Operation at high densities is favorable due to frequent fusion reactions and facilitated access to detachment. Already in the very beginning of tokamak operation a limit of the maximum achievable density in tokamaks has been observed.
This is the so-called Greenwald density limit. 

relevent publications

P. Manz, T. Eich, O. Grover 'The power dependence of the maximum achievable H-mode and (disruptive) L-mode separatrix density in ASDEX Upgrade', Nuclear Fusion 63 076026 (2023)

T.Eich, P.Manz 'The separatrix operational space of ASDEX Upgrade due to interchange-drift-Alfvén turbulence', Nuclear Fusion 61, 086017 (2021)

G. Grenfell, P. Manz et al. 'Turbulence in the near scrape-off layer towards the L-mode density limit in ASDEX-Upgrade' Nuclear Materials and Energy 101277 (2022)

T. Nishizawa, P.Manz et al. 'Characterizing the flow and turbulence structure near the last closed flux surface in L-mode plasmas of ASDEX Upgrade' Physics of Plasmas 29, 072304 (2022)