The effect of temperature on frequency and instability variations in a smooth-bore magnetron

Abstract

In this paper, the frequency and instability variations under the influence of temperature effect in a cylindrical smooth-bore magnetron are investigated. To derive the eigenvalue equation, the Fourier transform of electrostatic flute perturbations together with the local approximation method along radial direction for perturbed density is applied to equations of the macroscopic fluid model and Poisson equation. The obtained eigenvalue equation is solved numerically by shooting to a fitting point method. The analysis of numerical results shows the change in frequency of second three azimuthal modes for the case when the perpendicular temperature is higher than the parallel temperature (T∥<T⊥), which is greater than the case when temperatures along azimuthal and radial directions are equal (T∥=T⊥) or T∥>T⊥. As the temperature rising, the frequency and growth rate instability increase except for Tr > Tθ that the growth rate instability is reduced until Tθ = 100 00k and then is increased. The minimum frequency variation is 0.002 GHz for the mode of l=1 at 2T∥=T⊥. The maximum change in frequency, in contrast, is 10.651 GHz for the mode of l=5 at 4T∥=T⊥. According to the obtained results, the temperature controlling could be help to frequency adjustment in magnetrons.