Zonal flow bifurcation and corresponding phase space topology. Left panel: zero Larmor radius with . Right panel: gyroaverage over finite Larmor radius showing bifurcated zonal flow for . The dashed lines show the zonal flow with the drift wave flow perturbation at maximum and minimum amplitude.
Location of the resonance layers given by when ρ is varied, for and 0.6 from top to bottom, respectively. The value , shown with the bold line, is the same used in the right panel of Fig. 1 , for which the fixed points of the single-mode Hamiltonian are also shown (for ) with the bold dashed line for even and dot-dashed line for odd n in Eq. (32) . The crossings with correspond to the (elliptic) O-points.
Topology change through separatrix reconnection when is increased from 0.2 to 0.855 to 1.8 for and . First panel has heteroclinic topology, second panel is the reconnection threshold and third panel has homoclinic topology.
Finite Larmor radius effects on phase space topology for the gyroaverage Hamiltonian in Eq. (30) with , k 1 and . As ρ increases from to , separatrix reconnection changes the topology from heteroclinic to homoclinic and ends with flow rectification.
Gyroradius-average-induced separatrix reconnection for increasing ρ: Top-left panel is for and . Top-right panelis for and . Bottom-left panel corresponds to and . Bottom-right has and .
Gyroaverage induced chaotic transport suppression in the heteroclinic topology for parameters .
Gyroaverage induced chaotic transport suppression in the homoclinic topology for parameters .
Shearless curve (red) embedded in the Poincare map of 80 particles for , , in the (a) heteroclinic ( , ) and (b) homoclinic ( , ) topologies. In both cases, the shearless curve is a robust transport barrier.
Evolution of the shearless curve as the parameter is increased, showing the destruction of the curve and the transition to a stochastic layer and to global chaos. Here ; from top left to bottom right .
Threshold for the destruction of the shearless curve for for (a) heteroclinic geometry when ) and (b) homoclinic geometry for ).
Fraction of thermal particles crossing from one side to the other of the barrier that would be present when , corresponding to (a) heteroclinic topology when ) and (b) homoclinic topology when ). In both cases and .
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