\section{Measurement Requirements}
\label{sec:meas}

This section contains the AHEPaM measurement requirements.
%----------------------------------------------------------------------------------
\subsection*{R-AHEPaM-020: Proton energy range}
\label{req:R-020}
The AHEPaM shall measure proton fluxes between 0.1\,GeV and 2.0\,GeV in at least 5 energy bands.

\paragraph{Justification:} Requirements for the \acf{AHEPaM} \cite[][, Molendi et al. 2020, issue 2.2]{molendi-etal-2020}


\paragraph{Verification:} Analysis/Test


\paragraph{Comments:} The required 5 energy bands for protons are driven by the need to sample the varying response of these particles to the Solar cycle as a function of energy. The division should roughly follow the energy distribution of primaries as estimated via simulations and should account for the fact that temporal variations are stronger at lower than at higher energies, see section~5 of the TN for more details. An indicative break up of energy bands would be: 0.1-0.3, 0.3-0.6, 0.6-0.8, 0.8-1.0, 1.0-2.0 (all expressed in GeV). Cosmic-Ray protons feature a continuum spectrum which implies that small gaps or superpositions between adjacent energy bands do not constitute a problem. %\acf{TN} 


\paragraph{CAU Response:} Providing several energy bands can be easily achieved. The different proton boxes introduced in the performance analysis in \cite{ahepam-djf} can be separated for different measured total energies (stopping) and deposited energies (penetrating particles). The performance analysis has shown that \acs{AHEPaM} will be able to measure protons over the entire required energy range. The amount of energy bands we can provide is only limited by statistics. The data is required to be send down at higher cadence and energy resolution not only to provide an accurate proton spectrum but for the purpose of correcting the electron spectrum. Based on this raw data, the required spectra in different resolutions as well as a deconvolution of the data based on the response functions determined form \ac{GEANT4} simulations will be provided by the \ac{AHEPaM}-team.



%----------------------------------------------------------------------------------
\subsection*{R-AHEPaM-021: Proton precision}
\label{req:R-021}
The AHEPaM shall measure proton fluxes with a relative precision of 0.5\% at the 95.45\% confidence level.

\paragraph{Justification:} Requirements for the \acf{AHEPaM} \cite[][, Molendi et al. 2020, issue 2.2]{molendi-etal-2020}

\paragraph{Verification:} Analysis/Test

\paragraph{Comments:} The requirement applies between any two energy bands, see the TN for further details. The requirement specifies the maximum systematic error allowed between bands. Statistical errors are covered in the other requirements. %\ac{TN}


\paragraph{CAU Response:} 
\todo[inline]{This requirement needs to be updated by ESA.}

\subsection*{\sout{R-AHEPaM-023: deleted}}


%----------------------------------------------------------------------------------
\subsection*{R-AHEPaM-023: Proton statistical accuracy}
\label{req:R-023}
The AHEPaM shall measure proton fluxes with a statistical accuracy of at least 1\% at the 95.45\% confidence level for a time resolution of 3\,ks in at least 2 energy bands, and for a time resolution of 10\,ks in at least 5 energy bands.


\paragraph{Justification:} Requirements for the \acf{AHEPaM} \cite[][, Molendi et al. 2020, issue 2.2]{molendi-etal-2020}


\paragraph{Verification:} Analysis/Test

\paragraph{Comments:} See comment to R-AHEPaM-020.


\paragraph{CAU Response:} The statistical uncertainties for the different channels and time resolutions are derived in detail in \cite{ahepam-djf}.


%----------------------------------------------------------------------------------
\subsection*{R-AHEPaM-024: Electron energy range}
\label{req:R-024}
The AHEPaM shall measure electron fluxes between 0.05 GeV and 1.0 GeV in at least 5 energy bands.


\paragraph{Justification:} Requirements for the \acf{AHEPaM} \cite[][, Molendi et al. 2020, issue 2.2]{molendi-etal-2020}


\paragraph{Verification:} Analysis/Test

\paragraph{Comments:} The required 5 energy bands for electrons are driven by the need to sample the varying response of these particles to the Solar cycle as a function of energy. The division should roughly follow the energy distribution of primaries as estimated via simulations and should account for the fact that temporal variations are stronger at lower than at higher energies, see Sect. 5 of the TN for more details. An indicative break up of energy bands would be: 0.05-0.2, 0.2-0.4, 0.4-0.6, 0.6-0.8, 0.8-1.0 (all expressed in GeV). Cosmic-Ray electrons feature a continuum spectrum, this implies that small gaps or superpositions between different energy bands do not constitute a problem.                      


