Update on Overleaf.

cau-ath-er_i1-0/report.tex

@@ -82,7 +82,7 @@ Energetic particles are typically measured with so-called particle telescopes wh
 \end{equation}
 where $E$ is the particle kinetic energy, $Z$ its nuclear charge, and $n_e$ is the electron density in the detector material, and d$x$ the detector thickness. For example, a 500 MeV proton looses less than 100 keV in a typical silicon solid-state detector (\acs{SSD}). This means that the total energy of a particle in the required energy range can not be measured within a reasonably-sized detector. That the deposited energy is proportional to $Z^2$ assures that protons and Helium nuclei can easily be distinguished. The difficulty lies in separating electrons from protons. If a particle is faster than the speed of light in the detector, it produces Cherenkov radiation. Because electrons in the required energy range basically travel at the speed of light in vacuum, \acs{AHEPaM} also uses this measurement technique to discriminate electrons from protons because the latter are much slower and therefore do not produce Cherenkov radiation. If the particle has enough energy, it can also produce a shower of secondary particles, an effect that is also used in \acs{AHEPaM}. Thus the driving requirements for \acs{AHEPaM} were the large energy range, the high counting statistics, and the discrimination between electrons and protons. These were met by using the combination of mutliple measurement techniques described in the following.
 
-To measure the low fluxes of \acs{GCR} particles \acs{AHEPaM} had to have a large collecting area, and a large field of view (\acs{FOV}), the product is equivalent to the "collecting power" or geometric factor. This is determined by the area of the front and rear detectors of the particle telescope, and by its length. The \acs{AHEPaM} developed in this contract maximizes the geometry factor by its compact design and by allowing to measure particles from the front and back, thus doubling the geometry factor. To achieve this, it is designed to be symmetric about its middle plane, as can be seen in Fig.\ref{fig:AHEPaM-concept} which shows a \acs{CAD} view of the arrangements of the various detectors in \acs{AHEPaM}. A particle entering \acs{AHEPaM} from the lower left will first trigger the front \acs{SSD} which is shonw in silver-grey. If it is an electron, it will produce Cherenkov radiation in the Cherenkov detector (shown in yellow), whereas slower protons or Helium nuclei will not. The particle then hits the next \acs{SSD} (shown in red), traverses the high-density \acs{BGO} scintillator, the central \acs{SSD}, and exits \acs{AHEPaM} on a "symmetric" path through the following \acs{BGO}, \acs{SSD}, Cherenkov, and final \acs{SSD} on the upper right. This design is extremely compact and thus maximizes the geometric factor of \acs{AHEPaM} and allows determination of the energy losses in multiple detectors. The process of energy loss is stochastic, the distribution of deposited energy is described by the Landau distribution which is so skewed towards larger energy depositions that only its most probable values is defined, but not its mean. Because this could mimick an energy deposition of a heavier particle, the \acs{SSD}s are arranged in back-to-back pairs and the minimum of the energy deposition is used for the data processing in \acs{AHEPaM}. Thus the five detectors seen in Fig.~\ref{fig:AHEPaM-concept} are actually pairs of detectors. The Cherenkov detectors only produces typically 200 photons per electron, they are read out with \acs{PMT}s which provide sufficient amplification of this very weak signal. The energy deposited in the high-density ($\rho =$ 7.13 g/cm$^3$) \acs{BGO} is converted into abundant scintillation light by that material which is read out with extremely compact photodiodes. That signal is proportional to the energy that the particle looses in the \acs{BGO}. The central \acs{SSD} performs another precise measurement of the particle's energy loss before it continues into the symmetric part of \acs{AHEPaM}. The energy resolution of an \acs{SSD} is inversely proportional to its area, therefore \acs{AHEPaM}'s \acs{SSD}s are divided into many segments which are amplified and read out separately. This segmentation also allows \acs{AHEPaM} to detect particle showers that high-energy particles can produce when they interact with matter, especially the high-density \acs{BGO}. Figure~\ref{fig:geometry_sketch} shows such an example for a 500 MeV electron. 
+To measure the low fluxes of \acs{GCR} particles \acs{AHEPaM} had to have a large collecting area, and a large field of view (\acs{FOV}), the product is equivalent to the "collecting power" or geometric factor. This is determined by the area of the front and rear detectors of the particle telescope, and by its length. The \acs{AHEPaM} developed in this contract maximizes the geometry factor by its compact design and by allowing to measure particles from the front and back, thus doubling the geometry factor. To achieve this, it is designed to be symmetric about its middle plane, as can be seen in Fig.\ref{fig:AHEPaM-concept} which shows a \acs{CAD} view of the arrangements of the various detectors in \acs{AHEPaM}. A particle entering \acs{AHEPaM} from the lower left will first trigger the front \acs{SSD} which is shown in silver-grey. If it is an electron, it will produce Cherenkov radiation in the Cherenkov detector (shown in yellow), whereas slower protons or Helium nuclei will not. The particle then hits the next \acs{SSD} (shown in red), traverses the high-density \acs{BGO} scintillator, the central \acs{SSD}, and exits \acs{AHEPaM} on a "symmetric" path through the following \acs{BGO}, \acs{SSD}, Cherenkov, and final \acs{SSD} on the upper right. This design is extremely compact and thus maximizes the geometric factor of \acs{AHEPaM} and allows determination of the energy losses in multiple detectors. The process of energy loss is stochastic, the distribution of deposited energy is described by the Landau distribution which is so skewed towards larger energy depositions that only its most probable values is defined, but not its mean. Because this could mimick an energy deposition of a heavier particle, the \acs{SSD}s are arranged in back-to-back pairs and the minimum of the energy deposition is used for the data processing in \acs{AHEPaM}. Thus the five detectors seen in Fig.~\ref{fig:AHEPaM-concept} are actually pairs of detectors. The Cherenkov detectors only produces typically 200 photons per electron, they are read out with \acs{PMT}s which provide sufficient amplification of this very weak signal. The energy deposited in the high-density ($\rho =$ 7.13 g/cm$^3$) \acs{BGO} is converted into abundant scintillation light by that material which is read out with extremely compact photodiodes. That signal is proportional to the energy that the particle looses in the \acs{BGO}. The central \acs{SSD} performs another precise measurement of the particle's energy loss before it continues into the symmetric part of \acs{AHEPaM}. The energy resolution of an \acs{SSD} is inversely proportional to its area, therefore \acs{AHEPaM}'s \acs{SSD}s are divided into many segments which are amplified and read out separately. This segmentation also allows \acs{AHEPaM} to detect particle showers that high-energy particles can produce when they interact with matter, especially the high-density \acs{BGO}. Figure~\ref{fig:geometry_sketch} shows such an example for a 500 MeV electron. 
 
