4. Drift velocity
To calculate a typical order of magnitude of the drift velocity between the ions and rest of the plasma, the radiation force will be approximately balanced by the retarding frictional force. The diffusion velocity is
Here, is the mass of a proton, k is Boltzmann's constant, is the charge of the element i in units of the fundamental charge e. The thermal diffusion coefficient is and the microscopic diffusion coefficient is . The effective gravity is zero in the direction (from the definition of the equipotential), and so the third term in parentheses above is zero. Also, the thermal diffusion term is typically small compared to the radiative term and so the diffusion velocity is determined only by the radiative forces, and the concentration gradient.
If the mass of species 1 (the stellar plasma - mostly hydrogen and helium) is neglected compared to the mass of species 2 (the diffusing ions), and ion shielding is neglected in the computation of the Debye length, Eq. 40 of Paquette et al. (1986) becomes
where is the density. To obtain a simple expression for the diffusion velocity, an initially chemically homogeneous star is assumed, so that and Eq. 9 are good representations. The diffusion velocity is then
This expression will overestimate the drift velocity as soon as a concentration gradient is established, as then in Eq. 11. However, with these points in mind, Eq. 14 is used as an estimate for the velocity in Eq. 4.
© European Southern Observatory (ESO) 1999
Online publication: December 4, 1998