STABILITY AND CONFINEMENT OF NONRELATIVISTIC SHEET ELECTRON-BEAMS WITH PERIODIC CUSPED MAGNETIC FOCUSING

Sheet electron beams focused by periodically cusped magnetic (PCM) fields are stable against low-frequency velocity-shear instabilities (such as diocotron mode). This is in contrast to more familiar unstable behavior in uniform solenoidal magnetic fields. Two rectangular-cross-section magnetic configurations capable of focusing in both transverse dimensions are investigated: (i) a closed-side two-plane PCM configuration that is topologically equivalent to conventional round-cross-section PPM focusing; and (ii) an open-side configuration that uses ponderomotive PCM focusing in the vertical plane and simple upsilon(z)B(y) Lorentz force focusing in the horizontal plane. Both configurations are capable of stable sheet beam confinement. The open-side configuration appears more practical both for focusing and for realizing matched (cold) beam conditions in which the beam envelope is free from oscillations. For realistic beams with finite emittance, the existence of a matched cold beam solution implies less emittance growth at beam injection.