[en] Conditions for production of an electron beam matched in the direction of transverse motion when passing through an induction linac focusing channel formed by solenoids with longitudinal magnetic fields are investigated in general. It is shown on the basis of the analysis of the task computer numerical solution results that for electron beams matching with the focusing channel is possible practically at any electron density distribution monotonously decreasing to the beam edge if the beam is emitted by a nonmagnetized cathode. Capacity of the focusing cchannel ld is sufficient for focusing the hihg-intense with longitudinal magnetic fie nontubular electron beams with any real phase volume value at the magnetic field intensity not exceeding some hundreds of gauss. Radius of the high intense electron beam during acceleration decreases insignificantly. The marked decrease of the beam radius can be attained by the adiabatic increase of the focusing field intensity along the accelerator