SpringerLink
Forum Springer Astron. Astrophys.
Forum Whats New Search Orders


Astron. Astrophys. 341, 560-566 (1999)

Previous Section Next Section Title Page Table of Contents

4. Drift velocity

To calculate a typical order of magnitude of the drift velocity [FORMULA] between the ions and rest of the plasma, the radiation force will be approximately balanced by the retarding frictional force. The diffusion velocity is

[EQUATION]

Here, [FORMULA] is the mass of a proton, k is Boltzmann's constant, [FORMULA] is the charge of the element i in units of the fundamental charge e. The thermal diffusion coefficient is [FORMULA] and the microscopic diffusion coefficient is [FORMULA]. The effective gravity is zero in the [FORMULA] 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

[EQUATION]

where

[EQUATION]

where [FORMULA] is the density. To obtain a simple expression for the diffusion velocity, an initially chemically homogeneous star is assumed, so that [FORMULA] and Eq. 9 are good representations. The diffusion velocity is then

[EQUATION]

This expression will overestimate the drift velocity as soon as a concentration gradient is established, as then [FORMULA] in Eq. 11. However, with these points in mind, Eq. 14 is used as an estimate for the velocity in Eq. 4.

Previous Section Next Section Title Page Table of Contents

© European Southern Observatory (ESO) 1999

Online publication: December 4, 1998
helpdesk.link@springer.de