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In this study, we investigate the interaction of jets with their environment at a microscopic level, which is a key open question in the study of relativistic jets. Using small simulation systems during past research, we initially studied the evolution of both electron–proton and electron–positron relativistic jets containing helical magnetic fields, by focusing on their interactions with an ambient plasma. Here, using larger jet radii, we have performed simulations of global jets containing helical magnetic fields in order to examine how helical magnetic fields affect kinetic instabilities, such as the Weibel instability, the kinetic Kelvin–Helmholtz instability (kKHI) and the mushroom instability (MI). We found that the evolution of global jets strongly depends on the size of the jet radius. For example, phase bunching of jet electrons, in particular in the electron–proton jet, is mixed with a larger jet radius as a result of the more complicated structures of magnetic fields with excited kinetic instabilities. In our simulation, these kinetic instabilities led to new types of instabilities in global jets. In the electron–proton jet simulation, a modified recollimation occurred, and jet electrons were strongly perturbed. In the electron–positron jet simulation, mixed kinetic instabilities occurred early, followed by a turbulence-like structure. Simulations using much larger (and longer) systems are required in order to further thoroughly investigate the evolution of global jets containing helical magnetic fields., This work is supported by NSF AST-0908010, AST-0908040, NASA-NNX09AD16G, NNX12AH06G, NNX13AP-21G, and NNX13AP14G grants. The work of J.N. and O.K. has been supported by Narodowe Centrum Nauki through research project DEC-2013/10/E/ST9/00662. Y.M. is supported by the ERC Synergy Grant “BlackHoleCam—Imaging the Event Horizon of Black Holes” (Grant No. 610058). M.P. acknowledges support through grant PO 1508/1-2 of the Deutsche Forschungsgemeinschaft. Simulations were performed using Pleiades and Endeavor facilities at NASA Advanced Supercomputing (NAS), and using Gordon and Comet at The San Diego Supercomputer Center (SDSC), and Stampede at The Texas Advanced Computing Center, which are supported by the NSF. This research was started during the program “Chirps, Mergers and Explosions: The Final Moments of Coalescing Compact Binaries” at the Kavli Institute for Theoretical Physics, which is supported by the National Science Foundation under grant No. PHY05-51164. The first velocity shear results using an electron positron plasma were obtained during the Summer Aspen workshop “Astrophysical Mechanisms of Particle Acceleration and Escape from the Accelerators” held at the Aspen Center for Physics (1–15 September 2013)., We acknowledge support by the CSIC Open Access Publication Initiative through its Unit of Information Resources for Research (URICI)