The kinetic effects of magnetic fields on the transport of relativistic jet in the intergalactic medium remain uncertain, especially for their perpendicular component. By particle-in-cell simulations, we find that when only jet electrons are fully magnetized, they are directly deflected by the magnetic field, but jet protons are mainly dragged by collective charge-separation electric field. However, when both electrons and protons are fully magnetized, the contrary is the case. Their balance tremendously distorts the jet density and electromagnetic fields, leading to enormous energy exchange between different species and fields. As a result, the electron spectrum energy distribution (SED) gets reshaped and the power law slope of the SED decreases as the magnetic field strength increases. In other words, we may infer that magnetic fields around the relativistic jet play a crucial role in shaping the observed SED.
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