Anomalous current penetration into a plasma is a fundamental process which is important in a number of plasma situations included in which are the formation of discharges and current sheath layers. A recently developed two and one‐half dimensional magnetostatic code has been applied to the simulation of this process. Many anomalous processes are involved here including anomalous resistance, anomalous heat conduction, anomalous electron viscosity, and the formation of complex magnetic structures. Of dominant importance is the anomalous resistivity. It is important to identify the instabilities and turbulent processes involved. The results show that the induced current excites lower hybrid turbulence which may be related to lower hybrid oscillations recently observed in microtor. Anomalous heating and heat transport are also observed. In some cases the magnetic field lines are observed to reconnect and form magnetic islands.