deletions | additions       diff --git a/Luminosity and Energy.tex b/Luminosity and Energy.tex  index 9597b67..65deab6 100644  --- a/Luminosity and Energy.tex  +++ b/Luminosity and Energy.tex 
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\subsection{Luminosity and Energy}  The detailed machine parameters can be found in Ref.~\cite{cite:1305.6498}, for the four centre-of-mass energies of interest: the Z pole ($\sqrt{s} \sim m_{\rm Z}$); the WW threshold ($\sqrt{s} \sim 2 m_{\rm W}$); the HZ cross-section maximum ($\sqrt{s} \sim 240$ GeV); and the top-pair threshold ($\sqrt{s} \sim 2m_{\rm top}$). (A 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 an instantaneous luminosity of $1.3\times 10^{34} \cms$ can be delivered at each interaction point. At lower centre-of-mass energies, the energy losses decrease steeply like $1/E^4_{\rm beam}$, 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 instantaneous 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, which gets tighter when  the beam energy decreases.) The values of the instantaneous 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, or total power consumption), taken from Ref.~\cite{cite:1305.6498}. \begin{table}  \begin{center}