The influence of space charge on electron beam dynamics in a toroidal, constant in time magnetic field of alternating sign is considered. It is shown that such a system can hold electron beams with current of about a few kiloamperes under the natural condition, that the magnetic field energy is higher than the accelerated electron beam energy. It is indicated that in the given case points of single-particle motion instability turn into narrow strips which can be slopped through by an appropriate choice of parameters. 5 refs.; 1 fig.; 1 tab.