Influence of an X-point on the L-H transition power threshold

It is well known that there is an up-down difference in temperature in tokamaks. In the collisional case this difference for ions is on the order of 1/(ω B i τ)>>1 for a circular cross section tokamak, where ω B i and τ i are the ion cyclotron frequency and collision time, respectively. Here we show that the presence of an X-point amplifies this effect and can lead to effects of order of unity, depending on the ion drift direction. This in turn leads to a strong increase of the pressure gradient in the vicinity of the X-point (if the drift of the ions is in the X-point direction). In the framework of the Alfvén-drift paradigm for the L-H transition, it provides an explanation for the difference in the power threshold for the L-H transition arising from the ion drift direction.