A Spin System Model for Coupled-Cavity Masers

The software for designing coupled-cavity masers has been extended to include the effects of the ruby spin system. Two computer programs based on the modematching algorithm are used. The first program calculates the magnetic susceptibility in the ruby-filled cavity. The second program uses this information to calculate the scattering parameters. The effects of the ruby spin system are modeled in both the absorptive and emissive states. Several examples of the model are presented. I. Introduction The ruby spin system is the collection of weakly interacting magnetic dipole moments associated with the chromium ions in the aluminum oxide crystal lattice. Macroscopically, they appear as a weak paramagnetic system. The population inversion achieved with the states of these dipoles in an external magnetic field is responsible for the amplification process in a maser. The recent 31.8- to 32.3-GHz (Ka-band) coupled-cavity maser design was done with a rectangular-waveguide mode-matching program developed by JPL [1]. The maser was designed with no explicit reference to the ruby spin system [2]. A better understanding of the maser and more accurate designs require that the effects of the spin system be included. The earlier version of the mode-matching program characterizes the dielectric media by a complex relative dielectric constant, but otherwise includes no losses. The original Ka-band coupled-cavity maser design used the complex relative dielectric constant to create a loss in the cavity containing the ruby crystal. This loss can be thought of as representing a spin system with infinite line width and no reactance. However, the quantum transitions of the ruby spin system behave as resonant circuits. They have both a finite line width and reactive behavior. In addition, these components are temperature dependent. Furthermore, when the spin system is inverted, by pumping the ruby, the resistive and the reactive components change sign. This article presents a model useful for designing coupled-cavity masers that includes these effects. An advantage of the model is its ability to predict the strength of the paramagnetic resonance. The strength of the spin resonance at a particular frequency is determined mainly by two factors. One factor is the polarization, direction, and strength of the rf magnetic field relative to the spin vector of the quantum transition. The rf magnetic field is determined by the geometry of the coupled cavities. The spin vector is determined by the strength and relative orientation of the external static magnetic field to the ruby c-axis. A second factor is the difference in spin population between the levels for which the transition