Turbulence spreading in gyro-kinetic theory

Abstract

In this letter a new operative definition for the turbulence intensity in connection with magnetized plasmas is given. In contrast to previous definitions the new definition satisfies a Fisher–Kolmogorov–Petrovskii–Piskunov type equation. Furthermore, explicit expressions for the turbulence intensity and the turbulence intensity flux, that allow for the first time direct numerical evaluation, are derived. A carefully designed numerical experiment for the case of a tokamak is performed to study the impact of turbulence spreading. The effective turbulence diffusion coefficient is measured to be smaller than the heat conduction coefficient and the turbulence spreading length is found to be of the order of the turbulence correlation length. The results show that turbulence spreading can play a role in the non-local flux gradient relation, or in the scaling of transport coefficients with the normalized Larmor radius, only over lengths scale of the order of the turbulence correlation length. A new turbulence convection mechanism, due to the drift connected with the magnetic field inhomogeneities, is described. The convective flux integrates to zero under the flux surface average unless there is an up–down asymmetry in the tubulence intensity. The latter asymmetry can be generated through a radial inhomogeneity or plasma rotation. It is shown that the turbulence convection can lead to a spreading of the order of the correlation length.