Intra-bunch energy spread minimisation for CLIC operation at a centre-of-mass energy of 350 GeV

The first stage of the electron-positron Compact Linear Collider (CLIC) is designed with a centre-of-mass energy of 380 GeV. A dedicated threshold scan in the vicinity of 350 GeV is envisioned with a total integrated luminosity of 100 fb$^{-1}$. This scan calls for a very small intra-bunch energy spread in order to achieve an excellent collision energy resolution. This paper presents an optimised assignment of RF accelerating gradients and phases in the CLIC main linac for operation at 350 GeV, which minimises the energy spread at the end of the main linac whilst preserving a small emittance growth. Variation of the bunch length and charge is studied in order to further reduce the energy spread; the effect on both the peak and total luminosity is discussed.