\paragraph{CAU Response:} Providing several energy bands can be easily achieved. The different electron boxes introduced in the performance analysis in \cite{ahepam-djf} can be separated for different measured total energies (stopping) and deposited energies (penetrating particles). The performance analysis has shown that \ac{AHEPaM} will be able to measure electrons over the entire required energy range. The amount of energy bands we can provide is only limited by statistics. The data is required to be send down at higher cadence and energy resolution not only to provide an accurate proton spectrum but for the purpose of correcting the electron spectrum. Based on this raw data, the required spectra in different resolutions as well as a deconvolution of the data based on the response functions determined form \ac{GEANT4} simulations will be provided by the \ac{AHEPaM}-team.




%----------------------------------------------------------------------------------
\subsection*{R-AHEPaM-025: Electron precision}
\label{req:R-025}
The AHEPaM shall measure electron fluxes with a relative precision of 1\% at the 95.45\% confidence level.

\paragraph{Justification:} Requirements for the \acf{AHEPaM} \cite[][, Molendi et al. 2020, issue 2.2]{molendi-etal-2020}


\paragraph{Verification:} Analysis/Test

\paragraph{Comments:} The requirement applies between any two energy bands, see the TN for further details. The requirement specifies the maximum systematic error allowed between bands. Statistical errors are covered in the other requirements. %\ac{TN}


\paragraph{CAU Response:}
\todo[inline]{This requirement needs to be updated by ESA.}

%----------------------------------------------------------------------------------
\subsection*{R-AHEPaM-026: Electron precision}
\label{req:R-026}
The AHEPaM shall measure electron fluxes with respect to proton fluxes measured by the AHEPaM with a relative precision of 2.5\% at the 95.45\% confidence level.


\paragraph{Justification:} Requirements for the \acf{AHEPaM} \cite[][, Molendi et al. 2020, issue 2.2]{molendi-etal-2020}


\paragraph{Verification:} Analysis/Test

\paragraph{Comments:} This is a requirement on the maximum acceptable systematic in the relation between electron and proton spectra. Statistical errors are covered in the other requirements.


\paragraph{CAU Response:} 
\todo[inline]{This requirement needs to be updated by ESA.}

%----------------------------------------------------------------------------------
\subsection*{R-AHEPaM-027: Electrons statistical accuracy}
\label{req:R-027}
The AHEPaM shall measure electron fluxes with a statistical accuracy of at least 5\% at the 95.45\% confidence level for a time resolution of 3\,ks in at least 2 energy bands, and 10 ks in at least 5 energy bands.

\paragraph{Justification:} Requirements for the \acf{AHEPaM} \cite[][, Molendi et al. 2020, issue 2.2]{molendi-etal-2020}

\paragraph{Verification:} Analysis/Test

\paragraph{Comments:} See comment to R-AHEPaM-024.

\paragraph{CAU Response:}
\todo[inline]{This requirement needs to be updated ESA.}
\todo[inline]{The statistical uncertainties for the different channels and time resolutions are derived in detail in \cite{ahepam-djf}. Based on this performance analysis, \ac{AHEPaM} will not be able to fulfill the original requirement given in \cite{athena-spec}.
This discrepancy between requirement and estimated performance has been discussed in a meeting on May 12th, 2022 \cite{moms-12-05-2022}.}


%----------------------------------------------------------------------------------
\subsection*{R-AHEPaM-028: Helium energy range}
\label{req:R-028}
The AHEPaM shall measure He ion fluxes between 1.0\,GeV and 3.0\,GeV in at least 1 energy band.

\paragraph{Justification:} Requirements for the \acf{AHEPaM} \cite[][, Molendi et al. 2020, issue 2.2]{molendi-etal-2020}

\paragraph{Verification:} Analysis/Test

\paragraph{Comments:} For He ions, one energy band is sufficient.

\paragraph{CAU Response:} The performance analysis in \cite{ahepam-djf} has shown that \ac{AHEPaM} will be able to measure helium ions over the entire required energy range.

\subsection*{R-AHEPaM-029: deleted}

%----------------------------------------------------------------------------------
\subsection*{R-AHEPaM-030: Helium relative precision}
\label{req:R-030}
The AHEPaM shall measure He ion fluxes with respect to proton fluxes measured by the AHEPaM with a relative precision of 5\% at the 95.45\% confidence level.


