Stark effect produced frequency shifts in the helium-neon laser

Charged-particle diffusion theory of the positive column of a gas discharge predicts the establishment of a radial electric field, which by the second-order Stark effect produces a shift of the atomic line center in a single-frequency helium-neon laser. These frequency shifts are estimated with a simple theory. The results are: i) the atomic line center is a function of radial position in the discharge tube; ii) the magnitude of the frequency shift is proportional to (
T_{e}/R)^{2}
(where T
e
is the electron temperature and
R
is the tube radius); iii) the pressure dependence of the shift is via changes in T
e
; and iv) the frequency shifts are independent of discharge current.