 \begin{figure}
 \begin{subfigure}[]{0.48\linewidth}
@@ -98,11 +98,36 @@ To measure the low fluxes of \acs{GCR} particles \acs{AHEPaM} had to have a larg
   \caption{Visualisation of a simulation run with an electron at 500~MeV entering from the left.}
   \label{fig:geometry_sketch}
 \end{subfigure}
-\caption{\acs{AHEPaM} combines three differnet measurement techniques.}
+\caption{\acs{AHEPaM} combines three different measurement techniques.}
 \label{fig:AHEPaM-measurement-concept}
 \end{figure}
 
-Key properties such as mass, power, volume, etc.\,of the AHEPaM developed under this contract are given in Tab.~\ref{tab:key-properties}. One can easily see that \acs{AHEPaM} is indeed very compact and is close to fulfilling the original measurement requirements. It is also clear that it is probably not possible to satisfy all the measurement requirements within the resource allocations foreseen for \acs{AHEPaM}. This is one of the lessons learned from the work performed in this contract. The measurement capabilities of \acs{AHEPaM} are summarized in Tab.~\ref{tab_TBD}. 
+Key properties such as mass, power, volume, etc.\,of the AHEPaM developed under this contract are given in Tab.~\ref{tab:key-properties}. One can easily see that \acs{AHEPaM} is indeed very compact and is close to fulfilling the original measurement requirements. It is also clear that it is probably not possible to satisfy all the measurement requirements within the resource allocations foreseen for \acs{AHEPaM}. This is one of the lessons learned from the work performed in this contract. The measurement capabilities of \acs{AHEPaM} are summarized in Tab.~\ref{tab:AHEPaM-data-products}. 
+
+
+\section{Expected Performance}
+\label{sec:performance}
+
+Detailed simulations were performed with \acs{GEANT4} \cite[]{agostinelli-etal-2003} to determine the geometry factors of different combinations of detectors in \acs{AHEPaM} which are key to understanding the expected performance of \acs{AHEPaM}. To increase counting statistics only particles from one hemisphere were simulated, exploiting the symmetry of \acs{AHEPaM} (see Fig.~\ref{fig:AHEPaM-concept}). Therefore, only results from one hemisphere (i.e., $2\pi$ sr) are reported here. During solar quiet times, i.e., in the absence of a solar particle event, the \acs{GCR} particle radiation background is essentially isotropic {\bf reference needed}. This, however, is also the situation when the count rates are small, in other words, it is the limiting case for determining \acs{AHEPaM}s measuring capabilities. This also means that the $2\pi$-sr results reported here can effectively be doubled, i.e., their uncertainties divided by the appropriate factor, $\sqrt{2}$. We do not correct for this geometric factor in this report because solar particle events can be very an-isotropic during their onset times, i.e., in the first hours of the event. 
+
+The concept for \acs{AHEPaM} which was developed in this contract continuously provides two classes of data products, high resolution and high statistics. The high-resolution data product is much better at discriminating between protons and electrons than the high-statistics data product. It requires particles to traverse the entire \acs{AHEPaM} particle telescope, i.e., to hit the front-most and rear-most detectors in fig.