The near separatrix region in tokamaks provides a new length scale parameter x0=(-dln p0/dx)-1 of the order of several Larmor radii. Modified drift and interchange instabilities occur in this region due to longitudinal losses. The related turbulence gives rise to perpendicular transport and regulates the width x0. The H-mode is set up when the shear flow stabilizes these instabilities leading to the condition rho = rho i/x0>cl where cl is of the order unity. The L-H power threshold depends strongly on the longitudinal loss mechanism. Classical thermal conduction provides a threshold scaling similar to the experimentally observed scaling, but the free-streaming loss yields a cubic dependence on B0.