Although bipolar jets are seen emerging from a wide variety of astrophysical systems, the issue of their formation and morphology beyond their launching is still under study. Our scaled laboratory experiments, representative of young stellar object outflows, reveal that stable and narrow collimation of the entire flow can result from the presence of a poloidal magnetic field whose strength is consistent with observations. The laboratory plasma becomes focused with an interior cavity. This gives rise to a standing conical shock from which the jet emerges. Following simulations of the process at the full astrophysical scale, we conclude that it can also explain recently discovered x-ray emission features observed in low-density regions at the base of protostellar jets, such as the well-studied jet HH 154.