TRANSPORT OF ELECTRON BEAMS WITH LARGE ENERGY SPREAD IN A PERIODIC LONGITUDINAL MAGNETIC FIELD

The transport of an electron beam with an energy spread of up to 75% is discussed. In the paraxial approach the particle motion in a periodic field with a non-zero aver- age component is described by a Mathieu-type equation. For specific energies in the beam spectrum the solution of this equation shows resonances between the period of the focusing field and the spatial Larmor period of the parti- cles. The powers of resonances drop with their harmonic number. Non-resonance transport is possible only at low average focusing field; then for all the energies the Lar- mor period is longer than the period of the focusing field. Practically, for short beam lines, transport is possible also at higher focusing fields. Low powers of resonance in this case do not significantly increase the beam radius along the length of the beam line. Calculations, made for the trans- port section between decelerator and depressed collector of the FOM fusion free-electron maser (FEM), where the electron energy in the beam varies from 50 to 350 keV, has shown that highly efficient transport is possible if the har- monic number is larger than 3 over the whole energy range.