A VARIATIONAL METHOD FOR SOLVING FAST MHD FLOWS - CONSEQUENCES FOR STELLAR AND EXTRAGALACTIC JETS

In order to achieve a fast MHD flow, a plasma ejected from the vicinit y of a star or a compact object must fulfill restrictive conditions, b ecause 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 ty pe of the partial differential equations, that pass from elliptical to hyperbolic and vice versa. We rounded these difficulties by using a v ariational method. We found a Lagrangian involving the two unknown fun ctions of the problem, the local Mach number and the flux function. Th e accretion disk imposes boundary conditions having some self-similari ty properties; which allows to minimize the Lagrange functional with a converging sequence of appropriate trial functions. Our results confi rm some previously published results, as, for instance, the cylindrica l self-collimation, but also indicate some limitations about the accel eration region. Applications of the method concern both kinds of jets launched by an accretion disk and provide observational quantities suc h as velocity, density, temperature, size, flux of kinetic energy, thr ust.