~\ref{fig:AHEPaM-concept}. The field of view for this data product is narrow and consequently its geometric factor ("gathering power") is limited, and hence only a small fraction of all particles is measured. The high-statistics data product, on the other hand, provides data at high counting statistics, but at the cost of reduced discrimination between electrons and protons. This is achieved by relaxing the requirement that all detectors of the \acs{AHEPAM} telescope are triggered which results in a larger geometric factor. The measurement capabilities of both data products are summarized in Tab.~\ref{tab:AHEPaM-data-products}. Comparison with the requirements listed in Tab.~\ref{tab:orig-meas-req} shows that \acs{AHEPaM} is close to meeting the measurement requirements for protons. In fact, accounting for the $2\pi$-sr simulation, the high-statistics data products meet the original requirement. However, those for electrons can not be met, primarily because their flux is much lower than the proton flux (see Fig.~\ref{fig:GCR-spec}). The flux of electrons above 50 MeV is neither affected by solar particle events, nor by Jovian electrons, it is dominated by the slowly varying galactic contribution {\bf reference needed!}. Thus, we propose to relax the requirement on electrons. 
+
+\begin{table}[]
+    \centering
+    \begin{tabular}{|l|l|l|l|}\hline
+%      Data  & Protons  & Electrons   &  Geometry \\
+%       Product & Protons  & Electrons   &   Factor\\ \hline
+      Data Product & Protons  & Electrons & Geometry Factor\\\hline
+      high resolution & 5 bands \@ 10 ks: 2.7\% & 5 bands \@ 100 ks: 6.1\%   & 2.9 cm$^2$ sr (uni-directional \\
+      & 2 bands \@ 3 ks: 3.1\%  & 2 bands \@ 50 ks: 5.5\%   &  \\
+      high statistics& 5 bands \@ 10 ks: 1.2\%  & 5 bands \@ 50 ks: 5.5\%   & 6.8 cm$^2$ sr (uni-directional) \\
+      & 2 bands \@ 3 ks: 1.4\%  & 2 bands \@ 50 ks: 3.5\%   &  \\\hline
+    \end{tabular}
+    \caption{Measurement capabilities of the current \acs{AHEPaM} design. Note that geometry factors are given as uni-directional. Because \acs{AHEPaM} measures in both the "forward" and "backward" directions, the geometry factors are effectively doubled.}
+    \label{tab:AHEPaM-data-products}
+\end{table}
+
+
 
 Explain interface of AHEPaM to S/C: simple, straightforward. Structural \& thermal modeling results.
 
@@ -114,7 +139,7 @@ Identify design drivers (large detectors, number of channels, mass of BGO, compl
 
 
 
-The proposed sensor design of the \acs{AHEPaM} is sketched in fig. \ref{fig:telescope-specs}. \acs{AHEPaM} utilizes a combination of \ac{SSD}, \ac{BGO} scintilators and Cherenkov detectors. The combination of these different measurement techniques allows for a separation of high energy electrons and protons. Fig. \ref{fig:basic-arrangement} shows the combination of those different sensors and their mounting (blue) on top of the housing of the different electronics boards (green). The entire instrument will be covered (purple) for thermal reasons. \\
+The proposed sensor design of the \acs{AHEPaM} is sketched in fig. \ref{fig:telescope-specs}. \acs{AHEPaM} utilizes a combination of \acs{SSD}, \acs{BGO} scintillators and Cherenkov detectors. The combination of these different measurement techniques allows for a separation of high energy electrons and protons. Fig. \ref{fig:basic-arrangement} shows the combination of those different sensors and their mounting (blue) on top of the housing of the different electronics boards (green). The entire instrument will be covered (purple) for thermal reasons. \\
 
 
 
@@ -160,11 +185,6 @@ The proposed sensor design of the \acs{AHEPaM} is sketched in fig. \ref{fig:tele
 
 
 
-\section{Expected Performance}
-\label{sec:performance}
-Compare measurement requirements and expected performance. Explain differences and why they are so.
-
-
 \section{Trades to be considered}
 
 Lessons learned