraphics[width=0.49\textwidth]{figures/AuAu10Vx50new.png} + & \includegraphics[width=0.49\textwidth]{figures/AuAu10Tr50new.png} + \\ + \textbf{3} & \includegraphics[width=0.49\textwidth]{figures/AuAu4Vx50new.png} + & \includegraphics[width=0.49\textwidth]{figures/AuAu4Tr50new.png} + \\ + +\end{tabularx} +\caption{Hit Rates per Sensor. Please note that only one half of the detector is shown. Due to symmetry +under change of the polarity of the magnetic field, the other half has to be able to handle the same amounts of hits.} +\label{tab:hitrates} +\end{center} +\end{table} + +The simulation results for the four experimental cases and the two detector setups are shown in +table \ref{tab:hitrates}. The color code marks the sensors of different stations. While we have a +very asymmetric hit distribution due to the large number of delta-electrons, the detector has to be +built symmetrical in both halves (rotated by 180 degree, not mirrored) to account for the +possibility to reverse the magnetic field. Due to that, only one half of the sensors is shown in +the diagrams. + +For the 3 available station types, different experimental cases are the ones generating the largest +occupancy at design interaction rate: +\begin{description} + \item[Station Type 0:] Au+Au, 10 AGeV, 50\% field, Vertexing. The inner sensors have 250 hits/frame, the outer ones 130 hits/frame. \\ + $\rightarrow$ 8 links are needed for the inner sensors, the outer could work with four. + \item[Station Type 1:] Au+Au, 10 AGeV, 50\% field, Tracking. The inner sensors have 30 to 110 hits/frame, the outer ones up to 20 hits/frame.\\ + $\rightarrow$ 4 links are sufficient for all sensors, the outer sensors could work with two. + \item[Station Type 3:] Au+Au, 10 AGeV, 50\% field, Vertexing. All sensors are below 30 hits/frame. \\ + $\rightarrow$ 2 links are sufficient for all sensors +\end{description} + + + + +\section{Possible Interaction Rates} +The current MVD was designed with two key numbers for interaction rates: 100~kHz Au+Au and 10~MHz +p+Au. + +The design of the internal Mimosis data buses was driven by the hit rate expected for the one +most exposed sensor. The worst case was identified as Au+Au at 10 AGeV and 50\% magnetic field in +the Vertexing setup. In all other cases the hit rates are drastically reduced and the reachable +interaction rates can be above the design value of 100 kHz. + +In table \ref{tab:interactionrate} we try to summarize which interaction rates can be accepted based on the +current simulations. The rates should be understood as minimum bias interaction rates averaged over +a period of about 100~$\upmu$s. This interval is roughly the time the internal buffer of the sensors are +able to store all data without loss as long as the internal data rate limits are not exceeded. +Issues like tracking efficiency loss due to event pile-up within one frame is not taken into +account. + +The table shows two interaction rates for all possible setups: The first is the nominal rate that +can be achieved with a setup optimized for the design value of 100 kHz Au+Au interactions. The +second one is the rate that can be achieved with slight modifications to the setup as discussed in +the comments column. + +\begin{table}[h] +\begin{center} +\begin{tabularx}{\textwidth}{cc|c|c|X} + && \multicolumn{2}{c|}{\textbf{Interaction Rate}} & \\ + \textbf{Setup} & \textbf{Case} & \textbf{standard} & \textbf{optimized} & \textbf{comment}\\ + \hline + Vertexing & 1 & 20 MHz & --- & \\ + & 2a & 250 kHz & (400 kHz) & with 30\% data loss in 2 most central sensors \\ + & 2b & 150 kHz & (350 kHz) & with 40\% data loss in 2 most central sensors \\ + & 3 & 300 kHz & (500 kHz) & with 20\% data loss in 2 most central sensors\\ + \hline + Tracking & 1 & 30 MHz & --- & \\ + & 2a & 400 kHz & 800 kHz & inner sensors with additional links \\ + & 2b & 150 kHz & 400 kHz & inner sensors with additional links \\ + & 3 & 1 MHz & 2 MHz & inner sensors with additional links\\ +\end{tabularx} +\caption{Achievable interaction rates in all studied experimental cases and for both detector geometries.} +\label{tab:interactionrate} +\end{center} +\end{table} + +In Vertexing Geometry, the limiting factor for heavy ion beam is in all cases the delta-electron load +on two of the innermost sensors of the first station (type 0). Their read-out bandwidth can not be increased +without substantial changes to the sensor itself. If we decide to accept some data loss from these 2 +sensors, the interaction rate can be doubled, before more sensors hit their rate limit. + +In Tracking Geometry, the limiting factor are the innermost sensors of the first station (type 1). +Here, the number of data output links can be increased from 4 to 8 to gain a factor of two in event +rate. The high rates affect 6 sensors, but due to symmetry under magnetic field reversal this +number increases to 12. An additional point is that this station is used twice in the Tracking +geometry and the additional links are not needed in the second station. This can be achieved using the same cable and front-end board hardware +with an appropriate connection scheme and leaving some links unconnected. The latter is named ``Type 1b'' +below. The feasibility of this needs to be investigated. + + +\section{Data Link Counts} +Each GBTx chip is able to transport