2000/09/27 by G. N. Throumoulopoulos, G. N. THROUMOULOPOULOS, H. Tasso +1 · 1 citation
Physics and Astronomy · #Bernoulli's principle #Compressibility #Differential equation #Fusion and Plasma Physics Studies #Magnetic confinement fusion research #Magnetic field #Magnetohydrodynamic drive #Magnetohydrodynamics #Partial differential equation #Plasma #Solar and Space Plasma Dynamics #Toroid #physics.plasm-ph
paper · pdf · doi:10.1017/s0022377800008849
Post script file, 17 pages, no figures, to be published in J. Plasma Physics
arxiv created 2000/09/27 · openalex publication_date 2000/11/01 · arxiv updated 2015/06/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
It is shown that the magnetohydrodynamic (MHD) equilibrium states of an axisymmetric toroidal plasma with finite resistivity and flows parallel to the magnetic field are governed by a second-order partial differential equation for the poloidal magnetic flux function ψ coupled with a Bernoulli-type equation for the plasma density (which are identical in form to the corresponding ideal MHD equilibrium equations) along with the relation Δ*ψ = V c σ (here Δ* is the Grad–Schlüter–Shafranov operator, σ is the conductivity and V c is the constant toroidal-loop voltage divided by 2π). In particular, for incompressible flows, the above-mentioned partial differential equation becomes elliptic and decouples from the Bernoulli equation [H. Tasso and G. N. Throumoulopoulos, Phys. Plasma 5 , 2378 (1998)]. For a conductivity of the form σ = σ( R , ψ) (where R is the distance from the axis of symmetry), several classes of analytic equilibria with incompressible flows can be constructed having qualitatively plausible σ profiles, i.e. profiles with σ taking a maximum value close to the magnetic axis and a minimum value on the plasma surface. For σ = σ(ψ), consideration of the relation Δ*ψ = V c σ(ψ) in the vicinity of the magnetic axis leads then to a proof of the non-existence of either compressible or incompressible equilibria. This result can be extended to the more general case of non-parallel flows lying within the magnetic surfaces.