\begin{table}%t1
\caption{\label{T:tab0}Summary of the notations used in this article to denote the various physical quantities and parameters involved in our description of high energy particle yield in supernova remnants (SNR). }
%\centering
\par
\begin{tabular}{cl}
\hline \hline 
\multirow{1}{40mm}{\bf Turbulence parameters} &
\begin{tabular}{cl} 
\multirow{1}{3mm}{$\beta$} & One D power-law spectral index of the  turbulence spectrum (Eq. (\ref{Eq:nus})) \\   
\multirow{1}{3mm}{$\eta_{\rm T}$} & Level of magnetic fluctuations  with respect to the mean ISM magnetic field  (Eq. (\ref{Eq:nus}))  \\  
\multirow{1}{3mm}{$\phi$} &  Logarithm of the ratio of the maximum momentum to the injection momentum (Eq. (\ref{Eq:BNRB0})) \\ 
\multirow{1}{3mm}{$\lambda_{\rm max}$} & Longest wavelength of the magnetic turbulence spectrum (Sect. \ref{S:Dup}) \\  
\multirow{1}{3mm}{$\ell_{\rm coh}$} & Coherence length of the magnetic fluctuations (Sect. \ref{S:Dup}) \\  
\multirow{1}{3mm}{$\sigma$} & Normalisation factor entering  the turbulent spectrum (Sect. \ref{S:Dup}) \\  
\multirow{2}{3mm}{$\delta_{\rm u/d}$} & Power-law energy dependance index of the relaxation lengths either up- \\ & or downstream (Sect. \ref{S:DoMF} and (Eq. (\ref{Eq:Elld})) \\  
\multirow{1}{3mm}{$H$} & Ratio of the upstream to the downstream diffusion coefficient at the shock front (Eq. (\ref{Eq:D}))\\  
\multirow{1}{3mm}{$\delta_{\rm B}$} & Ratio of the resonant to the non-resonant magnetic field strength at the shock front (Eq. (\ref{Eq:BRBNR}))    \\ 
\end{tabular} \\ \hline 
\multirow{1}{40mm}{\bf Relativistic particle parameters} &
\begin{tabular}{cl}
\multirow{1}{8mm}{$\xi_{\rm CR}$} & Ratio of the CR pressure to the shock dynamical pressure (Eq. (\ref{Eq:BRBNR}))\\  
\multirow{1}{8mm}{$r_{\rm L}$} &  Larmor radius of a particle  (defined using resonant magnetic field) \\ 
\multirow{1}{8mm}{$\rho$} & Ratio of the particle Larmor radius to $\lambda_{\rm max}/2\pi$  (also called reduced rigidity, see Sect. \ref{S:Dup})\\  
\multirow{1}{8mm}{$E_{\rm CR-max}$} & Maximal cosmic ray energy  (Sect. \ref{S:Dup}) \\ 
\multirow{1}{8mm}{$E_{\rm e-max}$} & Maximal electron energy  (Sect. \ref{S:Adva})\\ 
\multirow{1}{8mm}{$E_{\rm \gamma-cut}$} & Cut-off synchrotron photon energy  emitted by electrons at $E_{\rm e-max}$ (Sect. \ref{S:Adva}) \\  
\multirow{1}{8mm}{$E_{\rm CR-min}$} & Injection energy of the cosmic rays   (Sect. \ref{S:TDD}) \\ 
\multirow{1}{8mm}{$E_{\rm e-obs}$}& Energy of the electrons producing the observed X-ray filaments (Sect. \ref{S:Mfrel}) \\  
\end{tabular} \\ \hline \noalign{\smallskip}
  \multirow{1}{40mm}{\bf SNRs parameters} &
 \begin{tabular}{cl}
 \multirow{1}{12mm}{$V_{\rm sh,4}$} & Velocity of the SNR shock wave (in $10^4$ km~s$^{-1}$ unit)\\  \multirow{2}{12mm}{$B_{\rm d/u,-4}$} & Magnetic field amplitude at the shock front respectively in the \\ & down- and upstream medium (in $10^{-4}$ Gauss unit)\\  
 \multirow{1}{12mm}{$r_{\rm B}, r_{\rm sub}, r_{\rm tot}$} & Magnetic, sub-shock, and total shock compression ratios (Sect. \ref{S:Adva}) \\  
 \multirow{1}{12mm}{$\Delta R_{\rm X,-2}$} & X-ray filament deprojected width (in $10^{-2}$ parsec unit, Sect. \ref{S:Mfrel}) \\ 
\end{tabular} \\ \hline \noalign{\smallskip}
\multirow{1}{40mm}{\bf Equation parameters} &
 \begin{tabular}{cl}
\multirow{1}{12mm}{${y}(r)$} & $3 r^2/(r-1)$ (Eq. (19)) \\   
\multirow{1}{12mm}{${K}(r,\beta)$} & $q(\beta) \times (H(r,\beta)/r+1)$ (Eq. (36)) \\   
\multirow{1}{12mm}{${f}_{\rm sync}$} & $H(r,\beta)+r / H(r,\beta)/r_{\rm B}^2 +r$ (Eq. (39)) \\ 
\multirow{1}{12mm}{$g(r)$}  & $3/(r-1) \times (H(r,\beta)/r + 1)$  (Eq. (40)) \\  
\multirow{1}{12mm}{$C(\delta_{\rm d})$} &  $(E_{\rm e-max}/E_{\rm e-obs})^{\delta_{\rm d}}$  (Eq. (41)) \\
\end{tabular} \\\hline
\end{tabular}
\end{table}