Deformation of Gas Lenses by Gravity

If a cool gas is blown into a hot tube (Fig. 1), the gas heats lip first at the wall of the tube and remains cool longer at its center. The density therefore, is higher in the center of the tube and decreases toward the wall. The increase in density is accompanied by an increase in dielectric constant. In this way the gas acts as a positive lens.1,2 At the same time, however, the cooler gas tends to sink down because of gravity, thus causing an asymmetric density profile in a horizontal tube. 3 Though a simple approach already gives an estimate of this effect,4 a more rigorous theory is derived here using a perturbation calculation which determines the transverse convection currents from the unperturbed temperature profile and then uses the currents to correct the temperature profile.