Abstract
The Rack-Llewellyn-Pierce noise analysis, <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6,10,12,13</sup> which has been applied to the problem of microwave noise in electron beams of large transit angle, utilizes the sinusoidal solutions for a space-charge-limited, infinite parallel plane diode, as derived by Llewellyn <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> and Smullin, <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</sup> in the gun region and Ramo's solution for the lowest mode of a finite beam confined by an infinite longitudinal magnetic field in the drift space. <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">8</sup> In this calculation the input boundary condition which must be specified is the velocity modulation at the cathode. This was calculated by Rack <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">7</sup> as the mean square fluctuation of the instantaneous average velocity of all electrons crossing the plane of the potential minimum.
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