UC San Diego

Simple flux-gradient relations that involve time delay and radial coupling are discussed. Such a formulation leads to a rather simple description of avalanches and may explain breaking of gyroBohm transport scaling. The generalization of the flux-gradient relation (i.e., constitutive relation), which involve both time delay and spatial coupling, is derived from drift-kinetic equation, leading to kinetic definitions of constitutive elements such as the flux of radial heat flux. This allows numerical simulations to compute these cubic quantities directly. The formulation introduced here can be viewed as an extension of turbulence spreading to include the effect of spreading of cross-phase as well as turbulence intensity, combined in such a way to give the flux. The link between turbulence spreading and entropy production is highlighted. An extension of this formulation to general quasi-linear theory for the distribution function in the phase space of radial position and parallel velocity is also discussed.