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We argue that the non-perturbative Schwinger mechanism may play an important role in the hadronic production of charm. We present a flux tube model which assumes that the colliding hadrons become color charged because of gluon exchange, and that a single non-elementary flux tube is built up as they recede. The strong chromoelectric field inside this tube creates quark pairs (including charmed ones) and the ensuing color screening breaks the tube into excited hadronic clusters. On their turn these clusters, or 'fireballs', decay statistically into the final hadrons. The model is able to account for the soft production of charmed, strange and lighter hadrons within a unified framework.