Summary form only given, as follows. Collisionless shielding in one dimensional (highly magnetized) plasmas is paradoxical. The insertion of a positive test charge into such a plasma locally accelerates the plasma electrons causing them to move faster in the vicinity of the test charge. Since flux conservation requires that faster moving electrons have lower density, the density of the negatively charged electrons will decrease around the test charge. The plasma anti-shields the test charge; instead of decreasing the net positive charge near the test particle, the plasma will increase the net charge. This phenomena has been sporadically recognized in the literature, but, to our knowledge, has never before been observed. While we observe anti-shielding in a pure electron plasma when we employ unusual initial conditions, more commonly we observe the converse-shielding. We show that this shielding results from the presence of electrons trapped in the potential well of the test charge. While several different mechanisms are observed to trap electrons, an ubiquitous, fast acting, transit-time mechanism always traps electrons when the test charge is introduced adiabatically. That one dimensional (1-d), collisionless shielding requires trapping does not appear to have been previously recognized and the explanation of shielding given in many textbooks and papers is incorrect or incomplete. Because the trapping results from dynamical processes, we call the resulting shielding "dynamic" shielding. Both the observed and calculated magnitude of dynamic shielding can be significantly smaller than Debye shielding; eventually collisions transform the dynamic shielding to Debye shielding.
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