Thermal conductivity of a plasma in a toroidal magnetic field with random inhomogeneities

The ion thermal conductivity of the plasma in a tokamak is analyzed for the case in which there are random spatial fluctuations in the longitudinal field. This case may arise, for example, if there are independent fluctuations of the current in the longitudinal-field coils. The statistical characteristics of the field are found (the rms field and the average maximum and minimum fields). The ion thermal conductivity is found as a function of the rms field and the number of coils. The result depends on the small fluctuations in a nonanalytic manner. The transport which occurs is analogous to that which occurs in a tokamak with a regular corrugation, but the effect of the corrugation penetrates more deeply toward the center of the plasma.