Multipacting Modes of High-Frequency Gaseous Breakdown

A previously developed average electron theory for the ½-cycle multipacting mode of low-pressure, high-frequency breakdown (secondary electron resonance) has been generalized and extended to higher order modes. A semitheoretical plot of breakdown voltage $V$ vs the product of frequency times electrode separation $f\times d$ using representative fitting parameters is given for the ½- through $\frac{9}{2}$-cycle modes. In addition to the customary ½-cycle cutoff the theory predicts a modified cutoff in each of the mode transition regions. Breakdown data for internal metal electrodes at 2 microns pressure show the typical ½-cycle cutoff at about 100 Mc-cm/sec plus a newly observed $\frac{3}{2}$-cycle cutoff as indicated by a dip in the breakdown curve at about 450 Mc-cm/sec. The $\frac{3}{2}$-cycle dip exhibits a strong dependence on electrode surface conditions. The theory is compared with multipacting breakdown data from several sources covering a wide range of conditions, including microwave breakdown at sufficiently low pressures.