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Using a two and one-half dimensional (two-dimensional for fields, three-dimensional for particle velocities) particle-in-cell (PIC) code we simulate the dynamics of a highly-elliptic sheet electron beam focused by a periodically-cusped-magnetic (PCM) field array. For edge-focusing, a periodic-quadrupole-magnetic (PQM) array is placed along the sides. Very high-space-charge, low-voltage beams may be focused in this way, without disruptive diocotron instability. The PCM-PQM hybrid array appears convenient for two-plane matching of the beam to minimize beam ripple in both transverse dimensions.
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Booske et al. (1999) studied this question.
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