Abstract: In this paper, the expression descrbing the change of emittance for an axisymmetic electron beam in the case of stationary transportis derived with the general envelope equation presented in Ref. (1). The result suggests that the emittance change of a beam does not directly depend on the guiding magnetic field and the electrostatic field of the ion channel. but on the chang of the beam electron distribution. The cmittance change is essentially the consequnce of transferring between the space charge potential energy and the transveres effective thermal kinetic energy of the beam. The analytic results arc consistent with simulation very well. the effect of the canonical angular momentum on the beam emittance is qualitatively discussed.