We study by PIC simulation the dynamics of the electron flow along self magnetically insulated negative polarity cylindrical transmission lines (MITL) of fixed vacuum impedance. We find that the theoretical models of magnetic insulation predict correctly the steady state macroscopic measurable voltages and currents but we also observe that the flow is governed by regular quasi-cycloidal electron motion of fixed spatial period which scales with MITL radius. While this is not completely surprising, such regularity has not been observed before. When retrapping due to load mismatch is present, the flow shows additional interesting features.
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