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Schematic of a planar magnetron with a thin electron cloud stream.
Plot of the maximum temporal growth rate as a function of the surface density for a single thin electron cloud stream with the structure parameters of , , , and in a uniform applied magnetic field of and a A-K gap voltage of .
Plot of the amplitude of oscillating voltage as a function of time as obtained from the MAGIC simulation. Here, the parameters are , , , , , , , , and .
Plot of the temporal growth rate (solid curve) and the real frequency (dashed curve) as a function of wave number for the lowest resonant TM mode. The solid and dashed curves are obtained from Eq. (7) using the three electron cloud streams with surface densities and flow velocities , , , and , respectively. The circle and cross are the real frequency and instability grow rate from the MAGIC simulation, respectively. Here, the other parameters are the same as those in Fig. 3.
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