arXiv subjects

X. Z. Tang

Publications and source records attributed to X. Z. Tang.

5 recordsLinked to original sources

arXiv2006

A Proposed Experiment to Study Relaxation Formation of a Spherical Tokamak with a Plasma Center Column

A spherical tokamak (ST) with a plasma center column (PCC) can be formed via driven magnetic relaxation of a screw pinch plasma. An ST-PCC could in principle eliminate many problems associated with a material center column, a key weakness of the ST reactor concept. This work summarizes the design space for an ST-PCC in terms of flux amplification, aspect ratio, and elongation, based on the zero-beta Taylor-relaxed analysis of Tang & Boozer [Phys. Plasmas 13, 042514 (2006)]. The paper will discuss (1) equilibrium and stability properties of the ST-PCC, (2) issues for an engineering design, and (3) key differences between the proposed ST-PCC and the ongoing Proto-Sphera effort in Italy.

physics.plasm-ph↗

arXiv1998

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↗

arXiv1998

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↗

arXiv1998

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↗

arXiv1998

Anomalous scaling behavior in Takens-Bogdanov bifurcations

A general algorithm is presented for estimating the nonlinear instability threshold, $σ_c$, for subcritical transitions in systems where the linearized dynamics is significantly non-normal (i.e. subcritical bifurcations of {\em Takens-Bogdanov} type). The $N$-dimensional degenerate node is presented as an example. The predictions are then compared to numerical studies with excellent agreement.

physics.class-ph↗