The electric field within the streamer channel is a critical parameter in the calculation model for the nonlinear breakdown voltage of SF6, motivating the research presented in this paper. By using a 2D fluid model, we investigate the microscopic characteristics of the SF6 streamer channel in highly non-uniform fields and uncover a previously unexplained coherent structure: the spatial fluctuation of the electric field (SFEF). We validate the physical validity of SFEF by modifying model parameters that could potentially introduce non-physical effects. Further comparative analysis reveals that SFEF is driven by an ion-conducting channel formed due to the strong electronegativity of SF6. This ion-conducting channel exhibits local characteristics, which fundamentally arise from the slow response of charged species to local charge relaxation. We identify that some charge separation originates from the accumulation of negative ions at the rear edge of the streamer head due to strong electric field shielding in this region. As the streamer propagates, charge separation is continuously generated and passively carried into the streamer channel, ultimately forming the SFEF. Finally, we confirm that SFEF does not occur in uniform fields, indicating that it is a phenomenon exclusive to highly non-uniform fields. These findings provide a deep insight into the electric field within the SF6 streamer channel and offer a potential avenue for further investigation into the mechanisms of SF6 nonlinear breakdown voltage.