A variational method for solving fast MHD flows. Consequences for stellar and extragalactic jets.
Abstract
In order to achieve a fast MHD flow, a plasma ejected from the vicinity of a star or a compact object must fulfill restrictive conditions, because the flow is supposed to cross smoothly three critical surfaces, namely the slow magnetosonic surface, the Alfven surface and the fast magnetosonic surface. These surfaces are not known a priori. Moreover there are other mathematical difficulties due to the change of the type of the partial differential equations, that pass from elliptical to hyperbolic and vice versa. We rounded these difficulties by using a variational method. We found a Lagrangian involving the two unknown functions of the problem, the local Mach number and the flux function. The accretion disk imposes boundary conditions having some selfsimilarity properties; which allows to minimize the Lagrange functional with a converging sequence of appropriate trial functions. Our results confirm some previously published results, as, for instance, the cylindrical selfcollimation, but also indicate some limitations about the acceleration region. Applications of the method concern both kinds of jets launched by an accretion disk and provide observational quantities such as velocity, density, temperature, size, flux of kinetic energy, thrust.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 July 1994
 Bibcode:
 1994A&A...287..325R
 Keywords:

 Accretion Disks;
 Astronomical Models;
 Magnetohydrodynamic Flow;
 Plasma Jets;
 Calculus Of Variations;
 Density (Mass/Volume);
 Kinetic Energy;
 Lagrangian Function;
 Mach Number;
 Temperature;
 Thrust;
 Velocity;
 Astrophysics;
 MHD;
 METHODS: ANALYTICAL;
 INTERSTELLAR MEDIUM: JETS AND OUTFLOWS;
 GALAXIES: JETS