The density‐function method is applied to the one‐dimensional model of the traveling‐wave tube to determine the effect of velocity distribution on traveling‐wave tube performance. For narrow velocity spreads, a term is introduced into the root equation for the incremental propagation constants which is like the space charge term 4QCand directly added thereto. This term is proportional to the ratio of the variance of the distribution to the square of the gain parameterC. For a typical tube, thermal velocities are found to reduce the gain by less than one part in 104. In a tube employing confined magnetic focusing, and employing a high perveance beam, the velocity spread resulting from space charge lowers the gain by about 1 percent.