What is an acceptable dynamic vacuum pressure in the LHC arcs?

Beam-gas nuclear and Coulomb interactions introduce limitations on the tolerable vacuum pressure in the LHC and its upgrade. We discuss local pressure limits set by the heat load on the cryogenics system and by loss-induced quenches, as well as average pressure limits imposed by beam-lifetime degradation and emittance blow up. These pressure limits depend on the molecular species in the residual gas. We also consider the effect of Coulomb scattering, which strongly depends on the beam energy. An important ingredient to our discussion is the available cooling capacity, which we estimate for the nominal and ultimate LHC, as well as for two posible upgrade scenarios. The quoted pressure tolerances refer to the nominal LHC only. They would become significantly tighter for higher beam currents or for shorter bunches.