Axisymmetric equilibria of a gravitating plasma with incompressible flows

Abstract

It is found that the ideal magnetohydrodynamic equilibrium of an axisymmetric gravitating magnetically confined plasma with incompressible flows is governed by a second-order elliptic differential equation for the poloidal magnetic flux function containing five flux functions coupled with a Poisson equation for the gravitation potential, and an algebraic relation for the pressure. This set of equations is amenable to analytic solutions. As an application, the magnetic-dipole static axisymmetric equilibria with vanishing poloidal plasma currents derived recently by Krasheninnikov et al. (1999) are extended to plasmas with finite poloidal currents, subject to gravitating forces from a massive body (a star or black hole) and inertial forces due to incompressible sheared flows. Explicit solutions are obtained in two regimes: (a) in the low-energy regime β₀ ≈ γ₀ ≈ δ₀ ≈ ε₀ ? 1, where β₀, γ₀, δ₀, and ε₀ are related to the thermal, poloidal-current, flow and gravitating energies normalized to the poloidal-magnetic-field energy, respectively, and (b) in the high-energy regime β₀ ≈ γ₀ ≈ δ₀ ≈ ε₀ ? 1. It turns out that in the high-energy regime all four forces, pressure-gradient, toroidal-magnetic-field, inertial, and gravitating contribute equally to the formation of magnetic surfaces very extended and localized about the symmetry plane such that the resulting equilibria resemble the accretion disks in astrophysics.     

任意方向发射源在柱状多层介质中的电磁场的理论计算

针对柱状多层介质测井模型,本文给出了井轴上沿任意方向的发射源在介质空间的电磁场的理论公式,利用递推方法可以很方便地进行数值计算.文中还分别对轴向与径向的电偶极子源和磁偶极子源共4种情况,给出了井轴上接收区磁场强度与侵入半径的关系曲线.