Stationary symmetric magnetohydrodynamic flows

Abstract

The problem of translation symmetric stationary magnetohydrodynamic (MHD) flow is analyzed with respect to the different permitted flow regimes. A minimal set of equilibrium functions is constructed facilitating the complete explicit solution in the case of self-similar flow. It is found that limiting line and Alfvén singularities leads to a division in four distinct velocity regimes which cannot be connected by continuous flows. Instead, the three types of MHD shocks appear, enabling the system to pass from the high to the low speed regimes.

Stationary Two-Dimensional Magnetohydrodynamic Flows with Shocks: Characteristic Analysis and Grid Convergence Study

“…Hence the class of stationary field-aligned flow is an important class of MHD flows. One could even argue that 2D stationary flow problems in a finite domain with the magnetic field not aligned to the plasma flow are rare [19,23,30]. It is hard to define the boundary conditions consistently in that case.…”

The spectrum of MHD flows about X points

“…For compressible flows, this is not the case and the perpendicular component of the momentum equation yields an equation relating M to ψ and ∇ψ Goedbloed and Lifschitz 1997). This is the Bernoulli equation, which then, together with the modified Grad-Shafranov equation, determines the flux and the poloidal Alfvén Mach number.…”

Mode coupling in two-dimensional magnetohydrodynamic flows

“…Agim and Tataronis 1985). For a compressible plasma, this means that one has to solve these two coupled equations for the magnetic flux and the poloidal Alfvén Mach number, as is done, for instance, by Goedbloed and Lifschitz (1997). For an incompressible plasma, however, the poloidal Alfvén Mach number and the density profiles become flux functions, and the Bernoulli equation reduces to a definition of a Bernoullitype of function H, which, for a cylindrical geometry, takes the form (Nijboer et al 1998)…”