A high-luminosity superconducting twin $e^+e^-$ linear collider with energy recovery

Superconducting technology makes it possible to build a high energy $e^+e^-$ linear collider with energy recovery (ERLC) and reusable beams. To avoid parasitic collisions inside the linacs, a twin (dual) LC is proposed. In this article, I consider the principle scheme of the collider and estimate the achievable luminosity, which is limited by collision effects and available power. Such a collider can operate in a duty cycle (DC) and in a continuous (CW) modes, if sufficient power. With current SC Nb technology ($T=1.8$ K, $f_{\rm RF}=1.3$ GHz, used for ILC) and with power $P= 100$ MW, a luminosity $L \sim 0.33 \times10^{36}\,\rm cm^{-2}s^{-1}$ is possible at the Higgs factory with $2E_0=250$ GeV. Using superconductors operating at 4.5 K with high $Q_0$ values, such as Nb$_3$Sn, and $f_{\rm RF}=0.65$ GHz, the luminosity can reach $L \sim 1.4 \times10^{36} \,\rm cm^{-2}s^{-1}$ at $2E_0=250$ GeV (with P=100 MW) and $L \sim 0.8 \times 10^{36}\,\rm cm^{-2}s^{-1}$ at $2E_0=500$ GeV (with P=150 MW), which is almost two orders of magnitude greater than at the ILC, where the beams are used only once. This technology requires additional efforts to obtain the required parameters and reliably operation. Such a collider would be the best machine for precision Higgs studies, including the measurement of Higgs self-coupling.