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This paper intends to study an experimentally observed stabilizing phenomenon and to prove a mathematically rigorous stability result on the perturbations near a background magnetic field. Physical experiments and numerical simulations have observed a remarkable phenomenon that a background magnetic field can smooth and stabilize the electrically conducting turbulent fluids. To understand the mechanism of this phenomenon, we focus on a special 2D magnetohydrodynamic (MHD) system with anisotropic dissipation and partial damping and examine the stability near a background magnetic field. Due to the lack of full dissipation and damping, this stability problem is not trivial. Without the presence of a magnetic field, the fluid velocity is governed by the 2D Navier--Stokes equations in the whole space ℝ² with only vertical dissipation, and its stability (near the trivial solution) is still an open problem. However, when coupled to the magnetic field in such an MHD system, we are able to show that any perturbation near a background magnetic field is globally stable in Sobolev space H². This result reflects the observed stabilizing effect of the magnetic field. Mathematically, the MHD system obeyed by the perturbations can be converted to a system of wave equations which exhibits extra smoothing and stabilizing properties. These properties allow us to control the nonlinearity in the anisotropic Navier--Stokes equations and thus establish the desired stability result. [ABSTRACT FROM AUTHOR]

This paper reports the feasibility of the impregnation of no-insulation (NI) high-temperature superconducting (HTS) coils using solder. NI coils are widely studied and used in many situations. To utilize an HTS coil under high mechanical loads such as field coils for rotating machines, the HTS tapes must be stabilized mechanically. Epoxy impregnation is a common method to protect the HTS field from mechanical disturbances caused by the magnetic field and rotational vibration of the rotor to enhance the mechanical stability. However, traditional epoxy resins are electrical insulating materials which might cause the turn-to-turn contact resistance of NI coils to increase. Therefore, we proposed a new kind of impregnation method using the electrically conductive material, solder. Two coils were fabricated and tested for comparison. One is the NI coil without impregnation and the other is the NI coil impregnated with solder. The charge-discharge and sudden-discharge tests were performed in liquid nitrogen at 77 K. The experimental results were studied with equivalent circuit analyses. The results of this paper could provide useful data for the application of solder impregnated NI HTS coils. [ABSTRACT FROM AUTHOR]

This paper is concerned with an initial-boundary value problem for screw pinches arisen from plasma physics. We prove the global existence of weak solutions to this physically very important problem. The main difficulties in the proof lie in the presence of 1/x-singularity in the equations at the origin and the additional nonlinear terms induced by the magnetic field. Solutions will be obtained as the limit of the approximate solutions in annular regions between two cylinders. Under certain growth assumption on the heat conductivity, we first derive a number of regularities of the approximate physical quantities in the fluid region, as well as a lot of uniform integrability in the entire spacetime domain. By virtue of these estimates we then argue in a similar manner as that in Ref. 20 to take the limit and show that the limiting functions are indeed a weak solution which satisfies the mass, momentum and magnetic field equations in the entire spacetime domain in the sense of distributions, but satisfies the energy equation only in the compact subsets of the fluid region. The analysis in this paper allows the possibility that energy is absorbed into the origin, i.e. the total energy be possibly lost in the limit as the inner radius goes to zero. [ABSTRACT FROM AUTHOR]