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A. H. Boozer

Publications and source records attributed to A. H. Boozer.

4 recordsLinked to original sources

Resilient Stellarator Divertor Characteristics in the Helically Symmetric eXperiment

Resilient divertor features connected to open chaotic edge structures in the Helically Symmetric Experiment (HSX) are investigated. For the first time, an expanded vessel wall was considered that would give space for implementation of a physical divertor target structure. The analysis was done for four different magnetic configurations with very different chaotic plasma edges. A resilient plasma wall interaction pattern was identified across all configurations. This manifests as qualitatively very similar footprint behavior across the different plasma equilibria. Overall, the resilient field lines of interest with high connection length $L_C$ lie within a helical band along the wall for all configurations. This resiliency can be used to identify the best location of a divertor. The details of the magnetic footprint's resilient helical band is subject to specific field line structures which are linked to the penetration depth of field lines into the plasma and directly influence the heat and particle flux patterns. The differences arising from these details are characterized by introducing a new metric, the minimum radial connection $\text{min}(\delta_N)$ of a field line from the last closed flux surface. The relationship, namely the deviation from a scaling law, between $\text{min}(\delta_N)$ and $L_C$ of the field lines in the plasma edge field line behavior suggests that the field lines are associated with structures such as resonant islands, cantori, and turnstiles. This helps determine the relevant magnetic flux channels based on the radial location of these chaotic edge structures and the divertor target footprint. These details will need to be taken into account for resilient divertor design.

physics.plasm-ph

Advection and diffusion in a three dimensional chaotic flow

The advection-diffusion equation is studied via a global Lagrangian coordinate transformation. The metric tensor of the Lagrangian coordinates couples the dynamical system theory rigorously into the solution of this class of partial differential equations. If the flow has chaotic streamlines, the diffusion will dominate the solution at a critical time, which scales logarithmically with the diffusivity. The subsequent rapid diffusive relaxation is completed on the order of a few Lyapunov times, and it becomes more anisotropic the smaller the diffusivity. The local Lyapunov time of the flow is the inverse of the finite time Lyapunov exponent. A finite time Lyapunov exponent can be expressed in terms of two convergence functions which are responsible for the spatio-temporal complexity of both the advective and diffusive transports. This complexity gives a new class of diffusion barrier in the chaotic region and a fractal-like behavior in both space and time. In an integrable flow with shear, there also exist fast and slow diffusion. But unlike that in a chaotic flow, a large gradient of the scalar field across the KAM surfaces can be maintained since the fast diffusion in an integrable flow is strictly confined within the KAM surfaces.

physics.flu-dyn

Design criteria of a chemical reactor based on a chaotic flow

We consider the design criteria of a chemical mixing device based on a chaotic flow, with an emphasis on the steady-state devices. The merit of a reactor, defined as the $Q$-factor, is related to the physical dimension of the device and the molecular diffusivity of the reactants through the local Lyapunov exponents of the flow. The local Lyapunov exponent can be calculated for any given flow field and it can also be measured in experimental situations. Easy-to-compute formulae are provided to estimate the $Q$-factor given either the exact spatial dependence of the local Lyapunov exponent or its probability distribution function. The requirements for optimization are made precise in the context of local Lyapunov exponents.

physics.flu-dyn

Hamiltonian structure of Hamiltonian chaos

From a kinematical point of view, the geometrical information of hamiltonian chaos is given by the (un)stable directions, while the dynamical information is given by the Lyapunov exponents. The finite time Lyapunov exponents are of particular importance in physics. The spatial variations of the finite time Lyapunov exponent and its associated (un)stable direction are related. Both of them are found to be determined by a new hamiltonian of same number of degrees of freedom as the original one. This new hamiltonian defines a flow field with characteristically chaotic trajectories. The direction and the magnitude of the phase flow field give the (un)stable direction and the finite time Lyapunov exponent of the original hamiltonian. Our analysis was based on a $1{1\over 2}$ degree of freedom hamiltonian system.

physics.class-ph