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A numerical technique has been developed for analyzing the transverse modes of waveguide lasers with external mirrors. Propagation outside the guide is computed with the Fresnel-Kirchhoff diffraction integral and within the guide by decomposing the fields into the characteristic modes of the guide structure. The transverse modes of the entire waveguide-mirror system fall into a number of distinct classes: TE(0m), TM(0m), EH(1m), EH(2m), etc. For each class of modes, the, corresponding guide modes form a complete and orthogonal set and may be used as basis vectors to describe those modes. This reduces the mode analysis of the waveguide resonator to the diagonalization of a small (5 x 5 or 10 x 10) complex matrix. Guide losses, coupling losses, and mode shapes will be discussed for a number of interesting cases, with the Fresnel number of the waveguide ranging from 0.1 to 1.0 and with various values of mirror curvature and position. It will be shown that some vales of resonator parameters are particularly advantageous for achieving single mode operation.

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Collisions between gas atoms and charged particles in the positive column of a dc-excited gas discharge tend to cause an axial transport of gas between the ends of a discharge tube. Since, because of approximate charge neutrality, essentially equal forces are exerted on the plasma ions and electrons by the axial field, any net force on the gas must be balanced by an axial force exerted on the wall by the plasma. Earlier workers have treated this pumping by assuming that ions near the wall give their cathode-directed momentum to the wall rather than to neutral atoms, thus producing a net anode-directed force on neutral atoms close to the tube wall, this being the predominant force. Such a treatment is shown here to be an incomplete discussion of the forces acting on the neutral gas; moreover, the "wall pumping" force itself is shown to be incorrectly considered in the earlier work. At higher pressures, the principal gas pumping force turns out to be one which acts throughout the discharge volume, caused by the unequal radial distances traveled by ions and electrons between collisions with gas atoms. The pressure and radius dependences of gas pumping predicted by the present treatment differ substantially from those of earlier work. /»R pR FI(«)=(2T/IJ)/ r"dr" (dr'/r') J0 J r" xf rdf£n.(rrf-nMleE(z) (2.3) Jo nR pR V2(Z)=(2TT/7J) r"dr" (dr'/r') J0 J r"