New global periodic orbit collision/separatrix reconnection scenarios in the standard nontwist map in different regions of parameter space are described in detail, including exact methods for determining reconnection thresholds that are implemented numerically. The results are compared to a break-up diagram of shearless invariant curves. The existence of meanders (invariant tori that are not graphs) is demonstrated numerically for both odd and even period reconnection for certain regions in parameter space, and some of the implications on transport are discussed.In recent years, area-preserving maps that violate the twist condition locally in phase space have been the object of interest in several studies in physics and mathematics. These nontwist maps show up in a variety of physical models, e.g., in magnetic field line models for reversed magnetic shear tokamaks. An important problem is the determination and understanding of the transition to global chaos (global transport) in these models. Nontwist maps exhibit several different mechanisms: the break-up of invariant tori and separatrix reconnections. The latter may or may not lead to global transport depending on the region of parameter space. In this paper we conduct a detailed study of newly discovered reconnection scenarios in the standard nontwist map, investigating their location in parameter space and their impact on global transport.

The general, non-dissipative, two-fluid model in plasma physics is Hamiltonian, but this property is sometimes lost or obscured in the process of deriving simplified (or reduced) two-fluid or one-fluid models from the two-fluid equations of motion. To ensure that the reduced models are Hamiltonian, we start with the general two-fluid action functional, and make all the approximations, changes of variables, and expansions directly within the action context. The resulting equations are then mapped to the Eulerian fluid variables using a novel nonlocal Lagrange-Euler map. Using this method, we recover Lüst's general two-fluid model, extended magnetohydrodynamic (MHD), Hall MHD, and electron MHD from a unified framework. The variational formulation allows us to use Noether's theorem to derive conserved quantities for each symmetry of the action.

Extending the work of del-Castillo-Negrete, Greene, and Morrison, Physica D 91, 1 (1996) and 100, 311 (1997) on the standard nontwist map, the breakup of an invariant torus with winding number equal to the inverse golden mean squared is studied. Improved numerical techniques provide the greater accuracy that is needed for this case. The new results are interpreted within the renormalization group framework by constructing a renormalization operator on the space of commuting map pairs, and by studying the fixed points of the so constructed operator.In recent years, area-preserving maps that violate the twist condition locally in phase space have been the object of interest in several studies in physics and mathematics. These nontwist maps show up in a variety of physical models. An important problem from the physics point of view is the understanding of the breakup of invariant tori, which show remarkable resilience in the region where the twist condition is violated, called shearless tori. In terms of the physical system modelled, these tori represent transport barriers, and their breakup corresponds to the transition to global chaos. Mathematically, nontwist maps present a challenge since the standard proofs of celebrated theorems in the theory of area-preserving maps rely heavily on the twist condition. In this paper, we study the breakup of the shearless torus with winding number 1/γ 2 , where γ is the golden mean. This torus serves as a test case for improved techniques we developed. At the point of breakup the shearless torus exhibits universal scaling behavior which leads to a renormalization group interpretation.

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Electron thermal fluxes are derived from the power balance for Tore Supra (TS) and NSTX discharges with centrally deposited fast wave electron heating. Measurements of the electron temperature and density profiles, combined with ray tracing computations of the power absorption profiles, allow detailed interpretation of the thermal flux versus temperature gradient. Evidence supporting the occurrence of electron temperature gradient turbulent transport in the two confinement devices is found. With control of the magnetic rotational transform profile and the heating power, internal transport barriers are created in TS and NSTX discharges. These partial transport barriers are argued to be a universal feature of transport equations in the presence of invariant tori that are intrinsic to non-monotonic rotational transforms in dynamical systems.

Separatrix reconnection in the standard nontwist map is described, including exact methods for determining the reconnection threshold in parameter space. These methods are implemented numerically for the case of oddperiod orbit reconnection, where meanders (invariant tori that are not graphs) appear. Nested meander structure is numerically demonstrated, and the idea of meander transport is discussed.

The breakup of shearless invariant tori with winding number omega=(11+gamma)(12+gamma) (in continued fraction representation) of the standard nontwist map is studied numerically using Greene's residue criterion. Tori of this winding number can assume the shape of meanders [folded-over invariant tori which are not graphs over the x axis in (x,y) phase space], whose breakup is the first point of focus here. Secondly, multiple shearless orbits of this winding number can exist, leading to a new type of breakup scenario. Results are discussed within the framework of the renormalization group for area-preserving maps. Regularity of the critical tori is also investigated.

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