A method is presented for solving the equation which determines the modes of a helix with an electron beam [Chu and Jackson, Proc. Inst. Radio Engrs. 36, 853 (1948)]. The essential idea is to consider the modes as a perturbation of the modes produced by the cold helix. From the solution of the equation, the dependence of the amplification factor of the tube upon the geometrical parameters and the operating conditions is explicitly determined. The solution shows also that the tube will not amplify for too large values of the dc electron beam current.
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