Abstract
This paper analyzes the extraordinary mode eigenvalue equation to investigate the effects of temperature on frequency and growth rate of instability in a cylindrical smooth-bore relativistic magnetron. This analysis is based on the framework of the macroscopic fluid model as well as Maxwell's equations, which include electromagnetic and relativistic effects comprehensively. We applied linear perturbation theory around the steady state profiles with the local approximation for perturbed density along the radial direction to derive the eigenvalue equation. The derived eigenvalue equation was solved numerically using shooting to a fitting point method. Due to explosive emission, temperature of about 8 eV is reported [Andreev and Hendricks, IEEE Trans. Plasma Sci. 40, 1551 (2012)]. According to the findings of the current study for the first six azimuthal modes, temperature rise can lead to increasing frequency and decreasing instability in a relativistic magnetron. In addition, after a large number of pulses and rising temperature in the system, the effect of temperature should be considered as an effective element in the oscillations of frequency.
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