data from 10 sensor links. The total number of chips required +is slightly higher than the theoretical value because sensors from both sides of the detector are +read out through independent front-end boards and it is not foreseen to route links between the +sides of a detector station. + +The number of data links in each detector geometry, based on nominal interaction rates is summarized in +the table \ref{tab:linknormal}. The total amount of GBTx chips required are 76 or 84, depnding on +the detector geometry. + +\begin{table}[h] +\begin{center} +\begin{tabular}{c|c|c|c|c|c} + & \multicolumn{3}{c|}{\textbf{Sensors with ... links}}& \textbf{Total} &\\ + & $\quad$\textbf{2}$\quad$ & $\quad$\textbf{4}$\quad$ & $\quad$\textbf{8}$\quad$ & \textbf{Links} & \textbf{GBTx}\\ + \hline + \textbf{Type 0} & 0 & 0 & 8 & 64 & 8\\ + \textbf{Type 1} & 0 & 32 & 0 & 128 & 16\\ + \textbf{Type 3} & 112 & 0 & 0 & 224 & 26\\ + \hline\hline + &\multicolumn{3}{c|}{\textbf{Types}}&&\\ + \textbf{Vertexing} &\multicolumn{3}{c|}{0 + 1 + 3 + 3} & 640 & 76 \\ + \textbf{Tracking} & \multicolumn{3}{c|}{1 + 1 + 3 + 3} & 704 & 84 \\ +\end{tabular} +\caption{Number of links per station and number of links for each geometry.} +\label{tab:linknormal} +\end{center} +\end{table} + +If the total power consumption and amount of data links is a concern, the outermost sensors of each station could be run with +less links than the inner ones as shown in table \ref{tab:linklow}. This allows for a slight reduction only because all sensors of station type 3 are already at +the lower limit of possible configurations using only 2 links each. + +\begin{table}[h] +\begin{center} +\begin{tabular}{c|c|c|c|c|c} + & \multicolumn{3}{c|}{\textbf{Sensors with ... links}}& \textbf{Total} &\\ + & $\quad$\textbf{2}$\quad$ & $\quad$\textbf{4}$\quad$ & $\quad$\textbf{8}$\quad$ & \textbf{Links} & \textbf{GBTx}\\ + \hline + \textbf{Type 0} & 0 & 4 & 4 & 48 & 6\\ + \textbf{Type 1} & 16 & 16 & 0 & 96 & 12\\ + \textbf{Type 3} & 112 & 0 & 0 & 224 & 26\\ + \hline\hline + &\multicolumn{3}{c|}{\textbf{Types}}&&\\ + \textbf{Vertexing} &\multicolumn{3}{c|}{0 + 1 + 3 + 3} & 592 & 70 \\ + \textbf{Tracking} & \multicolumn{3}{c|}{1 + 1 + 3 + 3} & 640 & 76 \\ +\end{tabular} +\caption{Optimized for total number of data links: Number of links per station and number of links for each geometry.} +\label{tab:linklow} +\end{center} +\end{table} + + +If the detector is to support the ``optimized'' interaction rates, the number of links has to be +increased slightly as shown in table \ref{tab:linkhigh}. As mentioned before, in this case it makes sense to consider using two different versions of +station type 1 with different number of links. The total number of links required increases to 88 +and 96, respectively. + +\begin{table}[h] +\begin{center} +\begin{tabular}{c|c|c|c|c|c} + & \multicolumn{3}{c|}{\textbf{Sensors with ... links}}& \textbf{Total} &\\ + & $\quad$\textbf{2}$\quad$ & $\quad$\textbf{4}$\quad$ & $\quad$\textbf{8}$\quad$ & \textbf{Links} & \textbf{GBTx}\\ + \hline + \textbf{Type 0} & 0 & 0 & 8 & 64 & 8\\ + \textbf{Type 1a} & 0 & 20 & 12 & 172 & 20\\ + \textbf{Type 1b} & 0 & 32 & 0 & 128 & 16\\ + \textbf{Type 3} & 92 & 20 & 0 & 264 & 30\\ + \hline\hline + &\multicolumn{3}{c|}{\textbf{Types}}&&\\ + \textbf{Vertexing} &\multicolumn{3}{c|}{0 + 1a + 3 + 3} & 766 & 88 \\ + \textbf{Tracking} & \multicolumn{3}{c|}{1a + 1b + 3 + 3} & 828 & 96 \\ +\end{tabular} +\caption{Optimized for increased event rate: Number of links per station and number of links for each geometry.} +\label{tab:linkhigh} +\end{center} +\end{table} + + +\section{Possible Improvements} +Due to the large asymmetry of hits caused by delta-electrons, the total number of links that are +required increases quite drastically in the affected regions. In case the polarity of the magnetic +field is fixed, we can build the detector with about 20\% less links as only one side of the +detector will be hit by delta-electrons. + +The outer sensors in the last stations receive only a tiny amount of hits. It might be possible to +revise the sensor design to be able to run with only one active link to reduce the power +dissipation of the detector station and the total number of data links required. One links is able +to transport up to 20 hits/frame. + +The third station is planned to be equipped with a station type 3, while the (dropped) type 2 would +suffice to cover the whole acceptance of CBM. It should be discussed if the outer sensors can be +disabled to save on power and data rate. This results in about 100 links less and 30\% less power +consumption. + +If a station of type 1a is built, it should be considered to replace the type 0 station with a type 1a +with the outer sensors disabled. This would save yet another different station setup for a total of only +two different station types. + +% +% \section{Conclusion} +% +% Looks like we didn't mess it up completely although we designed the sensor without proper +% simulations. + +% \cite{Ablyazimov:2017guv} + + +% \begin{thebibliography}{1} +% +% \bibitem{Ablyazimov:2017guv} +% T.~Ablyazimov et~al., \emph{{Challenges in QCD matter physics --The scientific +% programme of the Compressed Baryonic Matter experiment at FAIR}}, Eur. Phys. +% J. \textbf{A53} (2017), no.~3, 60. +% +% \end{thebibliography} + + +