Anomalous Ion Heating from Ambipolar-Constrained Magnetic Fluctuation-Induced Transport

A kinetic theory for the anomalous heating of ions from energy stored in magnetic turbulence is presented. Imposing self consistency through the constitutive relations between particle distributions and fields, a turbulent Kirchhoff's law is derived that expresses a direct connection between rates of ion heating and electron thermal transport. This connection arises from the kinematics of electron motion along turbulent fields, which results in granular structures in the electron distribution. The drag exerted on these structures through emission into collective modes mediates ambipolar-constrained transport. Resonant damping of the collective modes by ions produces the heating. In collisionless plasmas the rate of ion damping controls the rate of emission, and hence the ambipolar-constrained electron heat flux. The heating rate is calculated for both a resonant and non-resonant magnetic fluctuation spectrum and compared with observations. The theoretical heating rate is sufficient to account for the observed two-fold rise in ion temperature during sawtooth events in experimental discharges