Transport of Resonance Radiation in an Infinite Cylinder

Abstract

The Holstein-Biberman integrodifferential equation for the transport of resonance radiation has been solved for a gas contained in a long cylindrical container. The solution involves the following assumptions: (i) The excited atoms are initially distributed uniformly along the axis of the cylinder; (ii) the pressure and temperature of the gas are such that the absorption coefficient has either a pure Doppler-broadened or a pure pressure-broadened profile; (iii) the radius of the cylinder corresponds to many optical depths at the frequency corresponding to the maximum of the absorption coefficient. It is also shown that steady-state solutions corresponding to a line source along the axis of the cylinder can be calculated by the same procedure. The geometry and the initial conditions considered here are of particular interest because the situation can be simulated experimentally. Hurst and Thonnard have pointed out that an approximate line of excited atoms can be produced by sending a well-collimated pulse of protons or electrons down the axis of a long cylinder containing the gas of interest. The present paper also considers the decay of resonance radiation from a steady state built up by a line source. The latter situation is even easier to arrange experimentally. All experimental work to date has concerned itself with situations where the initial distribution of excited atoms is not known, and theory and experiment can only be compared at times which are large enough so that the system has decayed to its lowest eigenmode.