Optimization of the snowflake diverted equilibria in the TCV tokamak
In support of the TCV experimental campaign aiming at studying H-mode plasmas with snowﬂake (SF) divertor, free boundary equilibrium and stability studies were performed with the SPIDER and KINX codes. Due to the high ﬂexibility of plasma shaping capabilities of TCV, SF divertor conditions can be reached for various plasma geometries. However, at high plasma current some conﬁgurations require poloidal ﬁeld (PF) coil currents close to the machine limit. This is particularly important when the equilibrium sensitivity to the edge pedestal proﬁles, which is higher than for standard X-point conﬁgurations, is taken into account. That is why the conﬁguration optimization should also include the proﬁle sensitivity study when planning the shot scenario.
Conditions are derived for the construction of total variation diminishing difference schemes with multi-point support. These conditions, which are proved for explicit, implicit, and semi-discrete schemes, correspond in a general sense to the introduction of upwind biasing.