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\section{\ref{sec:VHE-LHC} High-energy upgrades}  \label{sec:VHE-LHC}  \subsection{Interest of high-energy \subsection{Higgs physics in  $\epem$ collisions for Higgs physics} at $\sqrt{s} = 500$~GeV}  Both the $\epem$ Higgs factories discussed in Section~\ref{sec:Higgs} have high-energy upgrade projects. For the ILC, it is foreseen to double its length as to reach a centre-of-mass energy of 500 GeV, and it is not yet excluded to extend it by another factor of two towards $\sqrt{s} =$ 1 TeV, with a significant cost increase of about five billion dollars over the baseline project. Another linear collider project, CLIC~\cite{cite:CLICDR}, could also take over for the high-energy physics programme all the way to $\sqrt{s}=$ 3 TeV, which would require, however, a prohibitively high electrical power ($\sim 600$~MW).