Uniform plasma model of shot noise in gyroklystrons

Theoretical estimates of electron cyclotron shot noise in gyroklystrons have recently been confirmed at low currents. However at high beam current, the noise temperature is always reduced. We examine the effect of transverse collective effects on the shot noise. There are two collective effects; shielding, which reduces the noise; and instability, which increases it. It is shown that the effect of transverse shielding is negligible unless the gyrotron beam is extremely cold. Regarding instability, if the bare shot noise amplitude is denoted Ξ, then the shot noise, including the effect of instability, can be expressed as Ξ(1+A exp Γ), where Γ is the integrated growth. The effect of instability is then measured by two parameters, Γ and A. For a cold gyrotron beam, A is about 0.3, meaning about 10 dB of power growth is needed for the instability to manifest itself. Thermal effects both reduce A and Γ. For realistic gyrotron beams, about 20-25 dB of power e folds would be necessary for instability to manifest itself. To summarize, the theory developed explains the absence of instability in the measurements, but indicates that phenomena other than transverse shielding are responsible for the noise reduction