Abstract
A theoretical scheme is developed to deal with the problems of stellar winds in three-dimensional situations, and relativistic fluid equations are integrated formally under isentropic and quasi-stationary conditions, in a flat space-time.
The relativistic Euler equation for a one-component plasma is expressed in the same form as the ideal-MHD condition for the effective electromagnetic field which combines the inertial and pressure terms with the true electromagnetic field. This equation and that of mass continuity are integrated formally by introducing Euler-type potentials for the effective magnetic field and for the mass flux in the rotating frame, respectively. Functional form of one of these Euler potentials, which represents the total energy per unit charge in the rotating frame, is specified as an integral of motion. For an electron-proton plasma, the integrals for both components are combined to yield the energy integral of the plasma as a whole and the integrated Ohm's law, in the limit of vanishing mass ratio of an electron to a proton.
Maxwell's equations are divided in two parts: i.e., the co-rotational and non-corotational parts. It is shown that the electromagnetic potentials for these parts are derived from a scalar super-potential and a vector super-potential, respectively.
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Kaburaki, O. Euler potential method in three-dimensional stellar wind problems. Astrophys Space Sci 112, 157–174 (1985). https://doi.org/10.1007/BF00668417
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DOI: https://doi.org/10.1007/BF00668417