Some generalizations of the convective model of jet generation

TL;DR

This paper develops analytical solutions for the initial stage of jet formation in inhomogeneous plasma, extending the convective jet model to include arbitrary altitude dependencies and detailed velocity and magnetic field structures.

Contribution

It introduces generalized analytical solutions for jet velocity and magnetic fields considering arbitrary altitude dependencies, enhancing the understanding of jet generation mechanisms.

Findings

Velocity field increases exponentially poloidally and superexponentially azimuthally.

Jet rotation is differential with altitude-dependent azimuthal velocity.

Solutions are applicable to arbitrary dimensionless coordinates and include magnetic field components.

Abstract

For analytical description of the initial stage of jet generation in nonequilibrium inhomogeneous plasma in the magnetohydrodynamic approximation, possible generalizations of solutions of the nonlinear equation for the stream function are analyzed. The jet generation model is based on the mechanism of convective instability and the frozen-in condition of magnetic field lines and is characterized by a number of free parameters. The equation for the radial part of the stream function is satisfied by first-order Bessel functions. To satisfy all the conditions near the jet axis and on its periphery, the found solutions are smoothly joined at the boundary. The final analytical solution for the velocity field is applicable to arbitrary values of dimensionless coordinates. The poloidal velocity increases approximately exponentially, and the azimuthal velocity - according to a superexponential law. In this paper, the velocity field of the jet, which consists of seven sections, is calculated. The rotation of the jet turns out to be differential, and to obtain a solution in quadratures for the azimuthal velocity, one can use not only linear but also power dependences on the altitude. For the exponent n < 1, a noticeable increase in the azimuthal velocity with radius is observed immediately from the jet axis, and for n > 1, a region of relative calm is observed near the axis. The jet model is generalized to the case of an arbitrary dependence of the Brunt-V\"ais\"al\"a frequency on the altitude. The corresponding solutions are found for the radial and vertical velocity components. For the initial stage of development, the vertical and azimuthal components of the generated magnetic field of the jet were also found in the work.