Current Density Equation in Turbulent Magnetized Plasmas

A turbulent extension of Ohm’s law, derived from the self-consistent action-angle transport theory, is presented. The equation describes the steady-state profile of the current density in axisymmetric magnetized plasmas in the presence of magnetic turbulence. The hyper-resistive, helicity-conserving contribution, usually derived in the framework of magneto-hydro-dynamics, is recovered, and the hyper-resistivity is defined. Additionally, the generalized Ohm’s law contains an anomalous resistivity term, and a term proportional to the current density derivative. For given thermodynamic profiles, the numerical solution of the equation shows that turbulent contributions, besides regularizing the current density profile in the central region, lead to an increase of the total plasma current. This “turbulent bootstrap” effect provides a possible explanation to discrepancies recently observed between experimental current profiles and neoclassical predictions.