This paper describes a novel application of the field-gradient theory of plasma microwave harmonic generation, proposed by Krenz and Kino, to the case of a positive column placed through a rectangular waveguide. The distribution of 2nd-harmonic power between the TE 01 and T E n waveguide modes has been examined experimentally and found to be in agreement with qualitative predictions made from the gradient model. An inverse-cubic dependence between the 2nd-harmonic-conversion efficiency and electron-collision frequency, predicted by Krenz, has also been observed. A metal probe placed against the column, with the intention of introducing severe microwave-field gradients in the plasma, was seen to increase harmonic output by factors as high as 10 4 . When this effect was combined with plasma resonance at the fundamental frequency, a best overall conversion of about 25 % was produced for an input power of 500 mW at 2-42 GHz. At higher power levels, the plasma electron density appropriate for fundamental resonance could not be sustained, and the conversion efficiency fell. Experiments using 9-6 and 35GHz fundamental signals gave best conversion efficiencies to the second harmonic of only 2-5% and about 0-01%, respectively. It is concluded that the gradient model provides a satisfactory description of 2nd-harmonic generation in gaseous plasmas, but that devices based on this model do not operate efficiently at high power levels or at high microwave frequencies.
List of symbolsa,b -rectangular-waveguide dimensions {a > b) x, y, z = Cartesian co-ordinates: z is the direction of propagation; x ranges from 0 to b; y ranges from 0 to a r, 6 = cylindrical co-ordinates in xz plane centred on the rod E = microwave electric field in the plasma f, 8, y = unit vectors in the directions r, 8, y TT X = Hertzian vector of the electric type, directed along the x axis € r = relative permittivity of the plasma column P l = dipole strength of the plasma column k 0 = wavenumber for free space k g = wavenumber in guide Jo = Bessel function of first kind and zero order n e = average electron number density in the plasma m e = electronic mass e = electronic charge co = angular frequency of the applied microwave field i 2ci -current density generated at the 2nd-harmonic frequency T b = temperature of the oil bath containing the subsidiary assembly