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Manuscript Title: Transfer of line radiation in optically thick media allowing for transport of excitation energy: the resonant doublet.
Authors: C.V. Kunasz, P.B. Kunasz
Program title: SLAB3
Catalogue identifier: AAAH_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 10(1975)304
Programming language: Fortran.
Computer: CDC 6400.
Operating system: KRONOS.
Program overlaid: yes
RAM: 25K words
Word size: 60
Keywords: Radiative transfer, Resonant doublet, Excitation transfer, Migration of excitation, Boundary layer, Discrete ordinates.
Classification: 21.2.

Nature of problem:
When a confined volume of resonant vapor is excited by incident light, transfer of energy occurs both by photon scattering and by thermal motion of excited atoms with frequent excitation transfer. The random walk of a quantum of excitation may be terminated by quenching at a wall of the containing cell. This energy loss reduces the emergent radiative flux and creates a relatively under-excited boundary layer which may affect the emergent spectral profile. Our program calculates the emergent and internal radiation fields for a resonant doublet transition, the degree of excitation of the gas, and the fluxes of radiation through,and excitation into, the walls of the laboratory cell.

Solution method:
For each component of the doublet the equation of transfer for line radiation is coupled to the angle-dependent equation of transport for excitation, which is coupled to the other doublet component. The four coupled integro-differential equations are solved by an extension of the method of discrete ordinates. Total excitation in each transition, found by averaging the discrete streams of excited atoms, allows evaluation of the formal solution of the transfer equation for the detailed emergent radiation field.

The cell is assumed to have planar symmetry and to be illuminated by a uniform beam impinging at a specified angle to the normal. The resonant doublet is modeled by a three-level atom in which the two closely spaced upper states are coupled only by collisional transitions and in which hyperfine structure is completely ignored. Stimulated emission is neglected, necessitating the restriction to small fractional excitation. Broadened, white and monochromatic incident beams are treated in conjunction with Doppler, Lorentz and Voigt absorption profiles, and complete frequency redistribution is assumed. Though the densities of excited states are treated as functions of flight direction, their distributions over speed are approximated by a single velocity, and excitation transfer is assumed isotropic in the laboratory frame.

Running time:
For a simple case, e.g. gaussian profile with 2 streams per hemisphere and 6 frequencies representing each transition and a monochromatic input beam, the (1,0), (2,0), and (3,0) overlaps required 2, 0.6, and 4 s, respectively (NGRID = 20; see section 3.1.9). For a more compilcated case, e.g. Voigt profile with 2 streams, 20 frequencies sampling the profile for each transition and a white input beam, the (1,0), (2,0), and (3,0) overlays required 19, 12, and 14 s respectively (NGRID = 50). The (0,0) overlay time is negligible.