Space Charge Frequency Dependence of Magnetron Cavity

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Abstract
The effect on the resonant frequencies of a magnetron cavity produced by the presence of a thin layer of charge surrounding the cathode is investigated theoretically. The corresponding experimental procedure is the ``cold impedance testing'' of a magnetron with a hot cathode in the presence of a magnetic field and a low d.c. cathode‐anode voltage. A small amplitude theory is used, based on the single stream steady state. The correction to the frequency of the empty cavity due to a thin cloud of charge surrounding the cathode is given by a resonance‐like formula about the ``cyclotron frequency,'' eB/2πm. In the ``Rising‐Sun'' tube the curve of ν vs. νc for constant d.c. voltage is asymmetric, apparently because of the presence of the ``zero'' mode. The validity of the theory is limited to low level oscillations, but the comparison of theory with experimental results seems to support the existence of the single stream steady state for non‐operating magnetrons.