Alexander Wurm

Meanders and reconnection–collision sequences in the standard nontwist map

New global periodic orbit collision and separatrix reconnection scenarios exhibited by the standard nontwist map are described in detail, including exact methods for determining reconnection thresholds, methods that are implemented numerically. Results are compared to a parameter space breakup diagram for 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. Implications for transport are discussed.

Action principles for extended magnetohydrodynamic models

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 Lusts general two-fluid model, extended magnetohydrodynamic (MHD), Hall MHD, and electron MHD from a unified framework. The variational formulation allows us to use Noethers theorem to derive conserved quantities for each symmetry of the action.

Renormalization and destruction of 1/γ2 tori in the standard nontwist map

Extending the work of del-Castillo-Negrete, Greene, and Morrison [Physica D 91, 1 (1996); 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.Extending the work of del-Castillo-Negrete, Greene, and Morrison, Physica D {\bf 91}, 1 (1996) and {\bf 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.

Breakup of shearless meanders and "outer" tori in the standard nontwist map.

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 Greenes 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.

On reconnection phenomena in the standard nontwist map

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.

Temperature gradient driven electron transport in NSTX and Tore Supra

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.

Characterizing Volume Forms

Old and new results for characterizing volume forms in functional integration. 1 The Wiener measure Defining volume forms on infinite dimensional spaces is a key problem in the theory of functional integration. The first volume form used in functional integration has been the Wiener measure. From the several equivalent definitions of the Wiener measure, we choose one [1] which can easily be extended for use in Feynman integrals. We recall the CameronMartin and Malliavin formulae because they are, respectively, integrated and infinitesimal formulae for changes of variable of integration which can be imposed on volume forms other than the Wiener measure. 1.1 Definition The Wiener measure γ on the space W of pointed continuous paths w on the time interval T = [0, 1] w : [0, 1] −→ R , w(0) = 0, can be characterized by the equation

Fourier transforms of Lorentz invariant functions

Fourier transforms of Lorentz invariant functions in Minkowski space, with support on both the timelike and the spacelike domains are performed by means of direct integration. The cases of 1+1 and 1+2 dimensions are worked out in detail, and the results for 1+n dimensions are given.

Comment on: Path integral solution of the Schrödinger equation in curvilinear coordinates: A straightforward procedure [J. Math. Phys. 37, 4310–4319 (1996)]

The authors comment on the paper by J. LaChapelle, J. Math. Phys. 37, 4310 (1996), and give explicit expressions for the parametrization, its solution, and the Lie derivatives of the Schrodinger equation for the case of n-dimensional spherical coordinates.