\subsection{Luminosity and energy}
\label{sec:luminosity}

The TLEP collider complex consists of an accelerator ring and a storage ring~\cite{1112.2518}, the former delivering continuous top-up injection to the latter, so that a constant level of luminosity is provided in collisions. The current TLEP working points can be found in Ref.~\cite{cite:1305.6498}, for the four centre-of-mass energies of interest: the Z pole ($\sqrt{s} \sim 91$~GeV); the WW threshold ($\sqrt{s} \sim 161$~GeV); the HZ cross-section maximum ($\sqrt{s} \sim 240$~GeV); and the top-pair threshold ($\sqrt{s} \sim 350$~GeV). The possible upgrade to $\sqrt{s}=500$ GeV is discussed in Section~\ref{sec:VHE-LHC}. The 12 GV RF system is designed to compensate for the energy loss by synchrotron radiation at $\sqrt{s} = 350$ GeV, at which a luminosity of $1.3\times 10^{34}~\cms$ can be delivered at each interaction point (IP), in a configuration with four IPs. At lower centre-of-mass energies, the energy losses decrease steeply like $E^4_{\rm beam}$, and the RF power can be used to accelerate a much larger number of ${\rm e}^\pm$ bunches, from 12 bunches at 350 GeV all the way to 4400 bunches at the Z pole. As a result, the luminosity increases approximately like $1/E^3_{\rm beam}$ when the centre-of-mass energy decreases. (The smaller exponent is a consequence of operating at the beam-beam limit.) The preliminary values of the luminosities expected at each energy are displayed in Table~\ref{tab:lumi}, together with other important parameters of the machine (beam size, RF cavity gradient, number of bunches, and total power consumption), taken from Ref.~\cite{cite:1305.6498}. The last row gives the integrated luminosity expected at each interaction for one year of data taking (1 year = $10^7$ seconds).

\begin{table}
\begin{center}
\caption{\label{tab:lumi} Preliminary values of the luminosity for TLEP in each of the four planned configurations~\cite{cite:1305.6498}. Other parameters relevant for the physics potential of TLEP (beam size, RF cavity gradient, number of bunches, total power consumption and integrated luminosity per year at each IP) are also listed.}
\begin{tabular}{|r|r|r|r|r|}
\hline                         & TLEP-Z & TLEP-W & TLEP-H & TLEP-t \\
\hline\hline $\sqrt{s}$ (GeV) &     90     &    160     &   240      &   350    \\ 
\hline L ($10^{34}~\cms$)  & 56  & 16 & 5 & 1.3 \\
\hline \# bunches & 4400 & 600 & 80 & 12 \\
\hline RF Gradient (MV/m) & 3 & 3 & 10 & 20 \\
\hline Vertical beam size (nm) & 270 & 140 & 140 & 100 \\
\hline Total AC Power (MW)  & 250 & 250 & 260 & 284 \\ 
\hline ${\rm L_{\rm int}}$ ($\inab$/year/IP) & 5.6 & 1.6 & 0.5 & 0.13 \\ \hline
\end{tabular}
\end{center}
\end{table}