\subsection{Higgs physics at higher energy}

The possibility of further increasing the centre-of-mass energy of the ILC by another factor of two to $\sqrt{s}=$ 1 TeV has also been considered. The other linear collider project, CLIC~\cite{cite:CLICDR}, could provide a higher-energy physics programme all the way to $\sqrt{s}=$ 3 TeV. It would require, however, considerably more electrical power, estimated at $\sim 600$~MW. 

The ultimate energy-frontier option for TLEP is of a very different and more ambitious nature. It would consist of using the 80~to~100~km tunnel to house a very-high-energy large hadron collider, the VHE-LHC. If equipped with magnets of 15~T, pp collisions could be produced at a centre-of-mass energy of 80 to 100 TeV, giving access to the direct production of new particles with masses of 10~TeV or more. For completeness, we also note that pp collisions with a centre-of-mass energy of 33 TeV could be obtained by re-using the LHC tunnel for a pp collider using 20~T magnets, the high-energy large hadron collider, HE-LHC.

\subsubsection{The Htt coupling}

As mentioned in Section~\ref{sec:ee500}, a centre-of-mass energy of 500 GeV cannot compete with the HL-LHC for the Htt coupling measurement. To reach an accuracy in $\epem$ collisions similar to the HL-LHC (less than 5\%), the upgrade of either ILC up to $\sqrt{s}=1$~TeV or CLIC up to $\sqrt{s}=3$~TeV is needed. A precision of 4\% on the Htt coupling would be achieved with an integrated luminosity of 1~$\inab$ (ILC-1000) or 2~$\inab$ (CLIC). On the other hand, an integrated luminosity of 3~$\inab$ with pp collisions either at the HE-LHC or the VHE-LHC would allow the precision on the Htt coupling to be significantly improved to a couple of per-cent or a fraction of a per-cent, respectively.

\subsubsection{The HHH coupling}

The measurement of the trilinear Higgs self-coupling $\lambda_{\rm H}$ would benefit substantially from higher energy, because of the fast increase of the double-Higgs-boson production cross section, in both $\epem$ and proton-proton collisions. Studies exist, albeit with different levels of maturity, for the sensitivity of the ILC~\cite{ILC:Physics}, CLIC~\cite{cite:CLICDR}, and HL-LHC~\cite{cite:ATLAS,cite:CMS} to these couplings. From the HL-LHC estimates and from the known HH production cross-section increase at higher energies~\cite{Mangano_Rojo_2012}, extrapolations for $3~\inab$ of pp collision data at the HE-LHC ($\sqrt{s} =$ 33 TeV) and the VHE-LHC ($\sqrt{s}=$ 100 TeV) can be inferred~\cite{Snowmass}. An executive summary of the achievable precisions is displayed in Fig.~\ref{fig:VHELHC}. 