\paragraph{Justification:} Requirements for the \acf{AHEPaM} \cite[][, Molendi et al. 2020, issue 2.2]{molendi-etal-2020}

\paragraph{Verification:} Analysis/Test

\paragraph{Comments:} This is a requirement on the maximum acceptable systematic in the relation between He-ion and proton spectra. Statistical errors are covered in the other requirements.


\paragraph{CAU Response:}
\todo[inline]{This requirement needs to be updated by ESA.}

%----------------------------------------------------------------------------------
\subsection*{R-AHEPaM-031: Helium statistical accuracy}
\label{req:R-031}
The AHEPaM shall measure He ion fluxes with a statistical accuracy of at least 10\% at the 95.45\% confidence level for a time resolution of 3 ks in at least 1 energy band.

\paragraph{Justification:} Requirements for the \acf{AHEPaM} \cite[][, Molendi et al. 2020, issue 2.2]{molendi-etal-2020}

\paragraph{Verification:} Analysis/Test

\paragraph{Comments:} The energy band is the same as specified in R-AHEPaM-028.

\paragraph{CAU Response:} As discussed in the performance analysis in \cite{ahepam-djf}, we are confident that the statistical requirement for helium ion can be fulfilled based on our results for the proton statistics.


%----------------------------------------------------------------------------------
\subsection*{R-AHEPaM-032: Particle discrimination}
\label{req:R-032}
The AHEPaM shall provide particle discrimination between protons, He ions, and electrons with a success rate $>95$\% (\ac{TBC}) and with off-diagonal terms in the confusion matrix $<5$\% (\acs{TBC}).

\paragraph{Justification:} Requirements for the \acf{AHEPaM} \cite[][, Molendi et al. 2020, issue 2.2]{molendi-etal-2020}

\paragraph{Verification:} Analysis/Test

\paragraph{Comments:} 

\paragraph{CAU Response:} Protons, He ions and electrons can be identified with less than 5\% contamination as shown in the performance analysis in \cite[][, see e.g. fig. 6 or table 2]{ahepam-djf}.


%----------------------------------------------------------------------------------
\subsection*{R-AHEPaM-023: Maximum flux}
\label{req:R-033}
The \ac{AHEPaM} performance requirements shall be met for count rates up to 15 particles cm$^2$\,s$^{-1}$ (\ac{TBC}). The \ac{AHEPaM} shall be functional within the requirements up to the levels given in the following table:

\begin{center}
    \begin{tabular}{|llr|}\hline
    species & energy band [GeV] & flux \\\hline
    Protons     & 0.1 - 2.0  & $3\cdot 10^5$ [m$^2$ s sr]$^{-1}$ \\
    Electrons   & 0.05 - 1.0  & $3\cdot 10^4$ [m$^2$ s sr]$^{-1}$ \\
    He ions     & 1.0 - 3.0  & $1\cdot 10^4$  [m$^2$ s sr]$^{-1}$ \\\hline
    \end{tabular}
\end{center}
%- 3.E5 particles/(m2 s sr)  in the 0.1-2.0\,GeV band for protons;\\
%- 3.E4 particles/(m2 s sr)  in the 0.05-1.0\,GeV band for electrons; and\\
% 1.E4 particles/(m2 s sr)  in the 1.0-3.0\,GeV band for He ions.

\paragraph{Justification:} Requirements for the \acf{AHEPaM} \cite[][, Molendi et al. 2020, issue 2.2]{molendi-etal-2020}

\paragraph{Verification:} Analysis/Test

\paragraph{Comments:} No degraded particle counting mode is required. The AHEPaM monitor is not meant to provide alarms for Athena instruments. Functional count-rate limits are currently expressed in terms of fluxes and can be convertred into particle rates once a general design of the monitor has been provided.


\paragraph{CAU Response:}This requirement can be easily fulfilled by the current design. The performance analysis in \cite{ahepam-djf} as well as our experiences from previous instruments (cf. \cite{ahepam-heritage}) show that the expected count rates during these high flux conditions are low enough such that our electronics can process all events. Furthermore, we plan to include an automatic switch-off of some of the \ac{SSD} segments during high-flux conditions which will reduce the geometric factor and the count rates if necessary. Such a feature has been sucessfully integrated in both \ac{SOHO}/\ac{EPHIN} and Solar Orbiters \ac{HET}.


