Transformation of fluctuations along magnetron injection beams

A generalized set of equations for evaluating transformation of fluctuations from one plane to another plane along the beam is derived by using the perturbation method. These equations are derived for the case of a magnetron injection gun and can be reduced to Llewellyn-Peterson and Van Duzer equations for O-type and M-type (Kino gun) configurations by appropriate substitution for the value of the angle θ (the angle between the cathode plane and the direction of the magnetic field). The noise transport coefficients for the case of a magnetron injection gun are evaluated both for temperature-limited and space-charge-limited cases and for several values of the perturbation frequency and angle θ. For the space-charge-limited case, both short and long Kino guns are considered. It is found that the values of the various noise transport coefficients which contribute toward noise at the output are reduced as the value of angle θ is increased. The results given in this paper indicate qualitatively that the noise content in a device using a magnetron injection gun is reduced as the value of θ is increased; this is in agreement with the previous results. For a quantitative evaluation of noise output, it is necessary to take into account the beam current and the various fluctuations simultaneously.