Abstract. The mechanism of the steep structure formation of the radial electric field is one of the key issues. Properties of the radial electric field transition are studied considering the effect of electrode biasing in this paper. The radial lectric field structure is determined by a charge conservation equation. From the nonlinear mechanism associated with the local current due to the ion bulk viscosity, a transition takes place. Various types of radial electric field structures with multiple peaks are allowed for the same boundary condition. The ion orbit loss term breaks symmetry of the radial current like the ambipolar radial electric field. When the electrode current is driven, it plays a role of a control parameter in a transition like the pressure gradient. Bifurcation diagram is given in the space of spontaneous and external drives. Differences of radial shapes of the solitary electric field due to the combination of the spontaneous and external drives are qualitatively demonstrated. This study clarifies the mechanisms of the nonlinear self-structure formation in the transport barriers.