The operational space of a tokamak is not particularly free and is limited by various phenomena. The high confinement required for fusion can presumably only be guaranteed in the H-mode. Thus, the L-H transition is of central importance for the operational space. At high densities, the operational space is limited by the Greenwald density limit. In H-mode, the maximum achievable pressures are limited by the MHD ballooning limit. All these limits depend on the transport characteristics of the underlying turbulence. 
The Seperatrix Operational Space (SepOS) concept is a semi-empirical model and describes the operational space of a tokamak. It is empirical because it relies on scaling laws of the gradient decay lengths at the separatrix. However, it has a strong theoretical basis. It can be compared to the liquid droplet model of nuclear physics. 

In SepOS, the turbulence suppression from L-mode to H-mode is a combination of three effects. The diamagnetic, shear flow and the electromagnetic stabilization. The shear flow stablize the turbulence by removing energy from the turbulence via the Reynolds stress. The orientation of the vortices strengthens the shear flow. the vortices are thinned out and absorbed. In addition, there is diamagnetic stabilization. The transport is mainly caused by interchange modes. Drift waves can depelete the charge separation of the interchange modes and thus reduce them. Electromagnetic stabilization is not suppression in the true sense of the word. As the heating power in H-mode is higher than in L-mode, the transport in H-mode is also higher than in L-mode. Turbulence is not suppressed. In H-mode, the turbulence is only lower in relation to the heat output. The turbulence at the edge in H-mode is electromagnetic. With increasing plasma beta, the range of electromagnetic turbulence in the wave number space becomes larger and the electrostatic turbulence smaller. This effect is treated additionally.     

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

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)

O. Grover, T. Eich, P. Manz et al. 'Reduced model for H-mode sustainment in unfavorable ∇B drift configuration in ASDEX Upgrade', Nuclear Fusion 64, 056020 (2024)