Emittance growth of an intense electron beam in a focusing channel

We use the single-particle radial equation of motion to identify nonlinear forces which lead to an emittance growth in a focusing channel consisting of solenoids. For a uniform density beam, the two dominant effects are the axial velocity variations within a solenoid due to the particles´ azimuthal velocity and changes in the particle´s energy due to radial motion and the radial electric space-charge field. We derive estimates for the emittance growth for a space-charge dominated beam due to these effects, both for the case of a hard focus to a small beam waist and for the case where there is gentle beam scalloping. We also briefly catalog less important emittance growth mechanisms