  Supernova remnants (SNRs) are likely to be significant sources of cosmic rays
up to the knee of the local cosmic-ray (CR) spectrum. They produce gamma-rays
in the very-high-energy (VHE) ($E>0.1$ TeV) range via: hadronic interactions
with the interstellar medium and leptonic interactions with soft photons.
Current observations have lead to the detection of about a dozen of VHE SNRs
and future instruments should increase this number. The details of particle
acceleration at SNRs, and of the mechanisms producing VHE gamma-rays at SNRs
are poorly understood. We aim to study the population of SNRs detected in the
TeV range and its properties, and to address fundamental questions of particle
acceleration at SNR shocks: What is the spectrum of accelerated particles? What
is the efficiency of acceleration? Is the VHE emission dominated by hadronic or
leptonic interactions? By means of Monte Carlo methods, we simulate the
population of SNRs in the VHE domain and confront our simulations to H.E.S.S.
Galactic Plane Survey (HGPS). We explore the parameter space: the slope of
accelerated particles $\alpha$, the electron-to-proton ratio $K_{\rm ep}$, and
the efficiency of particle acceleration $\xi $. We found sets of parameters for
which $\gtrsim 90$\% of realisations are found in agreements with the HGPS
data. These parameters are found $ 4.2 \gtrsim \alpha \gtrsim 4.1 $, $10^{-5}
\lesssim K_{\rm ep} \lesssim 10^{-4.5}$, and $0.03 \lesssim \xi\lesssim 0.1 $ .
We were able to strongly argue against some regions of the parameter space:
$\alpha \lesssim 4.05$, $\alpha \gtrsim 4.35$, or $K_{\rm ep} \gtrsim 10^{-3}$.
Our model is so far able to explain the SNR population of the HGPS. Our
approach, confronted to the results of future systematic surveys, will help
remove degeneracy in the solutions, and to better understand particle
acceleration at SNR shocks.
