Some generalizations of the convective model of jet generation
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916447918227456 |
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| author | Artekha, S. N. |
| author_facet | Artekha, S. N. |
| contents | 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-Väisälä 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_16035 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Some generalizations of the convective model of jet generation Artekha, S. N. Plasma Physics Solar and Stellar Astrophysics Space Physics 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-Väisälä 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. |
| title | Some generalizations of the convective model of jet generation |
| topic | Plasma Physics Solar and Stellar Astrophysics Space Physics |
| url | https://arxiv.org/abs/2410.16035 |