Homoclinic tangle of the primary separatrix in the compact and closed versus open and unbounded magnetic topologies for divertor tokamaks

ABSTRACTThe simple map and the symmetric quartic map are the generic representation of the open-unbounded and closed-compact magnetic topologies for single-null divertor tokamaks, respectively. The map parameter represents the magnetic asymmetries. The two maps are used to calculate the homoclinic tangles in the two topologies in divertor tokamaks. It is found that as the magnetic asymmetries become larger, the homoclinic tangle of the simple map becomes extremely elongated radially as opposed to the homoclinic tangle of the symmetric quartic map which becomes wider poloidally.